hugo hugo january february polish mathematician educator obtained phd david university later professor jan university ukraine helped establish later known school mathematics credited discovering mathematician gave notable contribution functional analysis world war played important establishment mathematics department university revival polish mathematics destruction war author scientific articles books left legacy contribution branches mathematics functional analysis geometry mathematical logic notably regarded early founders game theory probability theory led later development comprehensive approaches scholars early life studies born january austria-hungary family jewish roots father local industrialist owner brick factory merchant mother née hugo uncle activist polish circle deputy diet regional assembly kingdom hugo finished studies gymnasium family wanted engineer drawn abstract mathematics began study works famous contemporary year began studying philosophy mathematics university transferred university university received having written doctoral supervision david title thesis des new applications principle start world war returned poland served polish legion lived academic career interwar poland period poland regained independence occurred worked ministry interior puppet state kingdom poland started work university later jan university poland acquired qualification associate professor professor university time taught course cutting edge theory integration courses offered outside france founded school mathematics active circle associated scottish cafe according circle gatherings generally preferred tea shop street world war september nazi_germany soviet_union invaded occupied poland pact signed earlier initially came soviet occupation considered escaping hungary ultimately decided remain soviets reorganized university ukrainian character appoint student dean mathematics department resumed teaching faculty department school strengthened polish refugees german occupied poland according experience period acquired physical disgust regard sorts soviet administrators politicians interwar period time soviet occupation contributed problems famous scottish book including recorded shortly captured nazis operation jewish background spent nazi occupation hiding friends small towns near near polish anti nazi resistance provided false documents forest ranger died earlier taught clandestine classes higher education forbidden poles german occupation worried possibility imminent death captured germans access scholarly material reconstructed memory recorded mathematics knew addition writing memoirs little published hiding cut reliable news course war devised statistical means estimating german casualties based sporadic published local press method relied relative frequency stated soldier died son second son son according student biographer mark told day life hours time germans left occupied poland soviets arrived left come world war days world war hiding heard rumor university transferred city poland acquire result agreement soviet ukraine initially doubts turned offers faculty positions way city began teaching university revived idea scottish book prominent aspiring write problems interest prizes awarded solution starting new scottish book likely preserved original scottish book war subsequently sent translated english help university renowned mathematics university later 1960s served visiting professor university notre dame university sussex mathematical contributions authored works unlike student tended narrowly field functional analysis contributions wide range mathematical sub disciplines including geometry probability theory functional analysis theory series mathematical logic wrote area applied mathematics enthusiastically collaborated engineers physicians words lawyers probably notable contribution functional analysis proof given fundamental tools branch mathematics interest games led propose early formal definition strategy anticipating john von complete treatment years later consequently considered early founder modern game theory result work infinite games students jan proposed early contributor founder probability theory time infancy considered actual mathematics provided measure description coin influence probability russian mathematician decade later offer precise definitions means events independent means random variable uniformly distributed hiding world war worked fair cake cutting problem divide resource people different preferences person believes received proportional share work initiated modern research fair cake cutting problem person sandwich propose method means legacy said discovered polish mathematician utter words integral park referred greatest mathematical discovery participant park discussion started mathematical society later evolved polish mathematical society member polish academy learning pan polish academy sciences polish mathematical society scientific society international scientific societies science published articles founded applications mathematics mathematical received honorary doctorate degrees warsaw university medical academy university university command foreign languages known point booklet famous ones polish french latin published posthumously polish academy sciences university sponsored year hugo celebrate contributions polish world science notable mathematician mark student wrote architects school mathematics poland wars individual helped raise polish mathematics ashes reduced second world war position new strength respect occupies man great culture best sense word product western civilization chief works mathematics sur der mathematical taxonomy sur liaison division des points ensemble uniting separating points finite set problems elementary mathematics heads tails rational dictionary


june june pioneering english computer scientist mathematician theoretical biologist highly influential development theoretical computer science providing concepts machine considered model general purpose computer widely considered father theoretical computer science artificial intelligence second world war worked government code school park britain centre time led section responsible german naval devised number techniques breaking german including improvements pre war polish method machine find settings machine played pivotal role cracking intercepted coded messages enabled allies defeat nazis crucial engagements including battle atlantic estimated work shortened war europe years war worked national physical laboratory designed ace designs stored program computer joined max newman computing machine laboratory victoria university manchester helped develop manchester computers interested mathematical biology wrote paper chemical basis predicted chemical reactions reaction observed 1960s prosecuted homosexual acts behaviour criminal act accepted treatment des chemical alternative prison died days 42nd birthday poisoning determined death suicide noted known evidence equally consistent accidental poisoning following internet campaign british prime minister gordon brown official public apology behalf british government way treated queen elizabeth_ii granted posthumous pardon early life born london father leave position indian civil service province british india father son clergyman john robert scottish family merchants based netherlands included mother wife née daughter edward chief engineer madras railways protestant anglo irish gentry family county county spent childhood county work brought family british india grandfather general army wanted children brought britain moved london born june recorded blue plaque outside house birth later hotel elder brother john father sir john 12th father civil service commission active childhood years parents travelled hastings england india leaving sons stay retired army couple hastings stayed lodge upper maze hill sea marked blue plaque early life showed signs genius later display prominently parents purchased house lived school holidays location marked blue plaque education school parents enrolled michael day school charles road sea age recognised talent early subsequent age went school independent school market town day term coincided general strike britain determined attend rode bicycle miles southampton stopping overnight inn natural mathematics science earn respect teachers definition education placed emphasis classics wrote parents hope fall stay public school aim educated solely scientific specialist time public school despite continued remarkable ability studies loved solving advanced problems having studied elementary aged encountered albert work grasp possible managed questioning newton laws motion text explicit christopher formed significant friendship fellow pupil christopher described love relationship provided inspiration future cut short death february complications tuberculosis contracted drinking infected cow milk years previously event caused great sorrow grief working harder topics science mathematics shared letter mother said sure found companion brilliant charming regarded interest work things astronomy introduced shared think felt little know energy interest work alive like speculated death cause unlikely apparently point life believed concepts spirit independent body surviving death later letter written mother said personally believe spirit connected matter certainly kind body regards actual connection spirit body consider body hold spirit whilst body alive awake firmly connected body asleep guess happens body dies mechanism body holding spirit gone spirit finds new body sooner later immediately university work studied undergraduate king college cambridge gained class honours mathematics age elected fellow king strength proved central limit despite fact committee failed identify proven published paper numbers application paper kurt results limits proof replacing universal based formal language formal simple hypothetical devices known machines decision problem originally posed german mathematician david proved universal computing machine capable performing mathematical went prove solution decision problem showing halting problem machines possible decide machine halt proof published shortly church equivalent proof approach considerably accessible intuitive church included notion universal machine known universal machine idea machine perform tasks machine church according church thesis machines capable computing john von acknowledged central concept modern computer paper day machines central object study theory september july spent time studying church princeton_university addition purely mathematical work studied built stages electro mechanical june obtained phd princeton systems logic based introduced concept logic notion relative computing machines augmented called allowing study problems solved machines returned cambridge attended lectures given foundations mathematics remarkably lectures reconstructed including students students notes argued disagreed defending view mathematics discover absolute truths second world war leading participant breaking german park historian wartime said needed exceptional talent needed genius genius september working time british code breaking organisation concentrated senior soon july warsaw meeting polish bureau provided british french details method code messages started work fragile approach problem polish method relied insecure indicator procedure germans likely change approach general based produced functional specification improvement polish september day declared war germany reported park wartime station major advances war indicator procedure german_navy developing statistical procedure making efficient use dubbed developing procedure working settings wheels dubbed end war development portable secure voice park statistical techniques trial different possibilities code breaking process innovative contribution subject wrote papers discussing mathematical approaches titled applications probability paper statistics value successor released national archives april shortly centenary birth mathematician said time fact contents restricted years demonstrated importance reputation park known colleagues treatise known book jack good worked quoted having said week june year bad attack hay fever cycle office wearing service gas mask bicycle fault chain come regular intervals instead having count number times went round bicycle time adjust chain hand pipes prevent stolen working talented long distance runner occasionally ran miles london needed high level meetings capable world class marathon standards tried british olympic team hampered injury time marathon minutes slower british silver medalist thomas richards olympic race time hours minutes athletic club best runner fact discovered passed group running awarded king george wartime services work remained secret years weeks arriving park specified machine help break effectively polish derived suggested mathematician gordon primary tools major automated attack messages jack good opined important contribution think design machine idea use effect logic sounds ear absurd contradiction searched possible correct settings message order settings settings suitable fragment probable possible setting order states states boat variant performed chain logical based implemented electrically detected contradiction occurred ruled setting moving possible settings cause contradictions discarded leaving investigated detail installed march late fellow gordon hugh alexander stuart barry frustrated building work poles set good working system signals people time translate signals summer considerable success shipping losses fallen tons month knife edge badly needed resources abreast german adjustments tried people fund proper channels getting finally breaking rules october wrote directly winston_churchill spelling difficulties named emphasised small need compared vast expenditure men money forces compared level assistance offer forces andrew biographer later wrote letter electric effect churchill wrote memo general read action day sure want extreme priority report november chief secret service reported possible measure taken park know prime minister response barry later recalled notice day rough ways began smooth operation end war naval decided tackle particularly difficult problem german naval december solved essential naval indicator system complex indicator systems services night conceived idea statistical technique later called analysis assist breaking naval sure work practice fact sure days actually broken invented measure weight evidence called ban rule certain sequences substantially reducing time needed test settings proposed marriage colleague joan clarke fellow mathematician engagement short lived admitting homosexuality fiancée reportedly revelation decided marriage travelled united_states november worked navy naval construction washington visited computing machine laboratory ohio reaction american design far enthusiastic pity way build machine stopping necessary converted extent thinking starting scratch design method good american program produce wheel order smile conception test hardly considered conclusive testing bounce electronic stop finding devices trip assisted bell development secure speech devices returned park march absence hugh alexander officially assumed position head alexander facto head time having little interest day day running section general consultant park alexander wrote follows contribution question mind work biggest factor success early days thought problem worth primarily responsible main theoretical work shared keen chief credit invention difficult absolutely pioneer work tends forgotten experience routine later easy felt magnitude contribution fully realised outside world july devised technique termed jokingly use messages produced germans new secret writer machine attachment park method wheel breaking procedure working settings wheels introduced team tommy flowers guidance max newman went build computer world digital electronic computer replaced simpler prior machine heath robinson superior speed allowed statistical techniques applied messages mistakenly said key figure design computer statistical approach undoubtedly fed thinking directly involved development following work bell pursued idea electronic speech telephone system war moved work secret service radio security service later park developed knowledge electronics assistance engineer undertook design construction portable secure voice communications machine intended different applications lacking capability use long distance radio case completed late war system worked fully demonstrating officials recording winston_churchill speech adopted use consulted bell development secure voice system later years war early computers test lived london worked design ace automatic computing engine national physical laboratory presented paper february detailed design stored program computer von incomplete draft report paper detailed according john superintendent mathematics division contains number ideas ace feasible design secrecy surrounding wartime work park led delays starting project disillusioned late returned cambridge year produced seminal work intelligent machinery published lifetime cambridge pilot ace built absence executed program number later computers world owe including english electric american version ace built death according memoirs german computer pioneer billing max institute physics published meeting took place interrogation form participants porter england german researchers like billing details und die appointed reader mathematics department victoria university manchester deputy director computing machine laboratory working software earliest stored programme computers manchester mark time continued abstract work mathematics computing machinery intelligence mind october addressed problem artificial intelligence proposed experiment known test attempt define standard machine called intelligent idea computer said think human tell apart conversation human paper suggested building programme simulate adult mind better produce simpler simulate child mind subject course education reversed form test widely internet test intended determine user human computer working undergraduate colleague began writing chess program computer exist programme completed dubbed tried implement mark lacking power computer unable execute programme instead played game simulated computer taking half hour game recorded program lost colleague said won game wife test significant provocative lasting contribution debate artificial intelligence continues half century invented method today solving matrix pattern formation mathematical biology end life turned mathematical biology publishing chemical basis interested development patterns shapes biological organisms central interest field understanding existence numbers plant structures suggested system chemicals reacting space termed reaction system account main phenomena instability system partial differential model system allows small random initial state drive development patterns published structure role dna understood work remains relevant today considered seminal piece work mathematical biology experiments suggest work partially explain growth feathers hair branching pattern lungs left right puts heart left chest found mice removal genes causes increase number increase overall size limb suggesting genes control digit formation tuning type mechanism later papers promised available collected works published conviction january started relationship arnold murray year old unemployed man met murray christmas outside cinema walking manchester oxford road invited lunch january house murray told acquaintance reported crime police investigation acknowledged sexual relationship murray homosexual acts criminal offences united_kingdom time men charged gross section criminal law amendment act initial proceedings trial held february solicitor reserved defence later convinced advice brother solicitor entered plea guilty case regina murray brought trial march convicted given choice imprisonment probation agreement undergo treatment designed reduce accepted option treatment called known des synthetic treatment continued course year treatment rendered caused fulfilling literal sense prediction doubt shall emerge different man found murray given discharge conviction led removal security clearance barred continuing government communications headquarters british signals intelligence agency evolved kept academic job denied entry united_states conviction free visit european countries time acute public anxiety homosexual spies soviet agents recent exposure members cambridge guy double agents accused espionage common worked park prevented official secrets act discussing war work death june found dead died previous day post examination established cause death poisoning body discovered apple lay half eaten bed apple tested speculated means fatal dose consumed determined committed suicide cremated june ashes scattered father andrew biographer david suggested scene disney film snow white seven favourite fairy tale noting words took especially keen pleasure scene wicked queen apple poisonous alternative death theories philosophy professor jack questioned aspects historical verdict suggests alternative explanation cause death accidental apparatus gold uses potassium dissolve gold apparatus set tiny spare room notes autopsy findings consistent poison ate apple bed unusual discarded half eaten addition reportedly borne legal setbacks treatment discontinued year previously good humour shown sign prior death setting fact list tasks intended complete return office holiday weekend time mother believed accidental resulting son storage laboratory chemicals biographer andrew suggests arranged experiment deliberately mother plausible recognition tributes biography published royal society shortly death wartime work subject official secrets act recorded remarkable papers written war diverse mathematical subjects quality work produced settled work big problem critical time work foreign office awarded award given annually association computing machinery technical theoretical contributions computing community widely considered computing world highest honour equivalent nobel prize june birthday biographer andrew unveiled official english_heritage blue plaque birthplace childhood home crescent london later hotel mark 50th anniversary death memorial plaque unveiled june residence march saint vincent issued set postage stamps celebrate greatest achievements 20th century carries portrait background repeated theory digital computing april work park named milestone october bronze statue sculpted john mills unveiled university surrey marking 50th anniversary death portrays carrying books campus examined bbc documentary entitled dangerous knowledge princeton alumni weekly named second significant alumnus history princeton_university second president james madison ton life size statue unveiled june park built approximately half million pieces welsh slate sculpted stephen having commissioned american frank honoured ways manchester city worked end life stretch road manchester city intermediate ring road named way bridge carrying road widened carries bridge statue unveiled manchester june park university manchester building street canal street memorial statue depicts father computer science sitting bench central position park shown holding apple cast bronze bench carries relief text motto founder computer science appear machine plaque statue feet reads father computer science mathematician wartime victim prejudice russell quotation mathematics viewed possesses truth supreme beauty beauty cold like sculpture sculptor buried old computer tribute godfather modern computers time magazine named important people 20th century stated fact remains keyboard opening word processing program working incarnation machine ranked bbc poll greatest following wide vote british writer mathematician james chose people feature book famous historical figures traits syndrome actor playwright jade portrayed solo musical icons lesbian gay history world vol guardian hero series writer garner chose hero described met whilst early 1950s garner remembered funny witty said talked named online resources lgbt history month icon boston pride named honorary grand marshal logo apple erroneously referred tribute bite mark reference death designer logo company deny homage design stephen recounted asking steve jobs design intentional saying jobs response god wish february papers second world war bought nation 11th hour bid national heritage memorial fund allowing stay park inducted legacy walk outdoor public display celebrates lgbt history people singer songwriter tribute song life work featured bbc children programme famous scientists absolute genius dick broadcast march world work public art recognise gay commissioned close park war time work carried commission announced owners based lgbt venue nightclub pink mark international day work unveiled ceremony birthday june placed outside pink alongside busy street old main road london passed occasions october inducted hall honor tributes universities research institutions computer room king college cambridge alma mater called room room university edinburgh school houses bust set prints university surrey statue main buildings faculty engineering physical sciences named istanbul university annual conference theory called days university texas austin honours computer science programme named scholars early 1960s stanford_university named sole lecture room hall mathematics building auditorium computer science department university northern france named honour named kurt department computer science catholic university chile university buenos_aires university puerto_rico los university colombia king college cambridge university wales universities belgium university university puerto_rico university university washington computer laboratories named university manchester open university oxford university university denmark buildings named road surrey research park way manchester inner ring road named university granite bench situated mall carved read left leg write university oregon bust hall computer science building road square named place faculty information technologies university technology slovakia lecture room named auditorium paris university lecture room named faculty mathematics computer science university lecture hall named paul university lecture room named largest conference hall amsterdam science park named king college london school natural mathematical sciences awards centenary prize university kent named college canterbury campus campus building named research centre premises shared microsoft university toronto developed programming language named faculty exact sciences university buenos_aires computer laboratory named campus state university brazil avenue largest named government apology pardon august john graham started petition urging british government prosecution homosexual petition received signatures prime minister gordon brown acknowledged petition releasing statement september describing treatment thousands people come demand justice recognition way treated dealt law time clock treatment course utterly unfair pleased chance deeply sorry happened behalf british government live freely thanks work proud sorry deserved better december william jones created petition requesting british government pardon conviction gross ask government grant pardon conviction gross convicted gross man forced undergo called therapy chemical years later killed aged driven terrible despair early death nation save remains shame british government british history pardon way healing damage act apology gay men known subjected laws petition gathered signatures request discouraged lord gave following opinion role justice minister posthumous pardon considered appropriate properly convicted time criminal offence known offence law prosecuted tragic convicted offence cruel absurd particularly poignant given outstanding contribution war effort law time required prosecution long standing policy accept convictions took place trying alter historical context right right ensure instead return times july bill introduced house_of_lords grant statutory pardon offences section criminal law amendment act convicted march late year letter daily_telegraph physicist stephen signatories including royal lord president royal society sir paul nurse lady worked war lord bill sponsor called prime minister david cameron act pardon request government indicated support bill passed reading lords october bill debated house_of_commons government elected proceed royal mercy december queen elizabeth_ii signed pardon conviction gross immediate effect announcing pardon justice secretary chris said deserved remembered recognised fantastic contribution war effort later criminal conviction queen officially pronounced pardoned august queen action fourth royal pardon granted conclusion second world war case unusual normally granted person technically innocent request family interested party condition met regard conviction letter prime minister david cameron announcement pardon human rights advocate peter criticised decision single fame achievements thousands convicted law received called new investigation death new inquiry long doubts true cause death including speculation murdered security services think murder state agents unlikely known evidence pointing act major failing possibility considered investigated centenary celebrations mark 100th anniversary birth centenary advisory committee year year long programme events world life achievements chaired barry cooper nephew sir john acting honorary president worked university manchester faculty members broad spectrum people cambridge_university park june google featured interactive visitors change instructions machine run symbols tape match provided sequence featuring google murray code park trust collaborated winning moves publish edition board game monopoly game squares cards revised tell story life birthplace park game includes replica original hand drawn board created william newman son mentor max newman played 1950s philippines department philosophy university manila hosted international conference philosophy artificial intelligence science march commemorate centenary birth india held celebrations programme attended students celebrations day conference manchester june day conference san_francisco organised birthday party centenary conference cambridge organised king college cambridge university_of_cambridge organised association europe science museum london launched free exhibition devoted life achievements june run july february royal mail issued stamp featuring distinction series london olympic torch flame passed statue gardens manchester evening june 100th anniversary birth june manchester city_council partnership lesbian gay foundation launched memorial award recognise individuals groups significant contribution fight manchester university_of_oxford new course computer science philosophy established coincide centenary birth previous events included celebration life achievements university manchester arranged british logic british society history mathematics june portrayal adaptations theatre breaking code play hugh play ran london west end beginning november broadway november april bbc television production broadcast united_states pbs performances played broadway production nominated tony awards including best actor play best featured actor play best direction play drama desk awards best actor best featured actor portrayed television film adaptation breaking code honour centennial american lyric theater commissioned exploration life death composer david titled life death opera historical life brilliant scientist opera receive concert performance october new_york_city november opera artistic works inspired life featured studio literature william gibson police jurisdiction featured novel novel dreams machines contrasts accounts lives ideas kurt novel speak written hall includes series fictional letters written best friend mother life detailing research artificial intelligence music electronic music duo released titled based material commissioned robert david mathematical sciences research institute tracks original machine sampled spanish group dedicated dubious digit concert memory mathematician musical work inspired life written chris pet shop boys entitled man future announced late performed pet shop boys juliet narrator bbc singers bbc concert orchestra conducted bbc royal albert hall july title choral work composer james mccarthy includes settings texts poets owen oscar robert burns illustrate aspects life premiered april centre london performed chorus commissioned work led david temple soprano harvey providing voice mother film drama documentary life aired channel_4 november released october known britain greatest film features henry historical drama film imitation game directed starring joan clarke released november released theatrically november breaking code park awards honours elected fellow royal society addition things named honour good frequency degree institute lecture machine examples patterns reduction switch articles jack mind computing machine journal jack father modern computer journal andrew august edward stanford encyclopedia philosophy winter stanford_university retrieved january andrew oxford dictionary national biography online oxford_university press subscription public library membership required gray paul march computer scientist time books andrew princeton_university press isbn originally published basis film imitation game george cathedral origins digital universe vintage isbn james information history theory flood new_york isbn works list publications microsoft academic search publications google scholar service provided google october computing machinery intelligence mind mind retrieved oral history interview nicholas metropolis charles institute university minnesota metropolis director computing services los national laboratory topics include relationship john von


michael michael march march norwegian mathematician home early age enrolled school following short period royal frederick university included stint assistant christopher hired mathematics teacher cathedral school met future renowned mathematician lasting impact mathematics worldwide said school privately friends remained early death moved royal frederick university worked death significant impact mathematics fledgling norway textbook volumes secondary schools widely faced competition christopher alternative offering sparking norway debate school textbooks early life career michael born son vicar wife grew siblings elder brother noted christopher early age sent cathedral school complete secondary education undertook studies mathematics enrolled student royal frederick university turbulent year norwegian history norway province denmark come swedish control january treaty kiel following norway declaration independence constitution sweden responded military campaign norway summer spokesperson student group opposed presence swedish troops country student community highly visible time university seventeen students year establishment private studies attended lectures given appointed position scientific assistant christopher lecturer university delivered lectures early mathematics teacher cathedral school position vacant school principal jacob invited brother christopher studied mathematics position decided instead concentrate christopher went research sanskrit language teaching drew inspiration joseph louis cathedral school met pupil quickly discovered talent proclaimed splendid genius report card school primary focus classical education latin privately personal support called important contribution mathematics close friends younger brothers studied friendly terms invited family residence occasions including celebrate christmas died tuberculosis age years death edited published complete works volumes complete works later life career published textbook mathematics page book named textbook mathematics followed second volume textbook mathematics consisting pages teaching experience background writing mainly abstract purpose books logical thinking instance field geometry readers figure instead putting paper books widely reprinted volumes respectively appointed lecturer royal frederick university claimed owed appointment absence travelling europe time taught mathematics military college death promoted professor royal frederick university later publications include plan spherical den textbook advanced mathematics influence including jacob born university met christopher professor published mathematics textbook secondary schools reaction books method teaching practically oriented wrote review book newspaper advised schools use public debate followed contributions claimed debate subject school textbooks norway textbook reprinted involved field insurance member private country public committee supervision insurance companies table member board directors insurance company founded student jacob legacy michael memorial prize teachers mathematics established awarded annually prize money nok taken found cover prize prize administered board norwegian mathematical society current board chairman tom professor university oslo street oslo gate named michael named gate christopher marriage children married twice wife born died years marriage daughters reached adulthood son married second wife born marriage produced sons christopher daughters reached adulthood michael died second wife thirty years


arnold ross arnold ross august september mathematician educator founded ross mathematics program number theory summer program gifted high school students born chicago spent youth ukraine studied ross returned chicago enrolled university_of_chicago graduate moore despite lack formal academic training received married wife bee ross taught institutions including louis university chair university notre dame mathematics department started teacher training program mathematics evolved ross mathematics program addition high school students program moved ohio_state university department chair forced retire ross ran summer program worked students summers program known ross significant work attendees continued prominent research positions sciences program inspired recognized highly influential ross received honorary doctorate professional association awards instruction service early life career ross born arnold august chicago ukrainian jewish immigrants child mother supported family physical ross returned ukraine mother assistance extended family stayed world war russian revolution broke events led widespread famine economic region ross learned russian behest mother developed love theater language ross mother encouraged read private library public library credited favorite uncle ray introducing mathematics uncle hired tutor talented son ross asked join money meant little inflation paid tutor boys pound french hard candy time ross taught textbooks geometric geometry teacher ask class prove justify ideas trial error universities closed famine university reopened let small group attend including ross ross left ussr intention returning chicago studying moore university_of_chicago negotiating way home worked family friend shop continued learn english lewis institute changed surname ross ross salary year shop term university_of_chicago moore course moore gave ross special attention knowing background arranged ross attend class sole undergraduate moore teaching style propose task students proving students respond counter defend ross found moore method exciting influenced ross ross graduated degree continued study eugene research assistant ross earned degree finished number theory university_of_chicago adviser ross entitled representation indefinite forms pay tuition quarter credits ross married bee singer musician daughter ross chicago neighbors received national research council fellowship worked national research council fellow california institute technology temple bell ross moved chicago led mathematics department experimental school started great depression people junior college taught physics ross assistant professor louis university stayed years interview said advocated student black woman south receive master degree mathematics exception led university admit black students despite idea widespread world war ross served research mathematician navy befriended hungarian mathematician louis recommended ross brown university summer school prepared young scientists assist war program ross attended occasionally worked proximity laboratory accepting position head university notre dame mathematics department set change school research climate inviting distinguished including paul ross professor ross mathematics program notre dame ross began mathematics program described act personal discovery observation experimentation high school junior college teachers program expanded national science foundation post funds teacher ross let high school students attend expansion ross mathematics program summer mathematics program gifted high school students program lasts weeks brings students prior knowledge topics program teaches number theory inspired motto think deeply simple things primary goal offer students intellectual experience described vivid life exploration program known intensity considered america rigorous number theory program according high schools don tell ross known leaves program unchanged program usually year students advanced students students admitted application includes set mathematical questions showing great learn year students meet daily lectures elementary number theory weekly problem encouraged think like scientists problems posed occupies free time ross designed daily problem sets questions contain signature directions prove salvage possible successful students asked return students future summers returning students daily lectures help years questions advanced courses graduate student problem sets graded daily live program funded 1960s national science foundation program supported summer programs science education returning students support program funded means including gifts donors scholarships businesses national security agency grant university mathematics department receives financial support clay mathematics institute program grew rapidly input prominent ram max 1960s 1970s ross brought including kurt ray teach regularly ross left notre dame chair ohio_state university mathematics department program followed summer program briefly moved university_of_chicago summers mathematician invitation program depends personal contacts word mouth recognized best mathematics programs high school students retirement death ross reached mandatory retirement ohio_state university professor emeritus continued run summer program stroke left physically impaired unable teach daniel led program ross exit counselor program ross received honorary doctorate university mathematics association america award distinguished service citation public service named american association advancement science fellow teaching awards include ohio_state distinguished teaching service awards membership national science foundation science education advisory board ross helped begin similar programs west_germany india australia consulted indian gifted children program assisted australian national university january summer program talented youth based ross helped start program germany previously created mathematics programs including teacher training program included high school students program columbus ohio inner city middle high school students called unlimited ross wife bee died left ross deep depression colleagues said lived summer program period later met french widow diplomat green married ross died september notices american mathematical society focus ran memorial articles ross expressed personal debts ross children legacy ross biggest contribution field research mathematics education programs run summer programs working students summer program graduates found roles prestigious research positions fields sciences ross program acclaimed highly influential ross program inspired similar programs closest likeness program mathematics young scientists boston university honors math camp southwest texas state university programs university_of_chicago university texas san_antonio inspired ross founders ross program alumni ross program went university_of_chicago years mathematics chair paul slowly supportive program later began gifted students program informally ross program ross students known study including attendees known arnold ross lecture series founded run american mathematical society puts high school audiences annually cities united_states ohio_state university organized reunion conferences ross program alumni friends ross series science lectures


pronounced april polish american mathematician participated america manhattan_project originated design weapons invented method suggested nuclear pulse propulsion pure applied mathematics proved proposed born wealthy polish jewish family studied mathematics institute earned phd supervision john von met warsaw invited come institute advanced study princeton new_jersey months spent summers poland academic years harvard_university cambridge massachusetts worked establish important results theory august sailed america time year old brother adam assistant professor university wisconsin madison united_states citizen october received invitation join manhattan_project secret los laboratory new_mexico worked calculations predict behavior explosive lenses needed type weapon assigned edward group worked super bomb war left associate professor university southern_california returned los work weapons aid female computers including wife found super design january came design basis weapons considered problem nuclear propulsion rockets pursued project proposed alternative nuclear thermal rocket harness small nuclear explosions propulsion project john studied problem inspiration field non linear science probably best known realising electronic computers practical apply statistical methods functions known solutions computers developed method common standard approach problems poland born april time kingdom austro hungarian empire known poles austrian partition newly restored poland second polish republic city took polish wealthy polish jewish family professionals immediate family hardly rich father born lawyer mother anna née born uncle architect building contractor lumber industrialist family lived temporarily vienna returned polish ukrainian war city experienced ukrainian siege entered gymnasium vii graduated studied mathematics institute supervision received master arts degree doctor science age published paper concerning function sets journal traveled studied vienna paris cambridge england met hardy mark member school mathematics founders hugo professors university school met long hours scottish café problems discussed collected scottish book thick provided wife major contributor book problems recorded contributed problems single author additional received copy book survived war translated english friend daniel published expanded version coming america john von met warsaw invited come institute advanced study princeton new_jersey months december year sailed america princeton went lectures heard james alexander albert tea party von house encountered suggested apply position harvard society following suggestion spent summers poland academic years harvard_university cambridge massachusetts worked john establish results theory appeared annals mathematics august brother sons year old adam ship headed america weeks later germans invaded poland months germans completed occupation western poland soviets invaded occupied eastern poland years rest family victims holocaust hugo hiding underground university warsaw sons killed massacre professors problem recorded scottish book survived nazi occupation feeding research institute adam eminent harvard received letter george hid house polish army gave chilling account chaotic scenes late later life described muse deeply forces invisible close idea god feel immediately estranged world tolerate recommended assistant professor university wisconsin madison united_states citizen year married french exchange student mount college met cambridge daughter claire madison met friend colleague collaborate number papers manhattan_project early asked von find war job october received invitation join unidentified project near santa new_mexico letter signed appointed leader theoretical division los national laboratory robert scientific director knowing area borrowed new_mexico guide book card found names wisconsin colleagues joan david joseph mysteriously disappeared introduction manhattan_project america wartime effort create atomic bomb calculations weeks reached los february project experienced crisis april discovered work gun type weapon like thin man developed parallel weapon little boy dropped hiroshima problem threatened waste enormous investment new site slow separation way prepare material suitable use bombs respond implemented august sweeping reorganization laboratory focus development type weapon appointed george head department professor harvard expert precise use explosives basic concept use chemical explosives crush material critical mass leads nuclear chain reaction releasing large energy cylindrical configurations studied von experience shaped charges armor piercing ammunition vocal advocate spherical driven explosive lenses realized symmetry speed compressed critical issues enlisted help design lens configurations provide nearly spherical enormous pressures high temperatures solid materials behave like meant calculations needed predict minimize nuclear calculations said problem simply stated difficult detail order magnitude discussion stressed pure necessity survey problem simple minded force massive numerical work primitive facilities available time von carry numerical led satisfactory design motivated advocacy powerful capability los began war years continued cold war exists remembered brilliant polish charming french wife told pure mathematician sunk low latest paper actually contained numbers points statistics branching processes inherent statistical fluctuations chain reaction implications regard speed symmetry november david addressed problem report entitled theory processes report probability generating functions early entry extensive literature statistics branching processes scope extended early manhattan_project attention focused use produce september arrived los shortly breathing life poisoned soon arrival super bomb group transferred new division headed formed relationship war post war los september left los associate professor university southern_california los_angeles january suffered acute attack life danger emergency brain surgery friends visited including nicholas metropolis los famous mathematician paul remarked stan like encouraging concerned state mental lost ability speak crisis friend asserted article attack changed personality turned rigorous pure mathematics speculative concerning application mathematics physics biology assertion accepted late april recovered attend secret conference los discuss weapons attendance included von metropolis stan participation manhattan_project efforts directed development super weapon based nuclear fusion development practical bomb extensive discussion participants reached consensus ideas worthy exploration weeks later received offer position los metropolis robert new head theoretical division higher salary returned los method late war sponsorship von metropolis began carry calculations general purpose electronic computer proving ground maryland shortly returning los participated review results calculations earlier playing recovery surgery thought playing hundreds games estimate probability successful outcome mind realized availability computers statistical methods practical john von immediately saw significance insight march proposed statistical approach problem material mentioned uncle metropolis dubbed statistical approach method metropolis published paper method learning breakthrough devised analog computer known later dubbed device performed mechanical simulation random computers improved speed methods useful particular calculations carried modern massively parallel parallel applications results accurate design august soviet_union tested bomb created supervision sought duplicate american effort weapon nearly identical fat man design based information provided spies hall david response january president harry announced crash program develop fusion bomb advocate aggressive development program lawrence came los conferred laboratory director george edward soon members short lived committee appointed study problem chairman time research use weapon create fusion reaction ongoing design essentially originally proposed concept close proximity bomb hope heat intense released bomb exploded self sustaining fusion reaction reactions hydrogen interest energy unit mass fuel released fusion larger heavy results calculations based concept scientists believed lead successful weapon moral economic grounds proceeding consequently senior people manhattan_project opposed development including clarify situation von resolved new calculations determine approach feasible carry studies von decided use electronic computers new computer princeton twin construction los enlisted follow completely different approach guided physical women computers carried extensive scenarios mechanical supplemented confirmed slide rule collaborated analysis scenarios results showed configurations reaction ignited self sustaining expertise analyze chain reaction complicated ones concluded self sustaining chain reaction place low considering late conclusions confirmed von results january idea channel mechanical shock nuclear explosion fusion fuel recommendation wife discussed idea mark told immediately saw merit noted soft rays bomb fuel strongly mechanical shock suggested ways enhance effect march submitted joint report describing innovations weeks later suggested placing rod cylinder center fusion fuel spark plug help initiate enhance fusion reaction design based ideas called staged radiation standard way build weapons described design september series differences scientists resigned los returned university_of_chicago time went leave visiting professor harvard semester submitted joint report design jointly applied patent soon involved dispute deserved credit war returned university deeply involved development weapons consultant wrote article history bomb presents opinion men contributed significantly breakthrough balanced view shared involved including mark attempted role bomb recalled reporters started father bomb sake history think precise father provided seed mother remained child guess basic fusion reactions confirmed feasible design hand prevent los testing device november explosion occurred ivy mike detonated pacific proving grounds device liquid fusion fuel immense utterly weapon success design stimulated intensive development practical weapons problem returned los attention turned away weapon design use computers investigate problems physics mathematics john helped metropolis bring line march explored ideas report studies problems mathematical physics high speed computing machines submitted june treated problems addressed framework traditional methods motion systems magnetic lines force soon experienced electronic time settled routine spending academic years university_of_chicago summers los summer visits joined study variation classic problem string masses held springs exert forces proportional displacement proposed add force component chosen proportional square cube displacement complicated broken linear function addition key element problem designated classical spring system described terms modes analogous occur stretched violin string system starts particular mode vibrations modes develop component expected energy mode transfer gradually modes eventually distributed equally modes roughly began happen shortly system energy lowest mode later essentially energy periodically reappeared lowest mode behavior different expected energy remained mysterious showed appropriate mathematical system described equation prototype partial differential solutions means behavior understood terms nuclear propulsion starting frederick considered nuclear propulsion aircraft rockets attractive possibility nuclear energy unit mass fuel million times greater available chemicals ideas pursued project explored use nuclear power rockets response question senator john congressional committee hearing outer space propulsion nuclear energy january replied future mankind extent involved going outside globe proposed contrast continuous heating rocket exhaust harness small nuclear explosions propulsion project study idea began ended partial nuclear test ban treaty banned nuclear weapons tests atmosphere space work project spearheaded physicist freeman commented decision end article death project appointed john research advisors laboratory director newly created positions administrative level division leaders held retired los capacity able influence guide programs divisions theoretical physics chemistry weapons health addition activities continued publish technical reports research papers introduced model extension theory acceleration cosmic rays paul mary titled early investigation chaos theory considered published use phrase chaotic behavior return years los visiting professor harvard mit university california san_diego university colorado boulder positions permanent appointed professor chairman department mathematics boulder colorado kept residence santa new_mexico convenient spend summers los consultant colorado rejoined friends research interests turned biology recognizing emphasis university colorado school medicine appointed professor held position death los colleague robert published report elementary attempts numerical modeling problems concerning rates evolutionary processes applied earlier ideas branching processes biological inheritance report william temple smith titled biology introduced new ideas distances retired colorado begun spend winter university florida graduate research professor university california davis university pattern spending summers colorado los winters florida continued died apparent heart attack santa paul noted died suddenly heart failure fear pain prove deposited papers american philosophical society library philadelphia continued live santa died april age husband buried french family cemetery paris impact legacy publication paper student death constantly writing mathematics list publications includes papers topics represented significant number papers set theory including cardinals abstract measures transformation theory theory group theory number theory theory march mathematical reviews database contained papers notable results work pivotal role development weapons changed world according stan barring accidents bomb rendered nuclear war impossible wife appeared television documentary day trinity method standard approach method applied vast number scientific problems addition problems physics mathematics method applied finance social science environmental risk assessment radiation therapy sports problem credited birth experimental mathematics inspiration vast field science prize lecture david campbell noted relationship described gave rise ideas chaos systems laboratory director los strong support mark founded center studies initiated distinguished scholar program provides annual award enables noted scientist spend year carrying research los anniversary original paper subject march issue journal chaos topic 25th annual international conference university southern mississippi university florida supported quarterly active online mathematical journals florida department mathematics sponsored annual lecture march centennial conference work non distance context molecular biology significant contribution sequence analysis contributions theoretical biology considered development cellular theory population biology pattern recognition generally colleagues noted greatest contributions clearly identifying problems solved general techniques solving los issued special issue science publication summarized accomplishments appeared book cardinals chaos similarly university california press issued compilation mathematical reports los collaborators career awarded honorary degrees universities new_mexico wisconsin pittsburgh


june april german mathematician scientist noted work analysis synthesis electrical filters work marked beginning field network synthesis prior work electronic filter design techniques accurately predicted filter behaviour unrealistic conditions required certain experience designer choose suitable sections include design placed field firm mathematical providing tools produce exact solutions given specification design electronic filter initially specialised general soon switched electrical engineering work german subsidiary bell telephone company brought contact leading american engineers field filters proved useful unable feed children german economic crisis 1920s moved studied early computer techniques prior returning germany rise germany career remote jewish ancestor shot dead fall berlin soviet soldiers manuscripts important unpublished works destroyed war family succeeded notes volume der published death legacy continues today network synthesis method choice network design life career early life family adolf born berlin germany june came long line academics early grammar school gymnasium gymnasium institution founded great grandfather school located named district berlin building exists primary school later attended gymnasium berlin father councillor professor railway engineering technical university berlin interested mathematics age thirteen continued demonstrate academically inclined grew briefly served german_army final stages world war married relation eventually fathered children career started field completely unrelated filters worked max von general publication field reasons clear changed field electrical engineering graduated applied physics technical university berlin spent period working mix branch bell telephone company applying probability theory telephone switching worked telecommunications related publications period telephone switching systems losses real relationship mix bell gave easy path collaboration engineers bell enormous help embarked study filter design bell forefront filter design time likes george campbell boston new_york making major contributions foster correspondence work recognised importance paper milestone filter theory inspired approach field network synthesis june presented thesis paper specified frequency dependence institute applied mathematics mechanics technical university berlin paper beginning modern network synthesis went work research assistant richard institute mathematics university obtained external university lecturer found support family economic crisis 1920s took family usa obtained scholarship fellowship study mit harvard_university worked bush building machines solution mathematical problems essentially computers interested solve linear systems aid filter designs work filter circuits completed met strong contacts key researchers field filter design bell included george campbell foster short worked wired radio company newark new_jersey returned intention building fast computer unable obtain funding depression got poorly german colleagues according correspondence usually brief business like rarely discussing issues depth contrast correspondence american european acquaintances warm technically deep included personal family news correspondence went american contacts included general_electric company roger julia paris pick hungarian theorist leaving technical institute mix sought active german electrical engineers society left falling wagner previously phd supervisor ally nazi era signed loyalty oath german professors adolf_hitler national socialist state rising force major obstacle work onwards anti jewish time forced academics leave posts including director mathematics institute richard jewish known jewish ancestor daniel banker frederick prussia revelation sufficient removed race laws future career gained title professor given chair children finding increasingly difficult support prompted return industry temporarily worked aircraft manufacturer works director laboratory mix berlin continue lecture technical university berlin volume main work theory linear circuits published original manuscript second volume destroyed result war able reproduce work able publish lost war time death family arranged publication papers second volume based surviving descriptions intended contents volume taking children stay relatives protect expected fall berlin russians advice returned berlin body located end war mass grave victims russian executions shot dead garden berlin soviet soldiers hostage soviet intelligence actively looking scientists use list people find unknown network synthesis major legacy contribution network synthesis passive networks considered founder field publication principle work english enthusiastically greeted happen seventeen years later prior network synthesis networks especially filters designed image method accuracy predictions response designs depended accurate matching sections achieved sections entirely internal filter possible perfectly match end reason image filter designers incorporated end sections designs different form improved match response choice form sections matter designer experience design calculation network synthesis entirely away need directly predicted response filter included synthesis treated network synthesis problem network analysis network analysis asks response given network network synthesis hand asks networks produce given desired response solved problem comparing electrical quantities functions mechanical realising completely analogous applying known mechanics problem according major tasks network synthesis address ability determine given transfer function network second find canonical minimal forms functions relationships transforms different forms representing transfer function finally general possible find exact finite element solution ideal transfer function zero frequencies given frequency infinite task find techniques achieving desired responses initially work revolved port transfer function voltage current amounting expression useful network produced breaking open branch network calling output following foster relationship expression port network transfer function discovered necessary sufficient condition port expressions actually built real circuit later papers networks transformation discovered solutions given expression obtained given solution group foster ladder filters included foster discovered element kind networks identified canonical forms filter minimal forms includes ladder networks obtained continued fraction expansion design filters application resulted filters known filters filters fast transitions given maximum variation known filters viewed special case filters arrived techniques flat filter independent discovery stephen arrived different method work initially ignored canonical forms use ideal circuits practical use engineers soon realised easily applied useful ladder ideal network synthesis began image design method choice work work contained second largely treatment ports thesis begins extend work showing global canonical form found general case element kind networks containing elements generation solutions element kind case extended work ports ports ports electrically symmetrical necessarily symmetrical finding number canonical circuits studied ports extended foster element ports showed equivalent networks derived linear publications referenced works


andrew andrew november october american mathematician young world war naval officer broke german japanese military codes succeeding years fundamental contributions widely varied areas mathematics including solution fifth problem leader reform innovation math mat teaching levels quantum logic important example theory named entire academic career harvard retired numerous academic scholarly leadership posts included harvard mathematics department harvard society presidency american mathematical society continued advise united_states government security commonwealth massachusetts math mat education children end life won cleveland prize distinguished service award american mathematical society member national academy sciences american philosophical society held chair mathematics natural philosophy harvard fond saying math mat aren convince true true notices american mathematical society called quiet giants twentieth century mathematics professor dedicated scholarship teaching service equal measure biography born california youngest children father henry botanist member society mother daughter swiss american andrew older brother henry grew new_york father curator new_york botanical garden briefly attending berkeley high school berkeley california graduated roosevelt high school winning scholarship yale_university mathematics education gone far self taught yale mathematician william urged try course mechanics normally intended learned year second year consultant end old campus sections year got plenty practice elementary problems don think exists problem classical kind pseudo reality problem second year students given haven seen month later enrolled differential course seniors temporarily replaced regular instructor found style different view mathematics vastly different important experience took lot courses including sophomore year graduate level real analysis starting course began sense mathematics yale competed times recently founded william mathematical competition placing country making second time fellow japanese attacked pearl harbor senior year applied commission navy graduation joined team working break japanese naval codes team included future collaborator robert yale professor marshall hall collaborated british researchers attacking german spent substantial time visiting washington called brilliant young yale graduate mathematician report visit recommendation navy colleague howard appointed junior fellow harvard early goal junior program allow young scholars showing extraordinary promise lengthy phd process years later harvard appointed assistant professor mathematics immediately recalled washington work related korean war returned harvard fall soon published important results fifth problem harvard awarded tenure following year january married jean met party featuring music tom worked years boston university daughters took chair mathematics natural philosophy oldest est scientific endowed retired harvard remained active service harvard chair society example mathematics particular promoting harvard reform project working massachusetts board education died complications following surgery teaching education reform said enjoyed helping people math colleague said regarded teaching mathematics like mathematics important genuinely fun fourteen brief attendance berkeley high school found bored semester geometry helping students including taking second half course soon began harvard regularly taught level including courses class presented framed print mother child recognition care created bridge courses math majors years time course designed teach new students accustomed learning mathematics secondary school reason construct mathematical effort led publication abstract analysis reviewer wrote unusual book working mathematician course knows difference chain feeling tries mathematical theory probably agree helping student reach inside view ultimate goal mathematical education usually attempt successfully oral teaching originality author tried attain goal textbook reviewer opinion succeeded remarkably impossible task readers probably delighted reviewer find page page discussions explanations standard mathematical logical procedures written style effort achieve clarity falling mars attempts talent exposition imply reader effort wartime memo important german colleagues wrote reader wonder left reader book swimming strokes nice read practice strokes actually water claim swimmer reader desires actually possess knowledge recovering depth let reader paper colors avoid confusion connecting links work notes exercises probability statistics drawn lectures code breaking colleagues war remained use national security agency training decades published openly science article wrote apparent arising attempts explain mathematics difficult convey proper impression mathematics ultimately difficulty stems fact mathematics easier subject sciences consequently important primary problems subject problems understood intelligent outsider solved carried point indirect approach clearly required great bulk pure mathematical research concerned secondary higher order problem statement hardly understood mastered great deal technical mathematics school mathematics study group helped define new math 1960s ambitious changes american elementary high school mathematics teaching emphasizing understanding concepts interested people learn new math effort spent months second years later gave talk described goal having find figure given appropriate activities right guidance end talk asked andy worried teaching math little kids wasn faculty research institutions spending time quick decisive response didn think ball helped found consortium published successful influential series reform textbooks college high school areas program teaching ideas based equal parts geometry concepts grounding real world manipulation power program faced heavy criticism mathematics community omission topics mean value perceived lack mathematical work world war navy signals intelligence group task collaboration british park penetrate german machine communications networks british great success networks german japanese naval coordination remained faulty assumption employed simplified version marshall hall observed certain berlin tokyo letter sets tokyo berlin corresponding letters sets direction devised novel statistical tests confirmed hypothesis result routine network work involved deeper math mat related groups problem turned japanese navy coral key tool attack form bound tail sums independent random work decade end war concentrated documenting work developing systems training new returned active duty korean war serving lieutenant commander nebraska avenue complex later home security division work period remains classified known recruited taught served advisory boards national security agency institute defense analyses continued recruit advise military end life mathematics research fundamental contributions widely varied areas mathematics including theory lie groups quantum mechanics according freeman famous classification birds frogs frog worked problem visionary grand theories fifth problem david posed problems felt central century mathematics research fifth problem concerns characterization lie groups actions spaces extent provide information sufficient determine geometry restricted version fifth problem solved asks specifically locally group lie group group structure structure strengthened real structure neighborhood element group law defined power series overlapping neighborhoods compatible power series definitions prior work special cases problem solved jan john von interest fifth problem began late 1940s sparked course took george published paper introducing small property lie groups existence neighborhood identity exists eventually crucial solution paper subject paper published concurrently montgomery leo restricted version fifth problem showing locally group lie group contribution prove true small property montgomery showed locally group property told story key insight proof apply fact functions finding solution took week leave write printed annals mathematics alongside paper montgomery paper year later removed technical conditions proof version fifth problem closer original considers locally group continuous action asked case action given real structure quickly realized answer negative attention centered restricted problem additional assumptions possible prove existence real structure group action smith remaining difficulties case quantum mechanics born rule states property quantum system defined operator space values property operator probability system observed particular square absolute value complex number obtained projecting state point space corresponding george asked born rule necessary consequence particular set quantum mechanics specifically measure projections space defined positive operator unit trace richard proved false dimensional spaces published shows true higher dimensions implies certain types hidden variable theories quantum mechanics strengthening previous argument john von von claimed hidden variable theories impossible pointed demonstration assumption quantum systems form expectation operators hold john stewart bell showed remove extra assumption von argument theory number smallest number contains independent set numbers require enormous effort max known precisely exact believed reach calculation given question competition motivated problem author robert significant progress numbers proof values found paper number smallest number complete edges colored colors necessarily contains triangle showed remains number exact value known proof construction complete copies triangle free regular edges called graham writes paper recognized classic development theory late 1960s doctoral advisor known contributions theory theory published contributions theory influential ones included seminal ideas early results theory 1950s 1960s attended monthly meetings theory air_force cambridge research laboratory previously worked abstract world leading experts theory time writes monthly meetings lived frequently posed mathematical problems rewarded quick response named work researcher eugene originally published research report concerns code order extended adding single check bit remarkable shows code highly having linear group namesake system generate weight linear codes particularly simple form self dual codes case student continued work area proving relationship weight codes known identity areas founded theory math mat contributions including work wrote research included intense interest problems publishing research elementary mathematics set constructed compass angle awards honors awarded american association advancement science cleveland prize work fifth problem elected national academy sciences american philosophical society fellow american academy arts sciences belonged france president american mathematical society times held numerous posts professional scholarly organizations including harvard department mathematics chaired organizing committee international congress berkeley california president congress harvard society held special honoring retirement seven years chairman year mathematics association america awarded charles distinguished service mathematics award past president association wrote thinking andy career natural reference total profession mathematician designing teaching courses advising education levels research consulting users mathematics acting leader profession math mat talent serving institution andy rare individual death page collection essays notices american mathematical society recalled life work eminent american mathematician calling quiet giants twentieth century mathematics professor dedicated scholarship teaching service equal measure selected publications research papers fifth problem proceedings international congress cambridge mass vol providence american mathematical society finite planes american journal mathematics measures closed space journal mathematics mechanics spaces illinois journal mathematics characterization ideals journal weight self dual codes identities international des nice paris relations canadian journal mathematics books andrew abstract analysis publishing reading don mills corrected reprint boston jones robert kelly william mathematical competition problems solutions mathematical association america isbn walter elementary course probability hills park press reprint book originally published national security agency office research development mathematical research division hughes original publications book extended different editions variations additional authors film andrew oriented games mathematical association america minutes black white produced richard long directed