Mathematics in Movies

This is a collection of movie clips in which Mathematics appears.

All clips mentioned below are available for viewing along with additional tech. info. To access the flash version (.swf) or watch the quicktime file (.m4v) please godirectly to the author's "Mathematics in Movies" web page at: http://www.math.harvard.edu/~knill/mathmovies/. Thank you.

OliverKnillDepartment ofMathematicsHarvardUniversity

HackersSome mathematical formulas in a visualization of a"worm". Features a young Angelina Jolie and a good olhexeditor which had already been useful to me on theAtari ST to "edit games".1995

Jane EyreSome arithmeticproblems on theblackboard, mostlywith wrongsolutions.1996

IntactoWhat is the chance to draw an ace in a randomly shuffledcard deck of 52. There is one chance in a million for aplane to crash and for it to crash, leaving you the onlysurvivor out of how many -- 237 passengers? Onechance in 237 million. Later in this convoluted thriller, aRussian Roulette variant appears, where 5 of 6 chamberscontain bullets.2001

NetworkArthur Jenson(played by NedBeatty) talks toHoward Beale(played by PeterFinch) about theonly primal force ofnature: money:"What do you thinkthe Russians talkabout? Karl Max?They get out theirlinear programmingcharts, statisticaldecision theories,mini-max solutionsand compute theprize-costprobabilities of theirtransactions andinvestments. Justlike we do. "1976

12 MonkeysA wonderful performance of Brad Pit. Here he talks aboutpredicting the future with a probability matrix. Asexpected with time travel stories, the storyline of 12Monkeys is intriguing.1995

AmarcordSolving thequadratic equation.A math scene inthis Fellini movie ispart of a largerselection ofdelightful schoolscenes.1973

The Maltese FalconLots of meta talk and meta-meta talk and twisted logicin this conservation about the black bird. The statement"Mathematically correct" flagged the movie clip for thiscollection [I added the last remark to add a metastatement about this caption]1941Play the flash version (.swf). or watch the quicktime file(.m4v)

Suspect X(IV)The two friends talkabout math, thefour color theoremand the 7 Clay mathproblems. (Thanksto Li Zhou for thesuggestion)2008

Suspect X (III)The end of a calculus class by Shigami.2008

Suspect X (II)A physics class byYukawa onquantummechanics.2008

Suspect X (I)The Gaussian Acceleration device appears early in thisJapanese thriller. The entire movie is math/physics heavysince Yukawa is a physisist and Shigami is amathematician.2008

The DamBustersOn the use ofCongruent trianglesto measuredistances. Alsosome applied mathproblems onbouncing balls onwater anddetonations inwater. Thanks toCraig Smorynski forthe suggestion.1955

>The Ice StormIts when they say 2*2 is equal to 4, it is not numbers, itis space. It is perfect space. But only in your mind. Youcan not draw perfect squares in the material world.[While this movie scene is harmless, the movie itself isdefinitely not PG13.]1997

FlippedThe area of arhomboid. Themovie clip of thisbeautiful love storystarts a bit earlier,in order to explainwhy Juli Baker is soabsent minded inschool.2010

The BankThe multiplication table and the compound interestformula.2005

CranfordOn addition ofincome numbersand a sentence onteachingmathematics orgeography. [As allBBC drama, thisminiseries containsdelightful actingand is built on awonderful scriptquite freely usingElizabeth Glaskellsoriginal text. ]2007

The Wild Blue YonderChaotic transport in the solar system. [ Actualdocumentary footage and interviews are combined to amovie. The interview is real and serious but the contextmakes it funny.] Thanks to Martin Lo to mention this tome. Lo appeared with two other mathematicians in thismovie.2005

The Wild BlueYonderRotating system. [Actual documentaryfootage andinterviews arecombined to amovie. Theinterview is real, thecontext makes itfunny.]2005

The killer inside meA brief moment sanity in this dark, dark movie when Lousolves some integrals. It is an extremely disturbingmovie because the dark side of Lou Ford, the psychotickiller, is not visible. Why the police men Lou does somemath in this scene is unexplained in the movie.2010

DesksetThe roof scene ofthis charmingTracy/Hepburnmovie featuressome"mathematical"questions. (Thanksto Shawn Jones forthe suggestion.)1957

Rites of Love and MathIn this movie of Edward Frenkel mathematical formulasare written onto skin. (Thanks to Andrew Ranicki for thesuggestion).2009

ArtificialIntelligence:AIAbout the fabric ofspace time and howhumans have triedto find the meaningof life in art, poetryor mathematicalformulas.2001

Drowning by NumbersCounting the stars. Once you counted the hundred, allthe other are the same. (Thanks to Andrew Ranicki forthe suggestion).1988

In JulyTheoretical andappliedcomputation of afree fall problem(Thanks to AndrewRanicki for thesuggestion)2000

The Knack ... and How to Get ItThe angle of incidence is equal to the angle or reflection(Thanks to Andrew Ranicki for the suggestion)1965

Rain Man3*82=246 = 250-4(Thanks to JoiaFelice for thesuggestion)1988

A Serious ManThe Uncertainty Principle in Quantum Mechanics. Theentire movie is a celebration of this principle startingwith the dead/alive cat scene, unsharp boundariessinging and TV receiption, accepting mysteries, cultureclashs, quantum tunneling between relationships etc,etc.One of the best Cohen brother movies. P.S. Can you spotthe error in the blackboard computation in this scene?The computation error probably has been implementedalso by purpose on a meta level.2009

ThreeO'Clock HighSome algebraproblems are visiblein a quiz. Todetermine whocheated, buddy hasto solve 2blackboardproblems on squareroots.1987

G.I. Joe - Rise of the CobraThe shadow determines the lattitude where the picturewas taken. Compare the idea of Eratostenes to measurethe shadows of a stick on different locations to get theradius of the earth. Thanks to Robin Zaruba.2009

TheHangoverMathematicalthoughts of Allen,when winning atVegas: from simplearithmetics toFourier theory. Howmany formulas canyou identify?2009

Time MachineMathematical work on a black board.2002

Breaking thecodeThe enigma and itscomplexity appearsin this movie aboutAlan Turing. Thanksto the university ofArizona movie club,where I had seenand learned aboutit.1996

Star trekYoung Spock learns Math. He memorizes the formula(4pi/3) r3 for the volume of the sphere, the square rootof 2396324 and the definition of dimensionalitylog(n)/log(d).2009

Star trek TheNextgenerationBarclay becomes agenius and arguesGrand UnificationTheory with AlbertEinstein (Thanks toJason Baumgartnerfor the suggestion)2002

Star trek The Next generationProbably the most hilarious statement about dimensionin the galaxy appears in the episode "Where silence hasLease": "Is the lack of a dimension a dimension byitself?" Negative dimension. Mathematicians have not yetcome up with this idea, but mathematicians have usedalso some time to come up with negative numbers.2002

Night at theMuseum IIWhat number is atthe heart of aPyramide?Pi=3.1415926 ...(Thanks to SusanMilano for thesuggestion)2009

Up in the airRyan and Natalie have a candid conversation aboutnumbers, frequent flyer milages mostly, "the miles arethe goal" but "Pi is just a number" comes up too.2009

Flatland: ThemovieSpherius showsArthur the thirddimension2007

Flatland (short)The sphere shows the third dimension. This movie wasdone at the animation workshop at the Carpenter Centerfor the Visual Arts at Harvard University. A productionbased on an idea by the American animator John Hubley(1914-1977) and directed by Eric Martin. (Thanks toJamie Clements for the suggestion). The movie can beobtained here.1965

The PinkPantherStrikes AgainTorture: finger nailson a blackboardfilled with wrongmathematicalcomputations like3x3=7.1976

ParenthoodIn this commedy with Steve Martin, a kid takes thesquare root of a large number.1989

Bedazzled(2000)The devil firstassigns Fermatstheorem but thencancels allhomework. (Thanksto Tyson Liskow forthe suggestion).2000

Fermat's roomThis brilliant movie is essentially about math only. A fewfamous math puzzles appear in this movie, where 4mathematicians are trapped in a room where the wallsslowly crush them. (Thanks to Evan Pellnitz for thesuggestion).more.2007

PhantomTollboothThe dodecahedronasks some riddlesto get toDigitopolis.Fibonnacci series,vectors and scalars,equivalencerelations and4827659 hairs.(Thanks to RonFisher for thesuggestion)1970

Pay it forwardPowers of three in a good pyramid scheme: select 3people to do good things for and then those 3 eachselect 3 more people, etc (Thanks to Carolyn Seubert forthe suggestion).2000

For a fewdollars moreCounting deadgangsters. (Thanksto Damien Brownfor the suggestion).1965

Smilla's Sense of SnowSmilla reads from Euclids book to Isaiah. (Thanks toSteen Grode for the suggestion)1997

Reality BitesAbout the Math inAstronomy1994

Smilla's Sense of SnowNatural numbers, negative integers, fractions. An IMDBreview quote: The absolute highlight of the movie is alittle speech Smilla gives about numbers. (Thanks toSteen Grode for the suggestion)1997

MerryAndrewIn this musicalcomedy, DannyKaye as MerryAndrew teachesNewton's law,geodesics andPythagoras (Thanksto Virginia Usnickfor the suggestion)1958

Butterfly DreamingOn the probability that two raindrops hit the same leaf.(Thanks to Susan Milano for the suggestion and toRobert and Anna Pollack, and the movie director RufusWilliams to make the movie available).2008

The OxfordMurdersLecture onWittgensteinspessimistic view onabsolute truthfollowed by rathershallow soundbites: the beautyand harmony ofnumbers, thegolden ratio,Fibonnacci,snowflakes and

s o a es a dcancer, the secretmeaning ofnumbers, thebutterfly whichflaps its wings toproduce a hurricanewhich nobody canpredict, logic andchance. Thanks toDetlev Beutner forthe suggestion.2008

October SkyFree fall differential equations as used in rocketry.1999

Little Big ManA lier dilemmaleads to the defeatof general Coster atthe battle of bighorn (Thanks toVirginia Usnick forthe suggestion).1970

Run Lola RunBeside the main theme of "sensitive dependence oninitial conditions", there is a "run of Lola" in which shewins in roulette twice betting on the same number 20.The first time, the initial input of 100 mark is multipliedby 35. The second bet multiplies the now 3600 by 35leading to a total win of 3500+126'000 = 129'500 hasan element of Grass's Blechtrommel cry, mathematicallyrelated to "resonance". (Thanks to Mark-WillemDogterom).1998

Its aMad,madworldSome divisionproblems appear inthis oscar winningcomedy when eightmotorists try tofigure out how tosplit the not yetfound treasure.(Thanks to PeteSwartz for thesuggestion)1963

A walk to rememberA tutoring scene with equilateral and isosceles triangles.(Thanks to R. Star Behar for the suggestion)2002

Old SchoolThis comedy notonly shows shots ofHarvard college butalso some rathertough math testproblems: likeHarriot's method ofsolving cubics(named afterThomasHarriot, you findHarriot's methodfor finding thethree solutionsx=e-b2/e,e,b2/e ofthe equation x3+3b2 x = 2 c3 here).Also Diophantineequations orintegrationproblems appear inthis test.2003

Last year in MarienbadIn this rather enigmatic movie, the enigmatic game ofNIM with a 7-5-3-1 initial condition is played twice.(Thanks to John Boller for the suggestion.)1961

Shrek theThirdMathematical logicin sentences2007

The HappeningDuring one of the "happenings", Julian tries to divert theattention to a math problem.2008

ApocalypseNowSurrounded byhorror, forms ofpoetry, physics andmath appear in amad form too.Photojournalist:"this is dialectics,simple dialectics. Itis very simpledialectics: 1through 9, nomaybes, nosupposes, nofractions. You can'ttravel to space. Youcan not go to spacewith fractions. Whatdo you land on: on

one quarter or3/8th? What do youdo when you go tovenus orsomething. Thatsdialectic. Physics.Dialectic logic is:there is only love orhate."1979

How green was my valleyA 100 gallon bath tub is filled from A with 20 gal/minand from B with 10 gal/min and leaks 5 gal/min. Howlong until it fills? Thanks to Orlando Figueiredo for thesuggestion.1941

Alice inWonderland[IMDb link]Riddle: Why is araven like a writingdesk? Carols ownanswer given in1896: Because itcan produce a fewnotes, tho they arevery flat; and it isnevar put with thewrong end in front!(Thanks to TaniaMoloney for thesuggestion).1951

Alice in WonderlandFooling around with complements. The unbirthday. Its asmall world, most people share an unbirthday. Carolmight have been inspired by the birthday paradox: in aclass of 23 the chance to have two kids with the samebirthday is already more than 1/2. (Thanks to TaniaMoloney for the suggestion).1951

NationalTreasureCracking apassword byknowing the lettersused.2004

National Treasure CodeThe Ottendorf Cipher, a book Cipher.2004

The wizardof ozThe scare crowtheorem: in anisoscele triangle,the sum of thesquare roots of twosides is the squareroot of the thirdside. (Thanks toWyley Beatty tosuggest this movie).1939Play the flashversion (.swf). orwatch the quicktimefile (.m4v)

The number 23Numerology with the number 232007

23A true story aboutGermanHackers/Spies.Numerology as inthe movie "Thenumber 23". Bachas a hackercomposingpalindromic music.(Thanks to FrankJosellis for thesuggestion).

1998

Antonia's LineAn algebraic topology class. (Thanks to Mark Barsamianfor the suggestion).1995

21The Newton method2008

21Cauchy plagiarism?2008Play the flash version (.swf). or watch the quicktime file(.m4v)

Collossus:The ForbinProjectThe mighty USdefense computer"Colossus" developscalculus tocommunicate withits buddy in theSoviet union.(Thanks to websitevisitor "Bob" to

suggest this.)1970

The bankPredicting the stock market using complex dynamics.2001

Little BigLeagueJoe can paint thehouse in a=5hours, Sam canpaint the house inb=3 hours. Howmuch time do theyneed if the paint ittogether?1994

The Office: Season 5 Epiosde 9Explaining a surplus to a 5 year old.2008

RevolutionaryRoadA mathematicianappears in thisthough provokingmovie.2008

Harold and KumarSolving an integration problem in calculus2008

Harold andKumarA poem about thenumber square rootof 3. (Thanks toYelena Melnichenkofor pointing outthat math scene).2008

Back to the Future Part IIIDok Brown: Clara was one in a million, one in a billion,one in a googolplex.1990

Once upon atime in thewestCounting horses1968

Once upon a time in the westThousands of Thousands. One calls them Millions1968

Jane Eyre (I)Some glimpses ofmathematics appearin the BBC drama:Jane Eyre tutorsfractions to Adelewho is later veryexcited about thecarriage.2006

Jane Eyre (II)An other glimpses of mathematics appear in the BBCdrama: Jane Eyre grades a fraction assignment of Adeleand is interrupted by Grace Pool.2006

Jane Eyre (III)An other glimpsesof mathematics: ahappy carriagescene, Rochesterimagines Janeteachingmathematics.2006

The Tenant of Wildfell HallA glimpse of geometry in painting?1996

MansfieldParkReciting a scenewith Fanny, Edmundand Mary,mentioning theteaching ofmathematics. Asfrequently done byJane Austen, thescene is also a playin a play where thedialog refers to theactual situation. Another mostdelightful example(not displayed inthis clip) is thelibrary scene whenSir Thomasunexpectedly comeshome from Antigua.1996

The prophecySimon: "See you kids. Study math. Its the key to theuniverse". (thanks to Bret Benesh for the suggestion).1995

Father of thebrideHow to get 8hotdogs and 8hotdog buns ifhotdog buns arebundled in 12.(Thanks to websitevisitor ReneePentecost tosuggest this).1991

Mean GirlsA scene showing a Highschool calculus class. (thanks towebsite visitor Lillian Tubbs to suggest this.)2004

Mean GirlsA scene showing acalculus contest inwhich a system oflinear equations aswell as a limitproblem appears(thanks to websitevisitor Lillian Tubbsto suggest this.)2004

The Clan of the Cave BearTeaching of mathematics at the time of the Neanderthalsmaybe 100'000 years ago.1986

Bedazzled(1967)The lier's paradoxin this Faustiancomedy in whichElliot sold his soulto have 7 wishesfulfilled.1967

The code conspiracyThe ulam prime spiral appears. One could overlook thatalmost nothing connected with codes, physics or mathdoes make sense in this movie, but that the blue pictureof the Ulam spiral is fake is slightly annoying.2001

The islandDiscovering adeterministicsystem for thelottery on theisland.2005

Good Neighbors, episode 1.1Tom Goods remembers to use Algebra to solve things.Introduce x as the unknown.1975

Cast Away[IMDb link]First scene: Lectureon search area on arock. Second scene:the path of the sunon the rock used asa calendar.2000

Eleventh hour: KryptosIan Hood, the special scientific troubleshooter for theBritish government has to solve a riddle from a friend.(Thanks to Robin Zaruba for the suggestion)2006

MariusBartender Cesarlectures Marius onmixing a picon-citron-curacao: onevery small third ofcuracao, one thirdof citron, then alarge third of picon.And to finish, alarge third of water.(Movie suggestedby Billy Carson)1931

The CroupierAbout the odds in poker.1998Play the flash version (.swf). or watch the quicktime file(.m4v)

Ma and PaKettleDifferent proofsthat 25/5 = 141949

CubePeople are trapped in a giant cube puzzle. A permutationriddle has to be solved.1997

HypercubePeople are trappedin a hypercubewhich implodes atthe end. Also timeis mixed up in thiscube.

2002

Its My TurnA lecture on the Snake lemma in homological algebra inwhich a student pretends to know things better.1980

Simpsonstreehouse ofhorror VIHomer enters a 3Dworld with differentmathematicaltopics.

1995

SneakersA lecture on computational number theory. A methodsuperior to the number field sieve is announced1992

EnigmaAbout cracking"Shark" arefinement of theEnigma code.1991

Simpsons First Season dvd2Bart Simpson solves a math problem at the learningcenter.1989

Straw DogsA blackboard withmathematicalastrophysicalformulas.1971

P.S.A blackboard in Columbia University with mathematicalformulas written by astrophysisist Peter, the ex-husbandof the main character Louise2004

Stand andDeliverStarting a difficultlecture.1988

Stand and Deliver, TicTacToeDrop out student learns calculus. TicTacToe method forintegration by parts. (Thanks to Matt Leingang for thesuggestion)1988

Stand andDeliver,GiggoloThe giggoloproblem.1988

ProofWork on the Riemann hypothesis2005

HitchhikersGuide to theGalaxThe number 422005

Abbott and Costello: In the navyAbbott and Costello do a Calculation trick to show that7*13 = 281941

PiNumerology,mathematics iseverywhere.1998

Monty Python's flying circusFootball game, the mathematicians Leibniz on thegerman team, Archimedes on the greek team.2005

Monty Pythonflying circus2/29Rhetorics and Logichave a lot ofcommon. The art ofarguing. What is anargument?2005

005

The SaintPiece of paper with mathematical formulas for coldfusion.

1997

Indiana Jonesand theRaiders ofthe Lost ArkBlackboard withsome physicsformulas1981

Good Will Hunting, Cayley formulaWill Hunting writes down Cayley's formula stating thatthe number of labeled trees on n nodes is nn-2. Thenlists 8 different unlabeled trees with 10 nodes. (Thanksto George Lowe for the suggestion)1997

Good WillHuntingA Blackboard inlinear algebralecture at MIT onParseval's identity inFourier theory.1997

A Beautiful MindMultivariable calculus lecture2001

DimensionsAn educationalmovie by Jos LeysEtienne Ghys andAurelien Alvarez(Thanks to PedramSafari forsuggesting this)

2008

Donald in MathmagiclandDonald learns the Math of Billiards1959

The Mirrorhas twoFacesCalculus lecture butthe actors mumbleabout prime twins.1996

InfinityAbakus scene and explanation how to compute the thirdroots1996

Jurassic parkChaos theory I1993

Jurassic parkChaos theory II1993

ContactInformation isencoded in a cube1997

ContactPrime numbers as contact (thanks to Misha Tiberend forsuggesting this).1997

Like MikeSupersized triangles(Thanks to CherylMcDuff for thesuggestion)2002

BigJosh helps a kid with algebra1988

Good Night,Mr BeanMr Bean watcheschess game andcounts sheepaddition problem togo to sleep

1995

Back to the Future Part IIIDok Brown: Clara was one in a million, one in a billion,one in a googolplex.1990

MissionImpossible IIIPendulum swing(Thanks to LesaVandiver for thesuggestion)2006

The Count of Monte CristoI offer something priceless. I offer knowledge. Abbe Fariateaches Edmond Dantesphilosophy, mathematics andeconomics.2002

CluelessThe math problem7x71995

The Da Vinci CodeThe Fibonnacci sequence 1 1 2 3 5 8 13.2006

ChaosThe popular bookof James Gleick onChaos2005

Casino RoyaleSome mathematical themes and patterns motivated bymathematics appear in the intro2006

Mr. HollandsOpusIf I'm forced tochoose from Mozartor Reading andWriting and Longdivisions, I chooselong division. - Youcan cut the arts,but the kids willhave nothinganymore to readand write about.1995

Numb3rs (intro to pilot)Mathematics is everywhere. It is also used to solvecrimes.2005

Numb3rs(pilot)Using statistics tofind location ofcriminal and theodds to win thelottery.2005

YakitateJapanepisode 40Encoding a messageas a number tobase 26. (Thanks tovisitor Chu-WeeLim to suggestthis).2004

Die hard III (St Ives)The classic St Ives riddle 7x7x7x7. (Thanks to CherylMcDuff for the suggestion)1995

Die hard III(bottle)A classic waterbottle riddle. Howto produce exactly4 gallons with a 3and a 5 gallon pan.(Thanks to CherylMcDuff for thesuggestion)1995

Fahrenheit 451Gray suited students recite multiplication tables.1966

CaddyshackIn one physicalmodel, the shortestdistance betweentwo points is astraight line - inthe oppositedirection.1980

LinksHere are some references and links to other collections.

entry [PDF] of Sofia projecthttp://world.std.com/~reinhold/mathmovies.htmlhttp://members.aol.com/vlorbik/tenpage/movies.htmlhttp://www.pbs.org/teachersource/mathline/concepts/movies.shtmhttp://www.math.tamu.edu/~dallen/hollywood/mathindex.htmMath in the movies for middle and high school teachersThe Countdown resource is a multimedia math education initiativeSimpsons MathEducation notes by Edmond Barbeau, Toronto

ThanksMany thanks to all the following 107 individuals for valuable suggestions on this page. This website would never be what it is without you:Danny Aarons, Roger Alperin, Vanessa Aslan-Blair, Mark Barsamian, Jason Baumgartner, Wyley Beatty, Detlev Beutner, Star Behar, BretBenesh, A.M. Bernard, Cheryl Bjurstrom, John Boller, Demien Brown, Ryan Brown, Martynas Buivys, Rebecca B. Candino, Jo Jo Cadray, RichCampbell, Becky Candino, Steve Cerce, Helen Chandler, Jamie Clements, Karen Conner, Keith Conrad, Ben Crossman, Jane Ries Cushman,Maureen Desmond, Mark-Willem Dogterom, Celeste Doolittle, Carlos Dutra, Randy Fee, Joia Felice, Ron Fisher, Orlando Figueiredo, DavidFlottum, Greg Friedman, Cassandra Fuller, Arturo Saenz Garcia, Jim Greene, Steen Grode, Malanie Gurk, Diane Harrington-Kelly, KathyHenderson, Tatiana Ioudovina, Jeanne Johnson, Erica Jones, Shawn Jones, Valerie Jones, Frank Josellis, Martha Kelly, Ruth Knill, AndreKristovskis, Claire Laurain, Matt Leingang, Chu-Wee Lim, Tyson Liskow, Martin Lo, George Lowe, Martha MacCormack, Pamela Martin,Christopher McDade, Judy McDarby, Cheryl McDuff, Paolo Macasaet, Bob McK., Hannah Maker, Sebastian Melmoth, Yelena Melnichenko,Susan Milano, Tania Moloney, Nicolae Moroi, Arturo Pacifico Griffini, Priyojit Palit, Michael Palme, Alison Peachey, Renee Pentecost, EvanPellnitz, Gregory Potter, Mason Porter, Andrew Ranicki, Linda Richard, Malik Richardson, Jose Rivas, Pedram Safari, Sharon Serano, CarolynSeubert, John Shaposka, Ionica Smeets, Craig Smorynski, Jack Snoeyink, Larry Staggs, James Stiehl, Barbara Stonewall, Pete Swartz, MishaTiberend, Lillian Tubbs, Virginia Usnick, Lesa Vandiver, Andy Ventress, Benjamin Volk, Shannon Wallace, Kelly Wedding, Art Weiss, KevinWestrich, Rufus Williams, Rose Wisneski, Carol Wood, Peter Wung, Robin Zaruba, Li Zhou

Oliver Knill Homepage: http://www.math.harvard.edu/~knill/index.html

Last update: July 9, 2011