1FOCUS
`
`
`THE NEWSLETTER OF THE MATHEMATICAL ASSOCIATION OF AMERICA
`ST
`
`
`
`Mathematician Awarded Nobel Prize
`
`
`
`3 MAA Secretary’s
`Report
`
`4 Joint Mathematics
`Meetings Update
`
`6 Search Committee
`Diary
`
`10 Networks in
`FOCUS
`
`13 More on the MAA
`Gopher
`
`14 Project NEXT is
`Launched
`
`17 News fromthe
`Sections
`
`33 Employment
`
` TheMathematical
`eeeae
`
`1529
`
`Keith Devlin
`
`The awarding of the Nobel Prize in econom-
`ics to the American John Nash on October
`
`11th meant thatforthe first time in the 93-year
`history of the Nobel Prizes, the prize was
`awarded for work in pure mathematics.
`
`Whenthe Swedish chemist, engineer, and phi-
`lanthropist Alfred Bernhard Nobel established
`the awards in 1901, he stipulated chemistry,
`physics, physiology and medicine,and litera-
`ture, but did not create a prize for mathematics.
`It has been rumored that a particularly bad
`experience in mathematicsat high school led
`to this exclusionofthe “queen of sciences”, or
`it may simply be that Nobel felt that math-
`ematics was not,
`in itself, of sufficient
`relevance to human developmentto warrant
`its own award, Whateverthe reason, the math-
`ematicians have had to make do with their
`own special prize, the Fields Medal, though
`this differs significantly from the Nobel Prize
`by being restricted to mathematicians whoare
`less than 40 years of age.
`
`It was the application
`of Nash’s work in eco-
`
`
`
`
`
`nomic theory that led to
`his recent Nobel Prize,
`which he shares with
`
`fellow American John
`
`
`Harsanyi and German
`Selten.
`Reinhard
`
`Nash’s contribution to
`
`the combined work
`
`which won the award
`
`
`was in game theory.
`
`Nash’s key idea—known nowadays as Nash
`equilibrium—was developed in his Ph.D. the-
`sis submitted to the Princeton University
`Mathematics Department in 1950, when Nash
`wasjust 22 years old. The thesis had taken him
`a mere two years to complete. He had received
`both his B.S. and M.S. degrees in an equally
`rapid three-year period starting in 1945 and fin-
`
`See Nobel Prize on page 5
`
`Growing Optimism that Fermat’s Last Theorem
`has been Solved at Last
`Keith Devlin
`
`old problem. On June 23, 1993, speaking to a
`packed audience at a mathematics conference
`at Cambridge University’s Newton Institute,
`Wiles had outlined a proof of a technical result
`about elliptic curves (a special case of the
`Shimura—Taniyama Conjecture), and claimed
`that this result implied Fermat’s Last Theorem
`as a consequence. The connection between the
`full version of the Shimura—Taniyama Conjec-
`ture and Fermat’s Last Theorem had been
`
`established by Kenneth Ribet of UC Berkeley
`in 1986.
`
`Hopesrose dramatically in late Octoberthat
`Fermat’s Last Theorem might have been
`solved at last, when, on October 25th,
`Princeton mathematician Andrew Wiles re-
`
`leased two manuscripts claimingto prove the
`result. The first of these papers, a long one
`titled “Modular elliptic curves and Fermat's
`Last Theorem”, contains the bulk of Wiles’
`argument. The second paper,titled “Ring theo-
`retic properties of certain Hecke algebras”,
`waswritten jointly by Wiles and a colleague,
`Richard Taylor, and provides a key step Wiles
`uses in his proof.
`
`The new announcement camejust over a year
`after Wiles madehisinitial dramatic announce-
`
`EighteenthStreet,
`Washington, DC20036
`You’ve been goodthis year. Give yourself a treat! See page 30
`
`Though the bulk of Wiles’ enormously com-
`plex proof was agreed to have been correct,
`within a few weeks a significant mistake was
`discovered in the part of the argumentthatled
`to the Last Theoremitself.
`
`ment that he had solved Fermat’s 350-year
`
`See Fermat on page 3
`
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`

`

`FOCUS
`
`FOCUS
`
`Editorial
`
`
`
`The Calculus Ultrafilter
`
`Printed on recycled paper. December 1994
`
`FOCUSis published by The Mathematical
`Association of America, 1529 Eighteenth
`Street Northwest, Washington, DC 20036-
`1385, six times. year: February, April, June,
`August, October, and December.
`Editor and Chair of the MAA Newsletter
`Editorial Committee: Keith J. Devlin,
`Saint Mary's College of California
`Associate Editor: Donald J. Albers,
`MAA Associate Executive Director and
`Director of Publications and Programs
`
`ManagingEditor: Harry Waldman, MAA
`
`Production Specialist: Amy S. Fabbri,
`MAA
`
`Proofreader: Meredith Zimmerman,
`MAA
`
`Copy Editor: Nancy Wilson, Saint Mary’s
`College of California
`Letters to the editor should be addressedto:
`Keith Devlin, Saint Mary's College of
`California, P.O. Box 3517, Moraga, CA
`94575; e-mail: devlin@stmarys-ca.edu
`
`The FOCUSsubscriptionprice to individual
`members of the Association is $6.00,
`included in the annual dues. (Annual! dues
`for regular members, exclusive of annual
`subscription prices for MAA journals, are
`$68.00. Student and unemployed members
`receive a 66 percent discount; emeritus
`members receive a 50 percent discount; new
`members receive a 40 percent discount for
`the first two membership years.)
`
`Copyright © 1994 by The Mathematical
`Association of America (Incorporated).
`Educational institutions may reproduce
`articles for their own use, but notfor sale,
`provided that the following citation is used:
`“Reprinted with permission of FOCUS, the
`newsletter ofThe Mathematical Association
`of America (Incorporated).”
`
`Second-class postage paid at Washington,
`DC and additional mailing offices.
`Postmaster: Send address changes to the
`Membership and Subscriptions De-
`partment, The Mathematical Association of
`America, 1529 Eighteenth Street Northwest,
`Washington, DC 20036-1385.
`ISSN: 0731-2040
`Printed in the United States of America.
`
`In September, William Dunham andI were the guests on National Public Radio’s Talk
`ofthe Nation, an hour-long talk show with listener phone-ins. The event that occasioned
`NPRto devote an entire show to mathematics wasthe publication in the late summer of
`our two most recent books, Dunham’s The Mathematical Universe (Wiley) and my own
`Mathematics: The Science of Patterns (W. H. Freeman, Scientific American Library).
`
`One of the phone-in comments came from a listener in California—Jim, I believe his
`name was—whosuggestedthat high schools spendfar too much time teaching students
`calculus, and that the time might be better spent providing instruction in other subjects.
`Radio being the medium it is, the responses Bill and I gave led the conversationin the
`direction ofthe ubiquity of mathematics, and then the host moved usonto other matters.
`Weneverdid get a chance to comebackto whatI think is a particularly important matter.
`The plain truth is I agree with the listener. I think schools do spend too muchtime,far
`too muchtime, teaching calculus. Come to that, I think colleges and universities spend
`too much time teaching calculus as well.
`
`In fact, I did begin my response by saying I thoughtthe listener’s point had somevalidity,
`but I quickly thoughtbetter offollowing up on the matter when I realized that I could not
`possibly make my case adequately in the ‘sound bite’ form ofa radio talk show. When
`treading on sacred and hallowed ground, one should tread slowly and warily. And the
`world of mathematics knows no ground more hallowedthan the teaching of calculus.
`
`I guessitis time I defined my terms. By ‘teaching calculus’ I (and presumablythelistener
`from California) mean the kind of activity that, judging from the results it produces,
`concentrates on developing in the studentthe ability to differentiate and integrate lots of
`functions. In nearly 25 years of college and university mathematics teaching, I have
`encountered scores and scores of students who had become quite expert in performing
`this task. Just over halfway through that 25 year period, I started asking those highly
`proficient differentiators and integrators to explain to me, in as simple a fashion as they
`could, just waar the processesofdifferentiation and integration actually are, and what
`exactly are those things called functions that these two processes appear to act upon.
`
`Ifyou have evertried this, you will surely not be surprised whenI say that I almost never
`received an answerthat indicated any real understanding onthe part ofthe student. Sure,
`some could give the standard limit definitions, but they clearly did not understand the
`definitions—andit would be a remarkable student who did, sinceit took mathematicians
`a couple of thousand years to sort out the notion of a limit, and I think most of us who
`call ourselves professional mathematicians really only understand it when westart to
`teach the stuff, either in graduate school or beyond. But I wasnot looking for a regurgi-
`tation of a formal definition. What I wanted was some sense of whatthe calculus is all
`about. Why was it invented? What were the basic intuitions that Newton and Leibniz
`drew on in orderto arrive at the notion of (what we now call) differentiation? Why was
`it necessary to develop an elaborate calculus, a battery of techniques to compute deriva-
`tives and integrals? What did they think of the fundamental theorem ofcalculus, and why
`wasthat result so important?
`
`Having students who graduate from high school, or college for that matter, without being
`able to differentiate or integrate does not bother me—especially since computers can do
`the whole job faster and more reliably than people. But having students graduate without
`a sense of whatthe calculus is abour bothers me greatly. The invention of the calculus
`was an enormously significant event in the history of humankind, having ramifications
`that affected most aspects of our lives in one way or another. Wefail our students badly
`if we do not convey to them somesenseofthat giant leap for mankind. A few will need
`to know the how of calculus, and that need can be handled whenit arises. In contrast, |
`think all should be aware of the what and the why.
`
`
`
`APPLE EXHIBIT 1034 - PAGE 0002
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`APPLE EXHIBIT 1034 - PAGE 0002
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`

`

`FOCUS
`December 1994
`
`For me, the present, sorry situation is
`summed up by a remark made to me by a
`seniorcolleague at my college, with whom
`I was speaking shortly after the radio
`broadcast. Striving to find a way to con-
`vey the fundamental idea ofthe differential
`calculus in a one-minute soundbite, I had
`likenedit to a movie film, where theeffect
`of continuous motion is achieved by the
`sufficiently rapid sequencing of a series
`of still pictures. My colleague, an accom-
`plished economist who had taken plenty
`of calculus coursesin his time, said thatit
`was only when he heard me makethat
`remark that he finally had any inkling of
`just what the whole thing was about. He
`had, you see, been taught the how,but no
`one had eventried to explain the what and
`the why.Like the vast majority of students,
`calculus had been presented to him as a
`large collection of mysterious procedures,
`whose invention could only have come
`froma mind very different from therest of
`humanity. In his case, that had been over
`thirty years ago. But as far as I can see,
`things have not changed very muchsince
`then. I think they should.
`
`—Keith Devlin
`
`
`The aboveare the opinions ofthe FOCUS
`editor, and do not necessarily represent
`the official view of the MAA.
`
`Secretary’s Report
`
`G. L. Alexanderson
`
`The Board of Governors met in Minne-
`apolis, Minnesota, on August 14, 1994.
`Thefollowingis areport ofactions taken.
`
`Fermat from page 1
`Part of the reason why mathematicians
`were so ready to give Wiles the benefit of
`the doubt when he madehis original June
`1993 announcement wasthat his track
`
`record was so good. He was not prone to
`jumping to conclusions. Moreover, the
`new techniques he had developed clearly
`represented a major advance that stood a
`high chance ofworking. True to his known
`caution, Wiles refused to release a copy of
`his manuscript. He wanted to wait until it
`had been thoroughly combed for hidden
`errors by a small numberof close col-
`leagues.
`
`His caution proved well founded when one
`of the inevitable number of small errors
`turned out to be not so small after all.
`
`Given Wiles’ previous caution, his deci-
`sion to release his work leads to increased
`confidence that this time, he is probably
`right. The newly released manuscript was
`circulating privately among a small num-
`ber of experts for several weeks before
`Wiles released it, and the inside word is
`that it looks good. In an e-mail message
`broadcast over the Internet on October
`25th, number theorist Karl Rubin of the
`Ohio State University said, “While it is
`wise to be cautiousfora little while longer,
`there is certainly reason for optimism.”
`
`The overall outline of the argument Wiles
`has just released is broadly similar to the
`one he described in Cambridge.
`
`mittee to constructslates of candidates
`for President-Elect, and the two Vice-
`Presidents for the 1995 election. Elected
`were Lida K. Barrett, John H. Ewing,
`RaymondL.Johnson, Sharon C. Ross,
`and Alan C. Tucker (chair).
`
`Institute in the History
`of Mathematics andits
`Use in Teaching
`Would you like to teach a course in the
`history of mathematics? Does your col-
`lege oruniversity plan to offer such a course
`soon for prospective teachers to implement
`the recommendations ofthe MAA, NCTM
`and NCATE? Do you want to learn how
`the history of mathematics will help you
`in teaching other mathematics courses?
`
`Ifyou answered “yes” to anyofthese ques-
`tions, you are invited to apply to attend an
`MAAInstitute in the History ofMathemat-
`ics and Its Use in Teaching. The MAA
`expects to receive funding forthis insti-
`tute, which will take place at American
`University, Washington, DC, June 5-23,
`1995, and for three additional weeks in
`June 1996, with work continuing through
`anelectronic network during the academic
`year 1995-96.The teachingstaff will con-
`sist of well-known historians of
`mathematics, including, in the first year,
`V. Frederick Rickey, Victor J. Katz, Steven
`H. Schot, Ronald Calinger, Judith
`Grabiner, and Helena Pycior. Activities at
`the institute will include reading of origi-
`nal sources, survey lectures, small group
`projects,field trips to three great libraries,
`and discussions of methodsofconducting
`a history of mathematics course. Partici-
`pants will be prepared to make
`presentations on their work at the Joint
`Mathematics Meetings.
`
`Applications are strongly encouraged from
`faculty teaching at small institutions, at
`minority-serving institutions, and institu-
`tions that prepare secondary teachers.
`Facilities at American University are fully
`accessible. Dormitory space for families
`of participants is available.
`
`On recommendation of the Committee
`on the Edyth May Sliffe Awards, a new
`A new Hedrick Lecturer was confirmed
`set of awards was added to honor junior
`by the Board: our First Vice-President,
`high school teachers. Up to now Sliffe
`Doris Schattschneider, ofMoravian Col-
`Awards were awarded only to teachers
`lege. She will be the Hedrick Lecturer
`For more information and application
`in senior high schools. In addition the
`forms, write to V. Frederick Rickey, Math-
`for the MathFestin Burlington, Vermont,
`Board approvedanewprizeforoutstand-
`ematical Association of America, 1529
`August 1995,
`ing research in mathematics by an
`Eighteenth St., N.W., Washington, DC
`The Board elected Professor Paul Zorn
`undergraduate.The prize will beawarded
`20036-1385, or contact him by e-mail at
`ofSt. OlafCollege to be the successorof
`jointly with the American Mathematical
`rickey @maa.org. Completed applications
`Professor Martha Siegel as editor of
`Society.
`will be due by March 15th and applicants
`Mathematics Magazine. Professor
`will be notified oftheir acceptanceby early
`Zorn’s five-year term as editor will be-
`April.
`gin in January 1996,
`(Note: This institute will be conducted subject
`to the MAA receiving funding.)
`
`The Board elected a Nominating Com-
`
`The Board passed a resolution of con-
`gratulations to Professor Dirk J. Struik
`for the occasion of his one-hundredth
`birthday, September 30, 1994.
`
`
`
`oy
`
`APPLE EXHIBIT 1034 - PAGE 0003
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`APPLE EXHIBIT 1034 - PAGE 0003
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`

`

`
`
`FOCUS December 1994
`
`Joint Mathematics Meetings Update
`
`AMS-MAA Session
`
`Panelists for the session You're the pro-
`fessor, what next? on Friday morning
`include Kenneth P. Bogart (Dartmouth
`College), Donald W. Bushaw (Washing-
`ton State University), Daniel L. Goroff
`(Harvard University), Edward P. Merkes
`(University of Cincinnati), Robert R.
`Phelps (University of Washington), Rich-
`ard D. Ringeisen (Old Dominion
`University), Stephen Rodi (Austin Com-
`munity College),
`Ivar Stakgold,
`(University of Delaware), and Guido L.
`Weiss (Washington University, St. Louis).
`AMSSession
`
`The Committee on Science Policy panel
`discussion on Friday at 3:1 Sp.m.is titled /s
`there a better way to support mathemat-
`ics?: A comparative view. Panelists from
`the U.S., Canada, and Europe will describe
`systemsofsupport in their countries, what
`they see as the best and worst aspects of
`those systems, and how theyrelate to the
`current U.S. system.
`MAA Session
`
`The contributed paper session on Recruit-
`ment and retention of women faculty is
`sponsored by the MAA Committee on the
`Participation of Women, not the Joint
`Committee on Womenin the Mathemati-
`cal Sciences.
`
`Activities of Other Organizations
`Thetitle of the Association for Womenin
`
`Mathematics’ Noether Lecture given by
`Judith D. Sally on Thursday morning is
`Measuring Noetherian Rings.
`Thetitle of the AWM panel discussion on
`Wednesday afternoon is AWM: Why do
`we need itnow? The National Association
`of Mathematicians’ Claytor Lecturer is
`James H. Curry (University of Colorado,
`Boulder), who will speak on Saturday af-
`ternoon on Endomorphisms and
`factorization ofpalynomials.
`NAM’s Cox-Talbot Addresswill be given
`on Friday evening by William A. Hawkins,
`Jr. (University of the District of Colum-
`bia, and the MAA), on Some perspectives
`about mathematics and underrepresented
`American minorities.
`The Mathematicians and Education Re-
`
`form Network (MER) banquet is on
`Thursday evening at 6:30P.m., not on
`Wednesday evening.
`The MAA panel discussion, Forum on the
`mathematical preparation of K-6 teach-
`ers on Thursday morning includes Judith
`Roitman (University of Kansas) as mod-
`erator; Mercedes A. McGowan (William
`Rainey Harper College), and Paul R.
`Trafton (University of Northern Iowa) as
`presenters; and Jerry L. Bona ( Pennsyl-
`
`vania State University), Marilyn E. Mays
`(North Lake College), and Alan C. Tucker
`(SUNY at Stony Brook) as respondents.
`The MAA panel discussion on the Marh-
`ematicalpreparationofthe technical work
`force on Thursday morning also includes
`Bruce Jacobs (Peralta Community College
`District) as a panelist.
`From noonto 1:00 p.m. on Thursday there
`will be an MAA Northern California Sec-
`tion business meeting and election of
`section vice-chair.
`The AMS Committee on Education will
`
`sponsor a panel discussion on Saturday
`morning, Can we evaluate teaching or
`research in the mathematical sciences?
`Recent reports urge departments to give
`more weightto teaching in evaluating fac-
`ulty. Many argue that this makes no sense
`sinceitis impossible to evaluate teaching.
`Others counterthatit is just as difficult to
`evaluate research, but somehow wedoit.
`This panel, organized by Ronald G. Dou-
`glas (SUNY at Stony Brook and chair of
`the AMS Committee on Education), will
`provide a range of views on the problems
`of evaluating teaching and researchin the
`mathematical sciences. Panelists are Wil-
`
`liam P. Thurston (Mathematical Sciences
`Research Institute), D. J. Lewis (Univer-
`sity ofMichigan), and Alan H. Schoenfeld
`(University of California, Berkeley).
`The MAAsession Shaping up: Expecta-
`tions for high school mathematics on
`Saturday afternoon includes Hyman Bass
`(Columbia University) as moderator; and
`Richard Askey (University of Wisconsin,
`Madison); Gail Burrill (Whitnall High
`School, Wisconsin); Wade Ellis (West
`Point and West Valley College); and A.
`Wayne Roberts (Macalester College), as
`Theprizeis to be awarded to an undergraduate student(or students having submitted
`panelists.
`joint work) for outstanding research in mathematics. Any student whois an under-
`There will be an MAA poster session on
`graduatein a college or university in the United States or its possessions, Canada, or
`Research by undergraduate students on
`Mexico,is eligible to be considered for this prize of $1000 andacertificate. A few
`Saturday from 3:00 p.m.to 5:00 p.m. spon-
`honorable mentions may be made,for which a certificate is awarded.
`sored by the CUPM Subcommittee on
`Undergraduate Research in Mathematics,
`the Mathematical and Computer Science
`Division of the Council on Undergradu-
`ate Research, and the Committee on
`Student Chapters. Posters are invited
`which describe either mathematical re-
`search
`projects
`of
`individual
`undergraduate students orthe way in which
`undergraduate research is organized and
`encouragedata giveninstitution. Prospec-
`tive exhibitors should contact John
`Greever (Harvey Mudd College).
`
`Undergraduate Research Prize Announced
`
`The American Mathematical Society and the Mathematical Association of America
`have established the joint Prize for Outstanding Research in Mathematics by an
`Undergraduate Student.
`
`The prize research need not be confined to a single paper; it may be contained in
`several papers. The paper, or papers, to be considered must be submitted while the
`student is an undergraduate; research paper(s) cannot be submitted after a student’s
`graduation. Publication of the research is not required.
`
`The research paper, or papers, may be submitted for consideration by the student or
`by anominator. All submissionsfor the prize must includeatleast oneletter of support
`from a person familiar with the student’s research, usually a faculty member.
`
`This year’s prize will be awarded for papers submitted no later than June 30, 1995.
`Papers to be considered for this prize should be sent together with supporting mate-
`rials to Professor Robert M. Fossum, Secretary, American Mathematical Society,
`Dept of Math, University of Illinois, 1409 W Green St, Urbana, IL 61801.
`Ae
`4)—
`4
`
`APPLE EXHIBIT 1034 - PAGE 0004
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`APPLE EXHIBIT 1034 - PAGE 0004
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`

`

`December 1994
`
`Nobel Prize from page 1
`
`ishing in 1948, at the Carnegie Institute of
`Technology (now called Carnegie Mellon
`University). The thesis was titled “Non-
`cooperative Games”.
`
`Ashort version of Nash’s Ph.D. thesis ap-
`peared as an announcement in the
`Proceedings of the National Academy of
`Sciences in 1950; that version, with a one-
`page proof, was titled “Equilibrium
`points-in n-person games”. A reworked
`version of the entire thesis was published
`in Annals of Mathematics in 1951, with
`the title “Non-cooperative Games”.
`
`In his thesis, Nash used Brouwer’s fixed
`point theorem (1926) to prove the exist-
`ence of an equilibrium point. Both the
`Proceedings announcement and the An-
`nals version use the more general
`Kakutani’s Fixed Point Theorem (1946)
`in place of Brouwer. Nash creditsthis sim-
`plification of the proof to a suggestion by
`David Gale, now professor emeritus of
`mathematics at the University of Califor-
`nia, Berkeley, then a graduate student in
`mathematics at Princeton.
`
`Game theory—the abstractstudy of games
`(draughts, chess, poker, and so forth)—
`becomes relevant to the more serious
`
`aspectsoflife whenits results are applied
`in warfare, political conflict, or economic
`competition. The gametheorist examines
`the strategies the players in such a “game”
`may adopt.
`
`A pure strategy in a game is a complete
`plan for every possible situation that the
`player might encounter during the course
`of play. When the pure strategies ofall
`players are submitted to an umpire, the
`entire course of play and the payoffs to the
`players are determined.
`
`However, not all games can be solved with
`pure strategies, and players mustthen use
`a mix of pure strategies by choosing the
`probabilities with which each purestrat-
`egy is played. For example, in the simple
`game where twoplayers simultaneously
`put down a penny, with one player win-
`ning ifthey both match (both headsor both
`tails) and the other winning otherwise, the
`pure strategies are “heads”or “tails” and
`the mixed strategies are the random fre-
`quencies with which a player choosesto
`play these purestrategies.
`
`Inhis thesis, Nash proved that in any game
`there exists at least one set of mixed strat-
`
`egies, with one for each player—a
`so-called Nash-equilibrium point—such
`that no player can improvehis or her po-
`sition by changing strategy. At a
`Nash-equilibrium point no one can im-
`prove his or her position, and adoption of
`those mixed strategies results in a stable
`situation,
`
`Nash used methodsfrom topologyto prove
`the existence of an equilibrium point. His
`result applies to any finite, non-coopera-
`tive game involving any numberofplayers.
`(The word “finite” here refers to the fact
`that the numberofpossible strategies is
`limited; “non-cooperative” meansthat no
`communication between players may take
`place, and no alliances may be formed.)
`
`Gametheory began to be applied in eco-
`nomics following the publication of the
`book Theory of Games and Economic
`Behavior by John von Neumann and Oskar
`Morgenstern in 1944. Their analysis was
`largely limited to games involving only
`two players. Nash’s proofof the existence
`of at least one equilibrium point in the
`much wider class of non-cooperative
`gameswith any numberofplayers has had
`a major impact on modern economic
`theory. If you think of economic behavior
`as a gamein whichthere are well-defined
`rules, and all the players try to maximize
`their payoffs, then in general it will be
`possible for any given player to improve
`his or her position by changing strategy.
`Consequently, players will keep changing
`their strategies until they reach a Nash-
`equilibrium point at which no player can
`improve his or herposition. In some cases,
`this analysis makesit possible to predict
`the likely strategies that economic actors
`will adopt in the long run—namely, those
`at a Nash-equilibrium point at which no
`player can change to improve his or her
`outcome.
`
`Anillustration of Nash’s notion of an equi-
`librium point that has a perplexing twist in
`its tail is provided by the so-called
`“Prisoner’s Dilemma” devised by Nash’s
`advisor at Princeton, mathematician Albert
`Tucker, a topologist turned gametheorist.
`Tucker created the paradox in 1950, the
`same year Nash wrote his thesis.
`
`The Prisoner’s Dilemmaasksus to imag-
`ine a scenario where two suspects are
`
`FOCUS
`
`caughtbythepolice, and, during the course
`of separate interrogations, are offered the
`following choice. Ifone confesses and the
`other doesnot, the confessor goes free and
`the other goesto jail for a long sentence; if
`neither confesses, each goes to jail for a
`short time; if both confess, each receives
`an intermediate jail sentence.
`Each reasonsthat heis better off confess-
`
`ing because if the other confesses, he
`reccives an intermediate sentence by con-
`fessing and a long sentence by not
`confessing; if the other does not confess,
`he goes free by confessing and receives a
`short sentence by not confessing. Since
`each reasonsthis way, each confesses, and
`so each is given an intermediate sentence.
`
`The strategy whereby both confess is the
`Nash equilibrium in the game because
`neither can improvehis position by chang-
`ing his strategy (because to renege on
`confessing means jail for a long time).
`
`What seemsparadoxical about this situa-
`tion is that, if both suspects continue to
`protest their innocence, they would both
`receive a short sentence. And yet, com-
`mon sense logic compels them both to
`confess and end up spendinglongertime
`behind bars.
`
`Born in West Virginia in 1928, Nash was
`appointed research assistant and instruc-
`tor at Princeton in 1950, and worked as a
`consultant for the Rand Corporation dur-
`ing the summers of 1950 and 1952.1In 1951
`he was appointed a MooreInstructorat the
`Massachusetts Institute of Technology,
`where he was promotedto assistant pro-
`fessor in 1953 and to associate professor
`in 1957. In 1956-57, 1961-62, and 1963-
`64, he wasa visiting memberatthe Institute
`for Advanced Study. After resigning his
`professorship at MIT in 1959, he was a
`research associate there in 1966-67.
`
`Since the mid- 1960s, Nash has lived in the
`Princeton area. As a visiting research col-
`laborator in the Mathematics Department,
`he makes use of computing and library
`facilities in order to carry out his own pro-
`gram of independent research.
`
`Nash is a recipient of the von Neumann
`Theory Prize from the Operations Research
`Society of America, and is a fellow of the
`Econometric Society.
`
`
`
`e)
`
`APPLE EXHIBIT 1034 - PAGE 0005
`
`APPLE EXHIBIT 1034 - PAGE 0005
`
`

`

`FOCUS
`
`Search Committee
`Diary
`Edward F: Aboufadel
`
`The search continues for the perfect math
`instructor. In this episode, our diarist be-
`gins his ascent, then breathesdeeply through
`a grueling schedule ofinterviews at the ER
`in Cincinnati. Intrepidly he struggles tofind
`that Yes among Maybes andNos asthe num-
`ber of applications climbs to over three
`hundred! Watch yourstep...
`
`I read, muchofthe night, and go south in
`the winter.
`
`T. S. Eliot
`“The Burial of the Dead”
`The Waste Land
`
`have donethis, since many havelittle to
`say about the fact that one of the respon-
`sibilities of the position, as stated in the
`advertisement, is to supervise secondary
`school student teachers. Silence on this
`topic is, of course, not the kiss of death as
`far as I am concerned, and perhaps when
`I am donereading all of the folders, ['l
`discover that practically no one has any-
`thing to say about supervising secondary
`schoo! student teachers. Afterall, it is not
`a commonresponsibility in academia, al-
`thoughit is an important one.
`
`December14, 1993: The big Reading
`of the Applications continues. Ihave come
`across twoapplicantsso far that I think are
`promising, and I wonder ifthe other mem-
`bers of the search committee will feel the
`same waythat I do. I guess I will find out
`next Tuesday.
`
`December 1994
`
`secretary’s watchful eyes.
`
`As a final touch, our secretary saves the
`cancelled stamps from the applicants’
`envelopes and sends them to a convales-
`cent home. The homeis somehowable to
`raise money from the cancelled stamps.
`Graduate students take note!
`
`Polonius. What do you read, my lord?
`Hamlet. Words, words, words.
`Shakespeare's Hamlet
`
`December20, 1993: Working an hour
`or two a day, I have now read through 167
`application folders. Some are complete,
`while others are missing letters of recom-
`mendation, but I am getting thegist of the
`quality of our applicants. Of the 167 ap-
`plications, I have ranked abouta fourth of
`them as either a Yes or a Maybe.
`
`It is interesting to see the many waysthat
`schools send out letters of recommenda-
`This week weare sending outour flyer to
`The greatest misfortune that ever befell
`tion. At some schools, there seems to be
`mathematics education departmentsthat
`man wasthe inventionof printing. Print-
`we have onalist. Our ad was in FOCUS
`an office which coordinates the sending
`ing has destroyed education.
`last week,andit is also now available on
`of the letters, so for some applicants, we
`have received just one envelope with all
`e-MATH, so by now people should know
`threeletters in it. These packets often in-
`aboutour position. That, in fact, seems to
`be the case, as during the past few days we
`clude a pagethat states that the applicant
`have been averaging twenty totwenty-five
`has waivedhis or herrights to see the let-
`ters. For other applicants, the letters come
`new applications per day. (The count on
`Friday was 107, so we must be closing in
`in one at a time, and we have applicants
`on 150 as ofthis writing.) Perhaps with
`that have only oneletter of recommenda-
`tion, while others have two or three. A few
`the semester ending, people are finding
`more time to sendletters out.
`have eight or nine. In our advertisement,
`weasked for three.
`
`Benjamin Disraeli
`Lothair
`
`December 4, 1993: Today I began
`reading the application folders.
`I read
`through fifteen of them in about ninety
`minutes. At thatrate, if we were to receive
`one thousand applications, I would spend
`one hundred hours reading through them.
`Let’s hope we don’t get that many.
`
`Whatcan I say about the folders I read? It
`wasvery interesting. At the risk of sound-
`ing like a form rejection letter, let me say
`that there are a lot ofaccomplished people
`out there. Some have very impressive re-
`search backgrounds, while others have a
`lot of teaching experience.
`
`With approximately twelve pieces of pa-
`per per candidate in hand,I have to grade
`these candidates as Yes, Maybe, or No.
`(Again, the question I am trying to answer
`is, “Should we interview this person?”)
`Twelve pieces of paper can actuallytell
`you a lot. You get a sense of where a
`candidate’s priorities are from whatis sent.
`
`Whenit comes to applying forjobs, there
`is one approach—thescattershot ap-
`proach— for which we young(and not so
`young) mathematicians have becomefa-
`mous. This approach is to take advantage
`of computers and copy machines and to
`apply for an