8/10/2019 Pure Math, pure Joy.pdf
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By DENNIS OVERBYE
Amathematician, the Hungarianlover of
numbersPaulErdos oncesaid,is adevicefor converting
coffeeintotheorems.Here,then,are a few
glimpsesintothe Truth Factory.The Mathe-maticalSciences
ResearchInstitute, sus-tainedmostlyby
theNationalScienceFoun-dation,sits ona
hillabovetheUniversityofCalifornia atBerkeley, where
itattractspeo-plefromaround theworldforstintsof upto ayearto
losethemselvesin subjectslikealge-braic geometryor
specialholonomy.
Considerit anembassyof anotherworld,a Platonicrealmof clarityand
beauty,offorms andrelations,wherethe answerstoquestions notyet
asked alreadyexist.
Higher mathematics asopposedtowhatwe doeveryApril15
hasbeenrele-
vanteversinceArchimedesleapedoutof hisbathshoutingEureka!
morethan2,000years ago.Nobody knows whensomeab-struse bitof
mathwillfloatoff a blackboardata placelikethis and become
oftendec-adeslater a keytoolin cryptography, biol-ogy,physicsor
economics (asin ABeautifulMind).
Takestringtheory,a mathematicallylabyrinthineeffortto construct
a so-calledtheoryof everythingout ofthe notionthat the
fundamentalelementsof natureare tinystringsflopping
andwrigglingin an11-di-mensional space-time.It hasbeencalledapiece
of21st-centuryphysicsthat fellby acci-dentintothe 20thcentury.
Intheir quest tonegotiatethis labyrinth,string
theoristshavemadea hottopicofsomethingcalled Riemannsurfaces,
inventedbythe GermanmathematicianGeorgFrie-drich BernhardRiemann150
years ago,but
theyhavealsohelpedblazenew fieldsofmathematics.
Sinceour theoriesare sofar ahead ofexperimentalcapabilities,we
areforcedtousemathematics asour eyes,Dr. BrianGreene,a
ColumbiaUniversitystringtheo-rist, saidrecently.Thatswhy
wefollowitwhereittakes usevenifwe cantseewhereweregoing.
Soinsomewaysthemenandwomenseenherescrutinizing marks ontheir
black-boardscollectively represent a kindof parti-cleaccelerator
ofthe mind.
But the unreasonable effectiveness of
mathematicsin explainingthe world,
asthephysicistEugeneWigneronceput it,is a mi-normotivationat
bestfor those immersedinthefield.Mostmathematicianssay theyareinit
forthe mathitself, forthe delirious questforpatterns, thethrillof
thedetectivechaseandthe lureof beautiful answers.
Mathis sense,said Dr.RobertOsser-man,a Stanfordprofessorand
deputydirec-torof theinstitute,quoting fromtheplay Co-penhagen.
Thatswhat senseis.
By SAM ROBERTS
LAST week, New Yorks
highest court foundthat the states financ-ing formula for
public
schools denies New York Citystudents their constitutionalright
to a sound basic educa-tion,but thecourtleft severalsound basic
questions unre-solved:
Does spending more mon-ey guarantee better educa-tion?
If New York City getsmore, wont other local dis-tricts in the
state receive less?
If not, wheres the addi-tional money going to comefrom?
The State Court of Ap-peals punted the last question,leaving it
to the Legislature todecide who should pay for fix-ing a process
that, the courtsaid, allocatesto cityschoolsa share ofstate aidthat
does not bear a perceptible relation to the
needs of city students.Frank J. Macchiarola, a former city
schools
chancellor and now the president of St. FrancisCollege in
Brooklyn, who was an adviser to theplaintiffs, said: The treatment
in urban schoolsis not as good as the treatment in suburbanschools,
and thats wrong. But the problem is thatthere are just totally
inadequate schools underthe present system.
The plaintiffs, a coalition called the Cam-paign for Fiscal
Equity, insisted they were notseeking equity merely for equitys
sake. Thejudges agreed that equality wasnt the goal.
The citys 1.1 million public school students 84 percent of them
racial minorities and 80
percent of them foreign born have a right notto equal state
funding but to schools that provide
the opportunity for a sound basic education, thecourt said.
Largely discounted by the court were thestates arguments: that
the citys schools havebeenmismanaged;that thecityitselfis
obligatedto spend more on education; and that perhapsseveral
hundred million dollars are wasted annu-ally by unnecessarily
diverting students to spe-cial education programs for the
disabled.
The court found that the system fails toattract and retain
experienced teachers, thatlarge class size affects student
performance andthat computers and library books are inadequate(not
just old and classics, as an appeals courtsuggested).
More money, it ruled, isone answer, if only a firststep.
In her dissent, Judge Su-san Phillips Read cautionedthat
educational deficien-cies are not always attributa-ble to the lack
of money ornecessarily cured by the infu-sion of more funds.
Still, it usually helps.The broad-range con-
sensus, said Dr. RobertBerne, senior vice presidentof New York
University, isthat money well spent willmake a difference for
kids.
Diane Ravitch, the edu-cation historian, agreed. Itsclearly
better to have moremoney than less money, shesaid, but the question
is howis it going to be spent?
Prodded by the plain-tiffs, thecourtconcurredwiththe need not
only for morefunds but for monitoring how
they are spent.It set three goals: that the state figure out
the actual cost of providing a sound basic educa-tion; that
every school receive the resources itneeds to do so; and that the
new scheme shouldensure a system of accountability to
measurewhether the reforms actually provide the oppor-tunity for a
sound basic education.
The first challenge for the Legislature, saidMichaelA.
Rebell,executivedirector andcounselfor the Campaign for Fiscal
Equity, is to deter-mine how much money do you need?
THE NEW YORK TIMES, SUNDAY, JUNE 29, 2003 7WK
Beautiful Minds
PureMath, Pure Joy
Doingthe math:clockwise, fromtop,SrikanthIyengar makinghiscaseat
theMathematical Sci-ences ResearchInstitutein Berke-
ley;wagingmen-talbattlewithaproof; takingnotesat a semi-nar;and
partici-patingin a ques-tion-and-answersession.
PhotographsbyEd AlcockforTheNew YorkTimes
Judges Keep the State After School
George M. Gutierrez for The New York Times
A classroom at one overcrowded New York school, P.S. 246 in the
Bronx, in 1999.
Ideas & TrendsPage 14
PUB:NYT PUBDATE:2003-06-29 SEC:WK PAGE:7 OUTPUT:Sat Jun 28
01:57:16 2003 JOB:116337536
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