Mathematics for Human Flourishing

TLDR: This paper aims to explore how the deeply human themes that drive us to do mathematics can be channeled to build a more beautiful and just world in which all can truly flourish.

Abstract: How can the deeply human themes that drive us to do mathematics be channeled to build a more beautiful and just world in which all can truly flourish?

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Claremont Colleges
Scholarship @ Claremont
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
Mathematics for Human Flourishing
Francis Su
Harvey Mudd College
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J
ANUARY8,2017FEBRUARY7,2017 / MATHYAWP
Whydoesthepracticeofmathematicsoftenfallshortofouridealsand
hopes?Howcanthedeeplyhumanthemesthatdriveustodomathematics
bechanneledtobuildamorebeautifulandjustworldinwhichallcan
trulyflourish?Igave thisRetiringPresidentialAddressatthe
A
MS‐MAAJointWinterMeetingsonJanuary6,2017attheendofm
y
termasPresidentoftheMathematicalAssociationofAmerica.Anaudio
recording(hp://bit.ly/math‐flourish‐audio)orvideorecording
(hps://youtu.be/xEtDvc1SWm8)isavailable.
Everybeingcriesoutsilentlytobereaddifferently.
―SimoneWeil,GravityandGrace
Christopherisaninmateinahigh‐securityfederalprisonnotfar
fromAtlanta. He’sbeenintroublewiththelawsincehewas14. He
didn’tfinishhighschool,hadanaddictiontoharddrugs,
andage
21,hisinvolvementinastringofarmedrobberieslandedhimin
prisonwitha32‐yearsentence.
Rightnow,you’veprobablyformedamentalimageofwho
Christopheris,andyoumightbewonderingwhyI’mopeningmy
speechwithhisstory. Whenyouthinkaboutwhodoes
mathematics–bothwhoiscapable
ofdoingmathematicsandwho
wantstodomathematics–wouldyouthinkofChristopher?
Andyethewrotemealeerafter7yearsinprison.Hesaid: “I’ve
alwayshadaproclivityformathematics,butbeinginaveryearly
stageofyouthandalsolivinginsomeadversecircumstances,I
nevercame
tounderstandthetruemeaningandbenefitofpursuing
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aneducation…overthelast3yearsIhavepurchasedandstudieda
multitudeofbookstogivemeaprofoundandconcrete
understandingofAlgebraI,AlgebraII,CollegeAlgebra,Geometry,
Trigonometry,CalculusIandCalculusII.” Christopherwaswriting
meforhelpinfurtheringhismathematicseducation.
Whenyouthinkofwho
doesmathematics,doyouthinkof
Christopher?
Everybeingcriesoutsilentlytobereaddifferently.
SimoneWeilisawell‐knownFrenchreligiousmysticandawidely
reveredphilosopher.Sheisprobablylesswellknownasthe
youngersisterofAndreWeil,oneofhistory’smostfamousnumber
theorists.
ForSimoneWeil,to‘read’someonemeanstointerpretormakea
j
udgmentaboutthem.She’ssaying:everybeingcriesoutsilentlyto
b
ejudgeddifferently. IsometimeswonderifSimonewascrying
outaboutherself. ForSimone,too,lovedandparticipatedin
mathematics,butshewasalwayscomparingherselftoherbrother.
Shewrites:
“At fourteenIfellintooneofthosefitsofboomlessdespairthat
comewithadolescence,andIseriouslythoughtof
dyingbecauseof
themediocrityofmynaturalfaculties…theexceptionalgiftsofmy
b
rother,whohadachildhoodandyouthcomparabletothoseof
Pascal,broughtmyowninferiorityhometome.Ididnotmind
havingnovisiblesuccesses,butwhatdidgrievemewastheideaof
b
eingexcludedfromthattranscendentkingdomtowhichonlythe
trulygreathaveaccessandwhereintruthabides.Ipreferredtodie
ratherthanlivewithoutthattruth.”
WeknowSimonelovedmathematicsbecausesheusedmathematical
examplesinherphilosophicalwriting. Andyou’llfindherin
photosofBourbakiwithherbrother.
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(Bourbaki,1937)
Ioftenwonderwhatherrelationshiptomathematicswouldbelikeif
sheweren’talwaysinAndre’sshadow.
Everybeingcriesoutsilentlytobereaddifferently.
AsMAAPresident,youmightthinkthatmyrelationshipto
mathematicshasalwaysbeensolid. Idon’tliketheword‘success’
b
utpeoplelookatmeandthinkI’msuccessful,asifthetrue
measureofmathematicalachievementisthegrantsI’vereceived,or
thenumerouspapersI’vepublished.
LikeChristopher,I’vehadaproclivityformathematicssinceyouth.
ButIgrewupinasmallruraltowninSouthTexas,withlimited
opportunities. Most
ofmyhighschoolpeersdidn’tevenaend
college. Ididbecausemydadwasacollegeprofessor,butmy
parentsdidn’tknowaboutthemanymathematicalopportunitiesI
nowknowexist.
MyloveformathdeepenedattheUniversityofTexas,andI
managedtogetadmiedtoHarvardformy
PhD. ButIfeltoutof
placethere,sinceIdidnotcomefromanIvyLeagueschool,and
unlikemypeers,Ididnothaveafullslateofgraduatecourseswhen
Ientered. IfeltlikeSimoneWeil,standingnexttofutureAndre
Weils,thinkingIwouldneverbeableto
flourishinmathematicsifI
werenotlikethem.
IwastoldbyoneprofessorthatIdidn’tbelongingraduateschool.
Thatforcedmetoconsider,amongotherthings,whyIwantedtodo
mathematics. Andinfact,thatisessentiallytheonebigquestion
thatI’dlikeforyoutoconsidertoday:
Whydomathematics?
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Thisisasimplequestion,butworthconsiderablereflection.
Becausehowyouanswerwillstronglydeterminewhoyouthink
shouldbedoingmathematics,andhowyouwillteachit.
WhyisChristophersiinginaprisoncellstudyingcalculus,even
thoughhewon’tbeusingitasafreemanfor
another25years?
WhywasSimonesocaptivatedbytranscendentmathematical
truths? Whyshouldanyonepersistindoingmathorseeingherself
asamathematicalpersonwhenothersaretellingherinsubtleand
notsosubtlewaysshedoesn’tbelong?
Andinthispresentmoment,theworldisalsoaskingwhatits
relationship
withmathematicsshouldbe. Amidstthegreatsocietal
shiftswroughtbythedigitalrevolutionandashifttoan
informationeconomy,wearewitnessingtherapidtransformation
ofthewaysweworkandlive. Andyetwehearvoicesinthepublic
spheresaying:“highschoolstudentsdon’tneedgeometry”or“let’s
leaveadvanced
mathforthemathematicians”. Andsome
mathematicianswon’tadmititbuttheysignaltheexactsamething
b
yrefusingtoteachlowe r‐levelmathcourses,orviewingthemath
majorasameanstoweedoutthosetheydon’tthinkarefitfor
graduateschool.
Ourprofessionisthreatenedbyvoiceslikethesefromwithin,and
without,whoareundermininghowsocietyviewsmathematicsand
mathematicians. Andtheviewofour
professionisdismal. The
2012reportfromthePresident’sCouncilofAdvisorsonScienceand
Technologypegsintroductorymathcoursesasthemajorobstacle
keepingstudentsfrompursuingSTEMmajors. Wearenot
educatingourstudentsaswellasweshould,andlikemost
injustices,thishurtsthosewhoaremostvulnerable.
Iwantus
asamathematicalcommunitytomoveforwardina
differentway. Itmayrequireustochangeourviewofwhoshould
b
edoingmathematics,andhowweshouldteachit. Butthisway
willbenolessrigorousandnolessdemandingofourstudents.
Andyetitwilldrawmorepeopleintomathematicsbecausethey
willseehowmathematicsconnectstotheirdeepesthumandesires.
Soifyouaskedme:whydomathematics?I
wouldsay:
mathematicshelpspeopleflourish.Mathematicsisforhuman
fl
ourishing.
Thewell‐livedlifeisalifeofhumanflourishing.TheancientGreeks
hadawordforhumanflourishing,eudaimonia,whichtheyviewas
thegoodcomposedofallgoods. Thereisasimilarwordin
Hebrew:shalom,whichisusedasagreeting. Shalomissometimes
translated‘peace’,buttheword
hasafarrichercontext. Tosay
‘shalom’tosomeoneistowishthattheywouldflourishandlive
well. AndArabichasarelatedword:salaam.
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