A discussion into Mathematical Inquiry and what is the spark that ignites it. I have used my own upbringing as an example

1. Mathematical Inquiry:whatis the sparkthat ignitesit?
By Claude Sajous. January 17, 2016 Page 1
Mathematical Inquiry: what is the spark that ignites it?
By Claude Sajous
January 17, 2016
I hope the followingwillinspire ayoung student,which youthe readermayknow of,whois
contemplatingMathematicsasa fieldof inquiry.
Nottoo longago duringthe normal course of my daya trainof thoughtpoppedintomymind
that beganwitha verycuriousseriesof wordsthatran as follows:“foreveryepsilonthere is a delta,
such that …”.This pattern repeateditself overandoveragain. I thenstoppedmyself andaskedwhere
didthisthoughtcome from? It didn’ttake longbefore Irecognizedthesewordsasthe beginningof the
Epsilon-Deltadefinitionof aLimit. For those whoare notfamiliarwiththe Epsilon-Deltadefinitionitis
withinthe contextof the mathematical subjectcalledCalculus.Iwasamusedasto whynow thiswould
justsuddenlypopintomymind.Literally,ithasbeenmanyyears since Igraduatedfromcollege andmy
daysstudyingCalculuswhere longgone.However,longasitmay be,there were principlesthatIlearned
fromway back thenthat I have carriedwithme to thisday.It is truly amazing.Itis thisthoughtthat led
me to think further about the world of Mathematics and mathematical inquiry in general and ask myself,
whysome studentspursue itandsome do not? Why it appealstosome andnot to others? Hence the
questionIdecidedtoask myself andponderon:what is the spark that ignitesmathematical inquiryin
an individual,especiallyayoung student?
To answerthisquestionIhadto lookback overthe yearsand in particularmyupbringing.My
parentswere notwealthy peoplebutwere firmly determinedtogive bothmyselfandmytwosistersa
solideducation.Theywere immigrantstothiscountryand settledinNew YorkCity. Aschildren,my
sistersandI were senttoa Catholicelementaryschool nearhome.Iwill refertothe school as Saint. G.
The nuns andpriestwhoran Saint G ElementarySchool didthe verybesttheycouldgiventhe resources
theyhad at theirdisposal.The school waslocatedonthe UpperWestSide of Manhattan and the
overwhelmingmajorityof studentscame fromBlue Collarworkingclassfamilies.Myfamilywas no
different. However,the mathematical curriculumthatwastaught to us - - at leastto my class - - was
lessthanup-to-par.Again,the teachersandAdministratorswere wonderful people buttheystruggled
withlimitedresourcesand havingtodeal with large classes. Asfarback as it maybe there isone very
distinctive factthatIrememberfromthose days. Asa graduating8th
graderI didnot know whata
negative numberwas! Thisbeingthe absolute truth! Amazingasthatmay be it became partof the
realityIhad to deal with.Iwas notalone.Noone frommy graduatingclass was taughtanythingabout
negative numbers! Itookthe High School entrance examandwasdefinitelyinforarude awakening.
Thisis whenmyparentstookoverand tooka more active role inmy education.Ihumblythankedthe
CatholicChurchfor havingprovidedme andmyclassmatesthe educationwe DIDreceive at SaintG,but
the time to move onwas now.

2. Mathematical Inquiry:whatis the sparkthat ignitesit?
By Claude Sajous. January 17, 2016 Page 2
Whenit came time for me to graduate my parentsdecidedtodosomethingdifferentwithme
and that wasto send me to a private HighSchool inManhattan. It wasa huge sacrifice forthemat that
time andone that wouldhave a profoundimpactonme goingforward.Itwas a small,private andvery
well runschool withverygood teachers.Inorderto preserve anonymityIwill refertothisschool as R
High School,for itsname beganwiththe letter R. It wasa strictschool where everystudentwore
uniforms. ItwaslocatedinMidtownManhattan off 6th
Avenue. Luckilyforme at that time Iwas an
obedientandpassive studentthatdidexactlywhathisparentstoldhimtodo. So off to private High
School I went.
It wasn’tuntil manyyearslaterthat I wouldbe challenged withthe conceptof predestination,
but as I lookback now,clearlyanelementof predestinationwasatwork. One of the firststudentsImet
at R High School and made friendswithwasa studentbythe name of Richard S. He wouldturnout to
be the single mostimportantperson of myentire 4yearcareer at R High School.RichardS not onlywas
a friendof mine anda fellowclassmate buthe became myMath Tutor andplayedanenormousrole in
helpingme fastforwardbothinknowledgeandinskill inordertosurvive my1st
year at R High School.
Richardwas brilliant.He wasthe onlykidthatI knew duringthose fouryearsthat scoreda perfect100
on hisChemistryFinal exam.Idon’tbelieve there wasanyone else whoachievedsuchafeat.I cannot
say forcertainif he wasa childprodigybuthe certainlywasexceptionallysmartandwasa straight-A
student. Itwas withthe helpof RichardS that the foundationwaslaid.He wasa verygoodtutor and
teacherinhisown right. I got hooked-upwiththe rightcrowd,andthankgoodnessbecause mydear
parentswere bleedingmoneyinorderforme to get back ontrack withgettingaqualityandcompetitive
education.
The firstyear wasthe foundationalyear; mycatch-upyear. Neverbefore didIstudysohard.I
was puttingin4 hour daysof studyingona dailybasis.The onlyplace tostudywas the kitchenandthe
onlyphone inthe apartmentwasin the kitchen!Youcan image! Man! Was it noisyat times,butIwas
youngand supremelydeterminedtosucceed.
Goingforward,it wouldbe mysophomore year - - Year 2 - - more than any otherthat wouldset
the course of historyforme.I had an outstandingMathteacher.In fact there were two.One Icannot
rememberhisname,andthe otherI will call him Mr.W forhis lastname beganwithW. Mr. W wasa
combinationHighSchool Mathteacher,Marine Corp drill sergeantandmotivational coach,all inone.He
was an extraordinarydisciplinarianthatnostudentdaredtomessaroundwith. In those days - - way
back inthose days - - teachersdidn’thesitate tograba studentbythe throat! Those were nononsense
days!A studentcame to school to dobusinessorelse!! Whatmy fellow studentRichardSdidtolay the
foundationinmyMath education, Mr.W wouldbuilduponbyfosteringdiscipline,awinningattitude
and mostimportantlythe confidence todispel all FEARasitrelatedtothe pursuitof the knowledge of
Math. Mr. W ledthe charge andwe studentswere more thaneagertofollow.Eventhe dumbest
studentinthe class - - if he/she followedthe patternandexample thatwaslaidoutby Mr. W - - would
endup learningalotand have the confidence togoforward. In hindsight,itisabundantlycleartome
that I alongwithmyfellowstudentswere bestowedwiththe privilegedof havinghada GREAT teacher.
At that time Ididnot love math - - remember,nottoolongagoas a graduating8th
grader I didnot even
knowwhata negative numberwas! - - butI now hada respectforthe subjectcalledMathematics. All

3. Mathematical Inquiry:whatis the sparkthat ignitesit?
By Claude Sajous. January 17, 2016 Page 3
the creditis due to Mr. W,our HighSchool math teacher. The school that I wentto participatedinthe
Regentexams.Suffice ittosaythat these were examsadministeredbythe State of New Yorkand given
inadditiontoa student’sHighSchool final exams. Studentswhotookthe annual Regentsexamand
passedwouldthengraduate withaRegentsendorsementontheirHighSchool diploma.The onlyreason
I mention thisisthatat the endof my sophomore yearIscoreda 98 on myGeometry Regent’sexam- -
the highestscore inmy class. Not evenmyesteemedfriendandbelovedTutor RichardS wasable to
replicate thatscore.Wow!I was dizzywithexcitementandknew forcertainIhad come a longway.
CertainlyitwasnotI who deservedthe credit.Yes,MomandDad had somethingtodowithit.It was
theirdecisiontoplace me ina small,private HighSchool.However, RichardS and Mr. W playedpivotal
rolesinshapingandmoldingme. First,asany house builderwill tell you,buildingthe foundationof a
house isthe most importantpart.In mycase, the foundationhadtobe re-built,asfaras Mathematics
was concerned.Second,the confidence Ineededtopushforwardhadto be imparted.Thirdly,any
debilitatingfearthatwouldhinderme hadto be completelyeliminated.Ican confidentlysaythatbythe
endof mysecondyearin HighSchool,the fearof Math was gone!All thankstoa greatTeacherand a
great Tutor.My desire tostudyMath was awakensimplybyemulatingothers whohadpavedthe way
for me.
I digressa momenttodiscuss Mr. W.Not onlywashe a greatMath Teacherbuthe alsogave a
great performance. IwenttoHigh School inthe dayswhenwe still hadreal chalkand a real
BLACKBOARD. Mr. W made the chalksing,hop,skipanddance on the blackboard.Hiscommand of the
subjectwasso overwhelmingitwasas if we were watchinga performance atRadioCity.He was in
complete control.Noaspectof the subjectwasbeyondhim.He wasa sternyet a fatherlyfigure who
made it hisbusinesstoinstillineachone of us the conceptthat Yes,we can, andthat Yes,it was
expectedofus to EXCEL inhis subjectmatter.Nothingelsewasaccepted.Hence,he raisedthe barvery
highand pushedusall to excel inMathematics. I am fullyaware thatwe are talkingonlyHighSchool
Math, but there isone thinghe succeededinandthat washe taughtus that there wasnothingtofear.
We as students,walkedonthe roadof mathematical inquirywithasmile onourfacesand witha
confidentdisposition. Whatwasthe sparkthat ignitedthe flame?Itwasthatof a GREAT teacher!
Fast forwardingtwoyears,itwasnow my turn to graduate fromHigh School.Tomy parent’s
great relief,IstayedandI graduated!Theyhadspenta small fortune onme and it wasnot yetover.
College wasonthe horizon. Igraduatedwitha desire tofurthermyeducation inScience andpossibly
pursue a Medical Career.Thiswasmy state of mindas a seniorinHighSchool. I respectedMathbuthad
no intentionof pursuingMathematicsasa majorin college.
My firstyearincollege wasuneventful.Iattendedalarge UniversityinNew YorkCity (NYU),
chieflysothatI can live at home andcommute to school.DuringmyfirstyearI spentway toomuch time
at the StudentCenterplayinggames.ThatyearI took2 semestersof Calculus.Againnothingeventful
happenedthatyear.I thinkthe shockof goingfrom a small private HighSchool toa verylarge University
withuntoldthousandsof studentsdefinitelyhadanimpact onme. Ittook time toadjust.Gone were the
close interactionbetweenstudentandteacher.There were toomanystudentsineachclass.I remember
one thingfor certain:myChemistrylablecture classhad400 students!Itwas insane andwaytoo
impersonal.MyCalculusprofessorwasverygood.Forthe firsttime everI hada womanMath teacher,

4. Mathematical Inquiry:whatis the sparkthat ignitesit?
By Claude Sajous. January 17, 2016 Page 4
but since somany thingswere newtome and somany thingswere goingonI hadtrouble focusingonly
on Math. That was the 1st
Year. Now,Year 2 wouldarrive!
In my sophomore year,somethingprofoundwouldhappenthatwouldaltermycollegecareer.
In myCalculusIIIclasswe hada verydifferentProfessor.He hadan accent.He wore a Turban on his
head.I believe - - to the bestof my knowledge - - he wasa SikhIndiannational. Idon’trememberhis
full name butI knowit beganwithA.I will refertohimas ProfessorA. Bythe way,one verygoodthing
for me at that time wasthat the Math classes,althoughnotsmall,were manageable insize andnottoo
big.It made a huge difference.Icouldnottake the 400 studentssize megaclasses!ProfessorAwasa
strict professorwhohada commandof hissubject,wasveryexpressiveinhisdeliveryandgave a great
performance whokepteveryone awake.He remindedme,ina way,to Mr. W from HighSchool.
ProfessorA was far more than a Math professor.He gave a performance andwasextraordinarily
entertaining.He hadeyesthatcouldglow withexcitementandspew fire ata student. Hisvoice would
reach feverpitch.He hopped,skippedanddancedandmade the chalkinhis handto do the same on the
Blackboard.It wasa wonderto behold. Asstudentswe listenedwithraptattention.Iforone was
mesmerized andattimesI feltIwas ina spell.Itwasduringthistime thatI revertedbackto the very
goodpractice of studyingeverysingleday.Notone daywentbywithoutme studyingmathematics. I
was enormouslygrateful thatthe foundationhadbeenlaidotherwiseIwouldnothave survived.
However,itwasnot somuch aboutme butabout ProfessorA. Hisenthusiasm, hiscommandof the
subject,andabove all,his FEARLESS approach to the subjectiswhatimplantedwithinme aninsatiable
desire toknowmore.It wasthenthat I stunnedeveryonewhoknew me thatIhad decidedtomajor in
Mathematics.UpongraduatingfromHigh School I had nosuch intention,butnow Ifeltthatmy shipon
the ocean of life hadbeenredirectedbyforcesbeyondmycontrol. Above all,Ilovedit! 
Richard S, Mr. W and now ProfessorA, these three would be the oneswhotookan 8th
grader
whodidnot knowwhata negative numberwastonow beingone who greatlydesiredtowalkthe
hallowedroadof mathematical inquiry.There are certainlygiftedindividualsbutIam not one of them.
The spark that ignitedthe mathematical inquirywithinme came fromwithout.First,the foundationhad
to be laid,or inmy case re-laid. RichardS tookcare of that.The discipline andconfidence hadtobe
instilled.Thatcame from Mr. W. The inspirationwasbornandthe call to follow wasgiven,andthat
came fromProfessorA. By then,the restwas history.One daywhile stillincollegeIcaughtup withmy
formerHighSchool classmate RichardS and toldhimof my decision.Wow!Didwe have agood laugh!!
Richardwho wasnothing lessthanbrilliantinscience wouldenduppursuingaLiberal Artsdegree in
English.He shockedeveryoneinsucha drasticaboutface.To thisdayI will neverfullyunderstandthe
reasonfor hisdecision.AllIcan possiblythinkof isthathisparents soterriblywantedhimtopursue
Medicine thathe may have inadvertentlychosentoforsake science tospite hisparents! Thatseems
harsh doesn’tit?It’sonlya thought.Thatis one of the reasonswhyIbelieve thatinguidingayoung
mind one mustgentlyprod,encourage,andguide butneverexerttoomuchpushthatmay well leadto
overtrebellion.
In the remainingtwoyearsIwouldenduptakingmany advancedcoursesinMathematicsand
one inparticularthat I rememberthatgave me a greaterdose of difficultythanotherswasa course in
Partial DifferentialEquations,a.k.a.PDQ.Thiscourse almosthadme pullingthe hairoutof my head.

5. Mathematical Inquiry:whatis the sparkthat ignitesit?
By Claude Sajous. January 17, 2016 Page 5
Many yearslaterwhenI wouldface strongheadwindsfromall the paradigmshiftsin Information
Technology,I wouldremindmyself againandagainthatif I couldsurvive PDQIcouldtake on anything
that the ComputerIndustry couldthrow myway! The mental discipline thatwasinstilledwithinme in
the pursuitof Mathematicswas invaluableand isstill treasuredtothisday.
As an individual whobelievesinEternity - - anyone whohasread the New Testamentwould
knowwhatI’m takingabout - - I lookforwardto settingaside acouple of centuriestopickup where I
leftoff! (Parenthetically,humorhasitsplace! We all needto laugha little!)
Today,withthe fusionof Finance andMath the burgeoningfieldof Quantitative Finance - - also
knownas Mathematical Finance - - offersa plethoraof new opportunitiesforthose whowantto pursue
thisverytraditional fieldand,yet,one thatcontinuestobe veryrelevantinourworldtoday.
Be well.
By Claude Sajous