The Words of Mathematics: An Etymological Dictionary of Mathematical Terms Used in English

264 Pages·1996·2.14 MB·English

by  Steven Schwartzman

The Words of Mathematics

The Words of Mathematics
An Etymological Dictionary of
Mathematical Terms used in English
Steven Schwartzman
Published and Distributed by
The Mathematical Association of America
© 1994 by
The Mathematical Association of America (Incorporated)
Library of Congress Catalog Card Number 93-80612
Print ISBN 978-0-88385-511-9
Electronic ISBN 978-1-61444-501-2
Printed in the United States of America
SPECTRUMSERIES
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ROGERHORN,Chairman
BARTBRADEN RICHARDGUY
UNDERWOODDUDLEY JEANNELADUKE
HUGHM.EDGAR LESTERH.LANGE
BONNIEGOLD MARYPARKER
ComplexNumbersandGeometry,byLiang-shinHahn
Cryptology,byAlbrechtBeutelspacher
FromZerotoInfinity,byConstanceReid
IWanttobeaMathematician,byPaulR.Halmos
JourneyintoGeometries,byMartaSved
TheLastProblem,byE.T.Bell(revisedandupdatedbyUnderwoodDudley)
LureoftheIntegers,byJoeRoberts
MathematicalCarnival,byMartinGardner
MathematicalCircus,byMartinGardner
MathematicalCranks,byUnderwoodDudley
MathematicalMagicShow,byMartinGardner
Mathematics:QueenandServantofScience,byE.T.Bell
MemorabiliaMathematica,byR.E.Moritz
NumericalMethodsthatWork,byFormanActon
OutoftheMouthsofMathematicians,byRosemarySchmalz
Polyominoes,byGeorgeMartin
TheSearchforE.T.Bell,alsoknownasJohnTaine,byConstanceReid
ShapingSpace,editedbyMarjorieSenechalandGeorgeFleck
StudentResearchProjectsinCalculus,byMarcusCohen,EdwardD.Gaughan,Arthur
Knoebel,DouglasS.Kurtz,andDavidPengelley
WordsofMathematics,byStevenSchwartzman
MathematicalAssociationofAmerica
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Thisbookisdedicatedtothememoryandthecontinuinginfluenceofmy
brother-in-law, Alain Levy, who loved science in both the familiar and
the etymological senses of the word, and who was well described as a
prince.
Contents
Introduction.................................................................................1
Acknowledgments...........................................................................9
Explanationoftermsandsymbols...........................................................11
Anetymologicaldictionaryofmathematicalterms............................................17
Appendix:Mathematicalentriesthatareetymologicallyrelated,groupedbyroots.............225
References................................................................................241
vii
Introduction
In recent years I’ve become very fond of asking my students why the White House is called the
WhiteHouse.Whenthequestionfirstcomesupthestudentsareusuallydumbfounded.Theywonder
if I could really be asking them that question in a mathematics class—or any other class, for that
matter—andtheytrytofigureoutwhatImightbedrivingat.Moreinterestingly,though,theyseldom
knowhowtoanswerthequestioneventhoughtheansweristrivial.TheWhiteHouseiscalledthe
WhiteHousefortworeasons:becauseit’swhiteandbecauseit’sahouse.
IstartedaskingmytrivialandseeminglyirrelevantquestionbecauseInoticedthatmoststudents
arenotgoodatusingmathematicalterminology.Manyofthemhaven’trealizedthattechnicalterms
aren’tjustarbitrarysyllablesdesignedtomaketheirlivesmoredifficult.ThepointItrytomakewith
my White House analogy is that most mathematical terms actually describe the things they refer
to.ThedifficultyisthatthedescriptionsareusuallyinLatinorGreekratherthanEnglish,andfew
studentsnowadayshavebeenexposedtothoseancientlanguages.
Thestudyoftheoriginsofwordsisknownasetymology:thisbookisanetymologicalguideto
themostcommonmathematicaltermsthatoccurintheelementary,secondary,andcollegecurricula.
Armed with this guide, students may find mathematics a little more understandable. Their non-
technicalEnglishvocabularyshouldalsoimprovebecausethesamerootsfoundintechnicalterms
occurinmanyotherwordsaswell,someofwhichwillbepointedoutinthisbook.Atatimewhen
many students’ English skills are very weak, it is important to stress English even in classes like
mathematicsandsciencethatnolongerfocusonlanguageasmuchastheyoncedid.
Historically speaking, there used to be less of a separation between mathematics and language
than there is now. As a teenager the great German mathematician Carl Friedrich Gauss was still
having trouble deciding whether to devote his life to mathematics or linguistics. His discovery of
a method for constructing a regular heptadecagon (a seventeen-sided polygon) tilted the balance
in favor of mathematics, though his knowledge of languages continued to serve him well as a
mathematician. His most famous book, Disquisitiones Arithmeticæ, was written in Latin, as were
manyothermathematicians’books.Evenasrecentlyasthefirstdecadesofthe20thcenturyvirtually
allcollegestudentswererequiredtostudyLatin,andusuallyGreekaswell;attheendoftheschool
yearthevaledictoryaddresswastypicallygiveninLatin.Timeshavechanged.Becauseknowledgeof
LatinandGreekisnolongercommon,teacherscanusetheexplanationsinthisguidetosupplement
theirexplanationsoftechnicalterms;theycan,forexample,askstudentstofindotherEnglishwords
thatseemtoberelatedtoagiventechnicalterm.
Atsomepointteachersshouldalsopointoutthatif“traditional”mathematicshadbeendiscovered
in America, mathematical terminology would be primarily in English. Compare modern physics,
muchofwhichhasbeencreatedinAmerica;oneofthe“flavors”ofquarkischarmed,whichwas
1
2 Introduction
previouslyanon-technicalEnglishword.Similarly,therelativelyrecentbranchofmathematicsthat
dealswithknotsclassifiesknotsaswildortame,andingametheoryaduelmaybenoisyorsilent.
Recent number theory deals with weird, untouchable, hailstone and lucky numbers. The English
wordsoftwareisrecognizedbymanycomputerusersallovertheworld,eventhoughtheymaynot
understandthecomponentssoftandwareortheimpliedcontrastwithhardware.
AlthoughEnglish mayseem quiteunrelatedto Latinand Greek(exceptforwordsthatEnglish
borroweddirectlyfromthoselanguages),allthreelanguagesareactuallydescendedfromacommon
ancestorthatweusuallycallIndo-European.Surprisingly,almostallthelanguagesofEurope,plus
Persian and many of the languages of India, belong to that same family. That is why the original
language, whose speakers even in ancient times spread out as far east as India and as far west
aswesternEurope,iscalledIndo-European.SomemodernIndo-EuropeanlanguagesareRussian,
German,Gaelic,Spanish,Yiddish,Catalan(spokeninSpain),Serbo-Croatian,Romansch(spoken
inSwitzerland),Hindi,Pashto(spokeninAfghanistan),Polish,Afrikaans(spokeninSouthAfrica),
Welsh,Romany(thelanguageoftheGypsies),Lithuanian,andUrdu(spokeninPakistan).Infact,
roughlyhalfthepeoplealiveintheworldtodayspeakanIndo-Europeanlanguage.
With the passage of time the variousIndo-Europeanlanguages have diverged phoneticallyand
semantically from the original source to the point where almost none of them remain mutually
intelligible;theonesthataremutuallyintelligible,likeSwedishandNorwegian,havedivergedfrom
each other only relatively recently. Even in rather different languages, however, the relationship
between certain words is still recognizable even after thousands of years. Compare Russian mat’
with Spanish madre and English mother. Not only do they sound similar, but their meanings are
identical. None of the three words was borrowed from any of the others; all three are directly
descendedfromacommonancestralword.Suchrelateddescendantsarecalledcognates,fromLatin
co-“together”andgnatus“born.”Cognatesmaybelikenedtosistersorcousins,whoalsocomefrom
acommonancestorbutdon’tcomefromeachother.Althoughmuchofourmathematicalvocabulary
inEnglishhasbeenborrowedfromLatinandGreek,manyofthosetechnicalborrowingsalsohave
nativeEnglishcognates,someofwhichwillbepointedoutinthefollowingpages.
ThisguidecanhardlygointoIndo-Europeanlinguisticsinmuchdepth.Still,itmightbehelpfulto
lookatafewgroupsofrecognizablecognates.Bycomparingthemembersofsuchgroups,linguists
havesetupaseriesofsoundcorrespondencesamongtheIndo-Europeanlanguages.Consonantsare
generally more stable than vowels, and among the consonants some are more stable than others.
Furthermore,agivensoundoftendevelopeddifferentlyindifferentphoneticenvironmentsandunder
differenttypesofstress.
The table below shows a few examples of typical Indo-European consonant correspondences.
Ofcoursethegivencorrespondencesapplyonlytonativewords,nottowordsthatwereborrowed
Original Original Native Greek Borrowing Latin Borrowing
root Meaning English root fromGreek root fromLatin
ped- foot foot pod- podiatrist ped- pedestal
ten- stretch thin tono- tone ten- tenuous
kerd- heart heart kard- cardiac cord- cordial
bheu- be,exist be phu- phylum fu- future
dhe- put,set do the- thesis fac- fact
wed- water water hudor hydrant und- undulate
gno- know know gnosko- agnostic gnoro- ignorant