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Simplicity, in
Mathematics and in Art
AllynJackson
Simplicityisashardtopinpointinmathematicsas
itisinart.Certainlybothsubjectshavetheirgreat
exemplarsofthequality.Butisthereadefinition
ofsimplicity?Acriterion?Ameasure?Orasure
pathtoit?
These kinds of f questions s were in n the e air at
aconferencecalledSimplicity:IdealsofPractice
in Mathematicsandthe Arts, which took place
attheGraduateCenteroftheCityUniversityof
New Yorkin early April2013.Insteadoftrying
to definitively y answer r such questions—surely a
doomedprospectanyway—theparticipantsgave
intothesheerjoyofdiscussioninthestimulating
atmosphereofeachother’scompany.Theconfer-
encefeaturedlecturesandpaneldiscussionsbyan
eclecticgroupoftwenty-fiveartists,architects,art
historians,mathematicians,andmathematically
inclinedphilosophers,aswellasafilmprogram.
The audience included academics s from nearby
institutionsandlocalartists;astheconference
offeredeasyandfreeonlineregistration,arandom
smatteringoffolkswanderedinoutofcuriosity.
NotanAbsoluteNotion
Simplicityoftenseemstobeatimeless,absolute
quality,andforgoodreason.PeterSarnak,Institute
for Advanced d Study y and d Princeton University,
offeredEuclid’sproofoftheinfinitudeofprimes
assimplicityparexcellence.Thestarkeleganceof
thisancientproofisasstrikingtodayasitmust
havebeentopeopleencounteringitthroughthe
millennia.Ofcourse,theproofisanexemplarof
simplicity,notadefinition.Indeed,CurtisFranks,
University of Notre e Dame, , argued d against the
Allyn Jackson is senior writer and d deputyeditor of the
Notices.Heremailaddressisaxj@ams.org.
DOI:http://dx.doi.org/10.1090/noti1028
possibility of f ever r establishing g for r all time an
absolutenotionofsimplicity.Whatwethinkofas
simpleemergesfromconventionsthataredeeply
embeddedin how we live andhow w we see the
world,andtheyhavealonggenetichistory.“Our
thinkingoccurswithinthoseconventions,”hesaid.
“Thereisnotreallyawayoutofthem.”
Asconventionsevolve,so donotionsofsim-
plicity.FranksmentionedGauss’s1831paperthat
establishedtherespectabilityofcomplexnumbers.
TheproblemGausswasworkingon—concerning
quadraticandbiquadraticresidues—hadonlyun-
satisfyinglycomplicatedandpiecemealsolutions
over Z. Over C,a farsimplersolution emerged.
Thecomplexnumbersrevealedsimplicitywhere
previouslytherehadseemedtobenone.
Mathematicsisnotengagedinastraightforward
march toward absolute e simplicity. Rather, , by
discoveringsimplicityanew,Frankssaid,“Wewill
be more e awake to o the changing g landscape of
mathematical thought.” ” He noted a parallel in
art,wheresomethingnew—liketheworkofAndy
Warhol or r Marcel l Duchamp—acts s as s a sort t of
“shocktreatment”thatcompelsanewperspective.
Several conference e speakers mentioned d the
artofFredSandback, whousedtaut t lengthsof
yarn torepresent outlines s ofthree-dimensional
shapes.Inphotos,theworkslookunimpressive;
as philosopher Juliet Floyd, Boston University,
noted,theyare“unphotographable”.Butwalking
aroundandthroughtheconstructions,shefound
themtobe“extremelymovingobjects”.Finnish
architectJuhaniPallasmaadescribedhowaSand-
backconstruction,merely“afewlinesstretched
inspace”,setsoffachainreactionintheviewer’s
mind,causingtheviewertoseefiguresofspecific
materialshapes,tofeeltheirweightandtexture.
“Theairinsidetheimaginaryfigureseemstoget
920
NoticesoftheAMS
Volume60,Number7
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denserandtohaveaslightlydifferentconsistency
fromtheairoutside,”hesaid.Simpleconstructions
thatholdmuchcomplexityandmeaning:That’s
justwhatmathematiciansseekintheirwork.
Pallasmaa’s erudite e lecture contained many
strikingquotations,includingthisoneofBalthus:
“Themoreanonymouspaintingis,themorerealit
is.”Thesamecanbesaidforarchitecture,Pallasmaa
stated. Could a similar statement be e made e for
mathematics? Are there mathematical results
thatareso natural, sopristinethat one cannot
perceivethefingerprintsofthemathematicians
whodiscoveredthem?Perhapsoneexamplewould
bethepreviouslymentionedproofoftheinfinitude
ofprimes,itsattributiontoEuclidnotwithstanding.
Perhaps others are found in n what Paul l Erd˝os
famouslycalled“proofsfromtheBook”.
PallasmaaalsoquotedthephilosopherGaston
Bachelard,whoinhisbookThePhilosophyofNo:
APhilosophyoftheNewScientificMind,statedthat
scientificthought“developsalongapredestined
path,fromanimismthroughrealism,rationalism,
andcomplexrationalism,todialecticalrationalism.”
Pallasmaadidnotsaythatmathematicsdevelops
inthisway;hispointratherwasthatartaspiresto
developintheoppositedirection,fromtherational
backtowards“aunifying,mythical,andanimistic
experience”.Perhapsmathematicsshuttlesback
andforthbetweenthetwoendpoints.
VisceralEncounters
Bachelard’s“predestinedpath”at timesechoed
throughtheconferenceincommentsthatseemed
toderivefromthemisconception,commonoutside
ofmathematics,thatthesubjectconsistsentirely
ofproofs,progressinginexorablyfromonelogical
steptothenext.Thismisconceptionwasvividly
counteredatvariouspointsduringtheconference.
In an n open microphone session, Blaise Heltai
pointedoutthatmathematicsandartareactually
very similarin process: When you u are e thinking
aboutamathematicalobject,youarerightinside
thething,tryingtopuzzleoutitsstructureand
secrets.You’renotthinkingabouthowtoprove
anything—that comes later. . The puzzling-out
resemblestheconceptualpartofdoingart.Heltai
hasaspecialperspective,asheisapainterwith
a Ph.D.in mathematics;he makes a living g as a
managementconsultant.
Thekindofvisceralencounterwithmathematics
thatHeltaireferredtoemergedatvarioustimes,
suchasin the lectureofDennisSullivan,CUNY
GraduateCenterandStonyBrookUniversity.When
as a graduate e student t he was s preparing g for
the preliminary y examination, , Sullivan n studied
JohnMilnor’sbookTopologyfromtheDifferential
Viewpoint. Sullivan n knew the book k inside and
out,everydefinition,everyproof.Thedaybefore
theexam,ashetookafinalglancethroughthe
book,itsuddenlyoccurredtohimthathecould
compressthecontentsintoasingle,simplepicture.
Movingbackandforthacrossthestage,heused
gesticulationstoindicatea2-sphereononeside,a
3-sphereontheother,anda“slinky”curvebetween
them.Thiscurve,representingthepreimageofa
regularvalueofamapfromthe3-spheretothe2-
sphere,providedamentalimagesummarizingthe
Pontryagin–Thomconstruction.Ifoneknowsthe
languageofmanifoldsandtransversality,Sullivan
claimed, one e can reconstruct t the whole theory
ofcobordism in differentialtopology just from
theintuitionconveyedbyhisslinkypicture.This
experiencemadehimrealize,“That’swhatitmeans
tounderstandapieceofmathematics.”
Thevisceralcomponentofmathematicalwork
surelyevokesstrongfeelings,butmathematicians
usuallydonotdiscusstheirfeelingsabouttheir
work,atleastnotinpubliclectures.Inanearlier
paneldiscussion,RiikkaStewen,FinnishAcademy
ofFineArts,askedwhethermathematicianshave
stronglove/hatefeelingsabouttheirwork.“Yes,
verystrongfeelings,”cametheimmediatereply
fromamathematicianonthepanel,AndrésVillave-
ces,NationalUniversity ofColombia.Thereisa
lonelinessintheworkofanartist,andmuchmath-
ematicalworksharesthisquality.Justasapainter
facesanemptycanvas,hesaid,“Mathematicians
areupagainsttheemptypageeveryday.”
Thelonging,evendesperation,thatisimplicit
in the remarks s of f Villaveces also emerged in
Sarnak’slecture,titled“Isthereaplacefor‘ugly’
mathematics?”.Sarnak consideredthe situation
where theonly known route to a proofis ugly,
in the e sense of f being g strewn n with long and
complicated calculations and verifications. The
question then becomes, , How w desperate are e we
for a a proof? When Sarnak k gave an example of
an ugly calculation connected with a beautiful
resultinthetheoryofautomorphicforms,Mikhail
Gromov,InstitutdesHautesÉtudesScientifiques
andNewYorkUniversity,pipeduptosay:“Maybe
themathematicsisfine,it’syourmindthat’sugly.”
ThentherewasGromov’slecture.Afishsays:
“Youwanttounderstandwhatwateris?Jumpin
andfindout.”Insteadofplungingin,youcould
study the chemical and physical properties of
water.Butwithouttheexperienceofplunginginto
water,youhavenoframeinwhichtotalkabout
whatwaterreallyis.Similarly,whentheexperience
ofplungingintomathematicsisabsent,thereis
noframeinwhichtotalkaboutwhatmathematics
is—muchlesswhatsimplicityinmathematicsis.
That’sa verbose description ofone moment
thatflashedbyinaninstantinGromov’sstream-of-
consciousnesslecture.HejumpedintoDescartes’s
timeless statement, “Cogito ergo sum m [I I think
August2013
NoticesoftheAMS
921
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thereforeIam]”.Theimportantthinghere,Gromov
said,istheergo,thetherefore.In asense,dogs
think:Muchofwhatgoesoninahumanbrainis
verysimilartowhatgoesoninthebrainofadog.
Surelydogsare.Butdogsdonotunderstandergo.
Thisergoisamajorsourceofthekindofthinking
thatischaracteristicofhumans,Gromovsaid.And
yet,“itiscompletelyhiddenfromus.Andthereis
agoodreasonwhyitishidden.Ifitsurfaces,you
die.Youwillnotsurvive.It’sagainstsurvival,it’s
againstevolution,it’sagainst[natural]selection.”
So it went. Gromov passed d so o quickly y over
so many y topics, diving to the depths, , all the
while leavening the presentation with flashes
of subversive humor. . The effect t was s dizzying.
Afterward,duringtheopenmicrophonesession,
an audience member demandeda one-sentence
summary—withanexample.Animpossiblerequest
tofulfill.Neverthelessitcanbesaidthatoneof
Gromov’smainmessageswas:Guardagainstthe
delusionoffalsesimplicity.Manythingsthatwe
assume at first glance to be simple e are e in fact
highlycomplex.
AfterseeingGromov’seffervescentmindbubble
overforthirtyminutes,audiencememberAlThaler,
knowntomanyforhislongserviceattheNational
ScienceFoundation andnow an adjunct faculty
memberatCUNY’sHunterCollege,commented,“I
couldneverlivelikethat.”
ContrastingGroups
TheSimplicity conferencewasthebrainchildof
mathematician Juliette e Kennedy, , University of
Helsinki,andtwoCUNYmathematicians,Roman
KossakoftheGraduateCenterandPhilipOrding
of Medgar Evers College. The conference was
somethingofafollow-uptoa2007symposium
calledAesthetics and Mathematics, which h took
placeinUtrecht andwasorganizedbyKennedy
and two University y of f Utrecht mathematicians,
RosalieIemhoffandAlbertVisser(Iemhoffwasone
ofthelecturersatSimplicity).Participantsinthe
2007symposiumcoulddropinatanartexhibition
attheMondriaanhuis,LogicUnfettered—European
andAmericanAbstractionNow,whichwascurated
byKennedy.
InadditiontothefilmprogramattheSimplicity
conference,therewasaninstallationofafewworks
byartistKateShepherdinthelobbyoutsidethe
hallwherethelecturesweregiven(Shepherdalso
participatedinoneofthepaneldiscussions).But
spaceconstraintsthere,aswellasthedifficultyof
securingexhibitspaceinNewYorkCity,meantthat
Simplicityofferedfewopportunitiestoexperience
art.Asaresult,artwasrepresentedmainlythrough
thepresenceandwordsoftheartiststhemselves.
By contrast, , the mathematicians couldactually
presentpiecesofmathematicsbyusingacomputer
andabeamer,orevenjustablackboard,inthecase
ofSullivan.Theytriedmightilytoavoidtechnical
details,withimperfectsuccess.
Another contrast was socio-economic. . As
Kennedy pointed d out t in a panel discussion,
the mathematicians and d philosophers at the
conferenceallworkinacademia,whichprovides
economicsecurityandsocialacceptability,while
artistsoftenleadfarmoreprecariouslivesonthe
fringesofsociety.Shenotedthe“heroic”efforts
thatmanyartistsmustputforthinordertocarry
outtheirwork.
What dideach groupabsorb from theother?
It’sdifficulttosay.Oneparticipantobservedthat
mathematicianstendto havea highopinion of
themselves and their own knowledge e and are
thereforenotsoopentonewideas,whileartists
arepretty much the opposite: Receptivenessto
impressionsandinfluencesfroma widevariety
ofsourcesistheartist’slifeblood.Oneartistwho
attended Simplicity,Miyuki Tsushima, saidshe
didn’tfollowallthedetailsofthemathlectures.
Shecouldsimplysitandlettheimpressionswash
overherasshemadesomesketchesforherlatest
work.
Aninspirationfortheconferencewastheso-
called twenty-fourth problem of f David d Hilbert.
Thisproblem, which Hilbert t considered d adding
tohisfamouslistoftwenty-threeproblemsthat
he presented at t the e International l Congress of
MathematiciansinParisin1900,wasunearthedby
RüdigerThiele,UniversityofLeipzig,frompapers
atthelibraryoftheUniversityofGöttingen.Partof
Hilbert’sdescriptionoftheproblemreads:“Criteria
ofsimplicity,orproofofthegreatestsimplicityof
certainproofs.Developatheoryofthemethodof
proofinmathematicsingeneral.Underagivenset
ofconditionstherecanbebutonesimplestproof”
(translation by Thielefromhisarticle“Hilbert’s
24thProblem”,AmericanMathematicalMonthly,
January2003).
Etienne Ghys, École Normale Supérieure e de
Lyon,pointedout thenaiveté ofimaginingthat
suchultimatesimplicity ispossible.Yet, as s the
conference highlighted, , simplicity y as a dream,
asanideal,remainsa powerfulguidinglight in
mathematicsandthearts.AsFrankssaid,there
arenoabsolutenotionsofsimplicity.Butdonot
relinquishthequest.“Onthecontrary,Iwantto
sayyes,findcriteriaforsimplicity,continuetodo
so,”saidFranks.Don’timaginethatthematterwill
everbesettleddefinitively;rather,“returntothe
taskoften.”
Materialsfromsomeofthelecturesareonthe
Simplicityconferencewebsite,http://s-i-m-p-l-
i-c-i-t-y.org,andvideosofsomeofthelectures
willbepostedsoon.
922
NoticesoftheAMS
Volume60,Number7
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924    
N
otices
of
the
AMs 
V
oluMe
60, N
uMber
7
doceamus . . . let us teach
Doceamu
s
between outreach and traditional mathematics 
scholarship is dependence on the cooperation of 
local school districts and state educational agen-
cies and of teachers at all levels.
Reaction to the 2001 articles was positive. Many 
institutions have faculty dedicated to outreach, but 
in many cases these faculty were hired in nontenure- 
track roles or pursued outreach activities only 
when the traditional requirements for tenure and 
promotion were met. This is because the typical 
reward system may not recognize that an outreach 
mathematician should be tenured and promoted 
in a manner cognizant of his or her outreach role 
as is the case in a traditional track of pure math-
ematical or educational research. Addressing this 
issue is critical to any effort to create an outreach 
position in a mathematics department.
At the time of the earlier articles, Dwyer was a 
tenure-track faculty member in the Department 
of Mathematics at the University of Tennessee. In 
spite of satisfaction with the job and a high level of 
support from the Tennessee mathematics faculty, 
for personal reasons, he moved to the M&S depart-
ment at TTU in 2003. When this position became 
vacant in 2002, there was mixed support to add 
faculty expertise in mathematics education, but 
Schovanec, then the department chair, recognized 
the potential of adding an outreach faculty mem-
ber. Moving to a new position had its challenges, 
including building confidence with the local K–12 
community, obtaining support of new colleagues, 
and a delay in the tenure and promotion process 
for the outreach mathematician.
Outreach Roles and Recognition
At TTU, there are basically three components in 
the outreach work: (1) on-campus activity teach-
ing courses, supervising students, and interacting 
Two articles describing early experiences of an 
outreach mathematician and the chairperson who 
advocated for such a role appeared in the Notices 
of the American Mathematical Society in 2001 
[1], [2]. Several years later, it is timely to reflect 
again on the evolving nature of this endeavor. The 
first author (Dwyer) of this essay is the outreach 
mathematician involved in the earlier articles. The 
second author (Schovanec) was the chair of the 
Department of Mathematics and Statistics (M&S) 
at Texas Tech University (TTU) at the time that 
Dwyer was hired in 2003. Schovanec now serves 
as the interim president of TTU and previously 
was the dean of the College of Arts & Sciences. In 
each of his administrative roles he has promoted 
outreach, engagement, and the associated reward 
structures within the university.
Background
Herein we define outreach for a mathematics 
department as any activity that enhances the 
teaching and learning of mathematics outside the 
department, in particular in K–12 education and 
community colleges. An outreach mathematician 
is not a mathematics education researcher but 
is likely to spend considerable time working on 
matters that are sometimes within the domain of 
mathematics education. A significant difference 
Revisiting an Outreach 
Mathematician
Jerry Dwyer and Lawrence Schovanec
Jerry Dwyer is professor of mathematics at Texas Tech 
University. His email address is jerry.dwyer@ttu.edu.
Lawrence Schovanec is interim president at Texas Tech 
University. His email address is lawrence.schovanec@
ttu.edu.
Members of the Editorial Board for Doceamus are: David 
Bressoud, Roger Howe, Karen King, William McCallum, 
and Mark Saul.
DOI: http://dx.doi.org/10.1090/noti1023
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A
ugust
2013 
N
otices
of
the
AMs 
925
administering outreach must be reconciled with 
the logistics of producing outreach scholarship. 
For example, one must address the use of human 
subjects, Institutional Review Board (IRB) approval, 
and access to K–12 populations, issues often for-
eign to traditional mathematics research. There 
are also both a shortage of appropriate publication 
outlets and reservations from colleagues concern-
ing the quality of scholarship that results from 
outreach activities. 
A significant development in support of out-
reach at TTU occurred in 2012 when the university 
adopted a revised tenure and promotion policy 
that recognized outreach and community engage-
ment as part of a faculty member’s contributions 
to teaching, research, or service. Even if a discus-
sion of outreach and community engagement does 
not rise to the university level, a mathematics 
department should consider amending the reward 
and promotion structure to take into account the 
nontraditional role of an outreach mathematician. 
The mathematics department at TTU has recently 
adopted such a clause in its promotion and tenure 
documents. For the record, Dwyer obtained tenure 
and eventually promotion to full professor, the 
first such case in his department. 
Institutional Perspective
From the viewpoint of Schovanec as chair and 
then dean, there are new opportunities, rewards, 
and frustrations related to outreach mathematics. 
As chair of a traditional research department at a 
large state university, he found enthusiasm and ap-
preciation for mathematics outreach at the higher 
levels of university administration not always com-
mensurate with departmental support. 
The goodwill and publicity derived from out-
reach activities translated into enhanced financial 
support of the department and a perception of 
departmental vitality. The Texas Senate recog-
nized the M&S department when it was awarded 
the Texas Association of Partners in Education 
Award, in large part due to activities initiated by 
Dwyer and his colleagues in the department. Pub-
licity events for major grants garnered significant 
attention and increased the visibility of the M&S 
department at local and regional levels. Further-
more, collaborations with local school districts 
and regional colleges and alliances with teachers 
enhanced student recruitment and presented 
greater opportunities for research and funding. 
Since Dwyer arrived at TTU, he has played a 
critical role in the growing culture of outreach 
and engagement that now receives greater institu-
tional recognition. Most recently Dwyer has been 
featured as an Integrated Scholar [4], a distinction 
that TTU has enlisted to recognize contributions 
to teaching, research, and service, where outreach 
is recognized as a component of all three areas. 
In 2006, TTU was the first Texas university to 
be included in the Community Engagement 
with faculty in other departments who have inter-
ests that are aligned with outreach activities; (2) 
organizing locally and regionally funded outreach 
activities such as K–12 school visits and summer 
programs; and (3) serving on national committees 
and participating on panels at various meetings. 
There has been a progression in how these roles 
have been developed. Master’s theses have been 
completed and a mathematics education concen-
tration has been added to the mathematics Ph.D. 
program that provides opportunities for train-
ing mathematicians in the newer outreach roles. 
Personal school visits have been reduced, while 
teacher workshops and collaboration with school 
districts have increased. Grant writing has evolved. 
Though proposals are still submitted to local foun-
dations with a history of supporting educational 
programs unique to TTU, a large commitment is 
now tied to substantial federal funding requests, 
often of a collaborative nature.
The major issues facing an outreach mathema-
tician are similar to those of traditional faculty. 
There is a need to seek funding and to publish 
scholarly articles. A progression from small funded 
proposals to larger ones has resulted in significant 
support for outreach projects. Some of the activi-
ties for which funding has been obtained include 
girls’ math clubs, pre-engineering and mathematics 
academy summer programs, and several National 
Science Foundation programs primarily related to 
teacher training and scholarship programs. Com-
mon objectives of these programs include: increas-
ing the number and diversity of students in STEM 
programs; enhancing undergraduate research 
opportunities in the sciences; and growing the 
number of teachers in STEM areas while enhancing 
opportunities for teacher preparation. 
One award, which is reflective of the matura-
tion of outreach activities at TTU, is the Integrated 
STEM Initiative on the South Plains [3, http://
www.depts.ttu.edu/stem/isisp.php]. This 
NSF program provides funding for the integration 
of outreach programs and stimulates changes in 
the campus culture related to STEM education 
and outreach. It may be argued that the hiring of 
an outreach mathematician provided the catalyst 
and leadership for a more cohesive campus-wide 
approach to outreach grant writing. As a result, 
over the last several years more than $12 million in 
funding has significantly affected STEM education 
and outreach projects at TTU. Somewhat ironically, 
in light of increased funding, a new challenge has 
been to maintain a focus on the original depart-
mental expectations of the outreach position. 
Dwyer has had to curtail his role in grass roots 
activities in order to administer existing projects 
and coordinate new collaborative programs.
The topic of publication can be a challenge 
for one in a nontraditional academic role such 
as an outreach mathematician. The demands of 
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926    
N
otices
of
the
AMs 
V
oluMe
60, N
uMber
7
Classification of the Carnegie Foundation for the 
Advancement of Teaching; it is regularly recog-
nized in the president’s Higher Education Com-
munity Service Honor Roll. This distinction is 
partially based on data reflective of TTU’s strategic 
priority to expand community engagement and 
evidence of extensive faculty-led community col-
laborations. Since 2009, TTU has annually assessed 
the institution’s community engagement activity 
utilizing Michigan State’s Outreach and Engage-
ment Measurement Instrument (OEMI). Texas Tech 
has been represented in national and international 
conversations on institutional mission and assess-
ment of community engagement.
Another promising development is the creation 
of a TTU university-wide multidisciplinary STEM 
Center for Outreach, Research, and Education. The 
center, for which Dwyer serves as director, is sup-
ported by six colleges at TTU. This university-wide 
participation in the center in some ways reflects 
both authors’ vision for the recognition and insti-
tutionalization of outreach at TTU.
References
[1.] J. B. Conway, Reflections of a department head on 
outreach mathematics, Notices of the AMS 48 (10), 
(2001), 1169–1172.
[2.] J. F. Dwyer, Reflections of an outreach mathemati-
cian, Notices of the AMS 48 (10), (2001), 1173–1175.
[3.] Integrated STEM Initiative on the South Plains (ISISP), 
NSF award No. 0930257, September 1, 2009–August 
31, 2014.
[4.] Bob Smith, Texas Tech Integrated Scholars, All 
Things Texas Tech, 3(2), (2011), http://www.depts.
ttu.edu/provost/attt/.
Call for Proposals
Workshop Program
AIM invites proposals for its focused workshop 
program.  AIM’s workshops are distinguished by 
their specific mathematical goals.  周is may involve 
making progress on a significant unsolved problem 
or examining the convergence of two distinct areas 
of mathematics.  Workshops are small in size, up to 
28 people, to allow for close collaboration among the 
participants.
SQuaREs Program
AIM also invites proposals for a new program called 
SQuaREs, Structured Quartet Research Ensembles.  
More long-term in nature, this program brings 
together groups of four to six researchers for a week 
of focused work on a specific research problem in 
consecutive years.  
More details are available at:
AIM, the American Institute of Mathematics, sponsors 
week-long activities in all areas of the mathematical 
sciences with an emphasis on focused collaborative 
research.
http://www.aimath.org/research/
deadline: November 1
AIM seeks to promote diversity in the research mathematics 
community.  We encourage proposals which include significant 
participation of women, underrepresented minorities, junior 
scientists, and researchers from primarily undergraduate 
institutions.
...writtenwordsendure
What We Are Doing
about the High Cost
of Textbooks
TheAIMEditorialBoard
Let’sbeginwiththeobvious:Thepriceoftextbooks
hasrisenmuchfasterthanthecostoflivingover
the last t thirty years, , but t there e has not t been a
significant increase e in their quality. . We don’t
proposetoanalyzetheeconomicandeducational
factorsthat underlie thisphenomenon.Instead,
we will describe our r efforts to o help lower r the
cost of textbooks for r standard d undergraduate
mathematicscoursesinNorthAmericancolleges
anduniversities.
TheAIMEditorialBoardconsistsofDavidAustin,George
Jennings,KentE.Morrison,Frank Sottile,and d Katherine
Yoshiwara.
DavidAustinisprofessorofmathematicsatGrandValley
StateUniversity.Hisemailaddressisaustind@gvsu.edu.
GeorgeJenningsisprofessorofmathematicsatCalifornia
State University, Dominguez Hills. . His s email l address s is
gjennings@csudh.edu.
Kent E. Morrison is emeritus professor of mathematics
atCalPoly,SanLuisObispo,and now affiliatedwiththe
AmericanInstitute of Mathematics.Hisemail addressis
morrison@aimath.org.
FrankSottileisprofessorofmathematicsatTexasA&M.His
emailaddressissottile@math.tamu.edu.
Katherine Yoshiwara is professor r of mathematics
at Pierce College. . Her email l address is yoshiwka@
piercecollege.edu.
MembersoftheEditorialBoardforScriptaManentare:Jon
Borwein, ThierryBouche,John Ewing, Andrew w Odlyzko,
AnnOkerson.
DOI:http://dx.doi.org/10.1090/noti1025
We make upthe AIM M (American n Institute of
Mathematics)EditorialBoard,whichispartofa
largerNSFproject
1
todevelopopensourcesoft-
wareandcurriculummaterialsforundergraduate
mathematicseducation. Opentextbookscan be
“openaccess”,meaningtheyarefreely available
indigitalformat,or“opensource”,meaningtheir
sourcefilesarefreelyavailable.Ourprojecthopes
toovercometwoobstaclesfacedbytextbooks:It’s
hardtofindthem,andit’shardtoknowwhich
onesaregood.
Let’ssay youarescheduledtoteachabstract
algebranext term.Howdoyouchoosethetext?
Youmayusethebookyouusedlasttime,orthe
bookyouhadasastudent(yes,Herstein isstill
availableinpaperbackfor$111),oryoumayask
yourcolleaguenextdoorforarecommendation.
Or you may decideto lookforan open source
textbook.
Searchforfreeabstractalgebratextsandyou
will get two o million n results or more. . You will
findthatthetop150entriesorsoactuallylook
promising, but t then you u notice e that t some are
duplicatesandsomearelinkstopiratedversions.
Manyofthempointtosupplementalnotes,exercise
solutions,andothermaterialrelatedtothebooks.
Veryfewareactuallylinkstoentiretextbooksthat
1
InformationaboutProjectUTMOST(UndergraduateTeach-
inginMathematicswithOpenSoftwareandTexts)canbe
foundathttp://utmost.aimath.org.
August2013
NoticesoftheAMS
927
canbeobtainedwithoutcost.Thenittakestimeto
followthelinksandreadenoughtodecidewhether
ornotabookisaviablecandidateforyourcourse.
Withourprojectweareworkingtofind,evaluate,
andpromoteopentextbooksinmathematics.We
have created d a short “approved list” of open
textbooksorganizedbycoursename,withalink
to each book’s s website. . We encourage authors
tomaintainanactivewebsitewithmoredetailed
informationabouttheirbooks,aswellaserrata
sheets,linkstoreviews,courseadoptionlists,and
contactinformationforcommentsandcorrections.
Such a website can help create e an n ecosystem
aroundabooksothatotherscancontributetoits
improvement.Anopentextbookcanbeashared
community resource that remains current and
won’tgooutofprint.
The criteria a we use e to o approve books are
describedindetailonourwebsite.
2
Inbrief,we
arelookingforbooksthatcanservewellasthe
requiredtextinacourse.Wecontactfacultywho
haveactuallyusedthebookstofindoutwhatthey
think.Dotheyrecommendthebookinquestion?
Would they y use it t again? Although h we do not
require that the books be available in n printed
format,werecommendthatauthorsarrangefor
printinganddistribution by companiessuch as
LightningSource,Lulu,Amazon,orBarnes&Noble.
Therearecurrentlytwenty-onebooksinthirteen
courses on the approved list. Some e of them
beganascommerciallypublishedtextbookswhose
copyrights were returnedtotheauthor.Others
beganaslecturenotesandevolvedintopolished
textswhileremainingopenaccess.
Tom Judson’s s AbstractAlgebra:Theoryand
Applications,first publishedby PWS in 1994, , is
anexampleofhowatextbookcanbecomeopen
source.Aftergettingthecopyrightback,Judson
released the text as open source e with h a GNU
Free Documentation License. . The e mathematics
departmentofVirginiaCommonwealthUniversity
took the LAT
E
X source, invested d some time in
formattingandediting,andarrangedforLightning
SourcetoprintandbindthebookandforAmazon
tosellit.Thepriceisonly$20(hardcover)andthe
entirePDFversionisavailablefornocostatthe
book’swebsite.Youandyourstudentscanprint
yourowncopiesorjustthepagesyouwant.You
canarrangeforaphotocopystoreoryourcampus
bookstoretoprintcopiesforallofyou,atacostas
lowas$10.Ofcourse,youdon’thavetoprintitat
all;youcanreaditonyourcomputerornotebook.
There isalsoa digitalversion in which each
chapterisaSagenotebookthatallowsimmediate
computationwithSage,andthereareSagenote-
booksthatcontainjusttheexercises.(Sageisfree
opensourcesoftware.)
2
http://www.aimath.org/textbooks/
SomeofthebooksarereleasedwiththeGNU
Free Documentation License mentioned above,
whilemanyhaveaCreativeCommonslicensethat
ismorerestrictiveinthatitdoesnotallowothers
tosellthebookforprofitbutdoesallowthemto
chargethenominalcostofprinting.Finally,afew
ofthebooksarecommerciallypublished,sothat
the publishersretain alltherightstoprintand
distributehardcopies,butwithopenaccessPDF
versionsthatcanbeprintedforindividualuse.
What motivatesauthorstoforego the oppor-
tunitytoearnmoneyfromtheirhardwork?For
many itistheexperiencegainedfromwritinga
commercially publishedbookthatdidnot yield
richreturns,sotheprofitmotiveisweakforthe
nextbook.Authorswouldlike theirwork to be
usedandappreciated,sotheywouldliketomake
itwidelyavailable.Formanyaprimarymotivation
isthedesireto do somethingbeneficialfor the
world.
Ifyou’dliketocontributetotheopensource
movement,herearesomethingsyoucando.Give
seriousconsiderationtoopentextbooks,andlet
your colleagues know about them,too. Let t the
authorsknowwhenyouusetheirtextsandbecome
partofthecommunitybygivingfeedback,tracking
errors and typos, and contributing supplemen-
tary material. Contribute a a book k review w to o the
OpenAcademicCatalogattheUniversityofMin-
nesota (http://open.umn.edu), where reviews
andratingsofopentextsinallsubjects—notjust
mathematics—arebeingcollected.
Now that we have e evaluated d a number r of
books,weseetheneedforpracticaladviceand
guidanceforauthorswhowanttoproduceopen
sourcematerials.Wearecreatingacollectionof
recommendedpracticesforallaspectsofwriting
andpublishingopenmathematicstextbooks,both
in the e current t environment, where e most t books
are read d in a static version as PDF files s or as
printed copy, , and d in the e new w environment t of
constantInternetconnectivity,mobiledevices,and
cloudcomputing.In afuturecolumn wewould
liketodiscussthechallengesandopportunities
thatanauthorfacesundertheserapidlychanging
conditions.
928
NoticesoftheAMS
Volume60,Number7
Mathematics People
A
ugust
2013 
N
otices
of
the
AMs 
929
Mathematics People
Smith Awarded Adams Prize
Ivan Smith of the University of Cambridge has been 
awarded the 2013 Adams Prize. This year’s topic was 
topology. 
According to Tim Gowers, chairman of the Adams 
Prize Adjudicators, Smith “has proved several beautiful 
and important results in symplectic topology. With Simon 
Donaldson, he found new proofs of some major results 
of Taubes that were simpler and that avoided delicate 
use of machinery from outside symplectic topology. With 
Paul Seidel, he attacked the problem of understanding the 
nature of Khovanov cohomology, a mysterious but very 
useful invariant. They developed a geometric definition 
that was later shown, by Smith and Abouzaid, to be an 
alternative definition of Khovanov cohomology. Also with 
Abouzaid, he showed that the famous homological mirror 
symmetry conjecture of Kontsevich is true for any product 
when it is true for the factors: this yielded new examples 
of manifolds for which the conjecture holds. With Seidel 
he proved a conjecture of Eliashberg and Gromov, showing 
that there are well-behaved exotic symplectic structures on 
Euclidean space. These are just a few of the achievements 
that caused Smith to stand out from a very strong field.”
The Adams Prize is awarded each year jointly by the 
Faculty of Mathematics at the University of Cambridge and 
St. John’s College to a young researcher or researchers 
based in the United Kingdom doing first-class interna-
tional research in the mathematical sciences. The prize is 
named after the mathematician John Couch Adams and 
was endowed by members of St. John’s College. It carries 
a cash prize of approximately £14,000 (about US$21,000), 
of which one-third is awarded to the prizewinner on 
announcement of the prize, one-third is provided to 
the prizewinner’s institution (for research expenses of 
the prizewinner), and one-third is awarded to the 
prizewinner on acceptance for publication in an interna-
tionally recognized journal of a substantial (normally at 
least twenty-five printed pages) original survey article of 
which the prizewinner is an author. 
—From a University of Cambridge announcement
Goldblatt Awarded Jones 
Medal
Robert Goldblatt of the Victoria University of Welling-
ton has been awarded the 2012 Jones Medal by the Royal 
Society of New Zealand. According to the prize citation, 
Goldblatt was honored “for his profound and world-
leading research in modal logic and category theory, and 
his lifetime of dedicated service to mathematics.” He “has 
become one of the world’s leading authorities in modal 
logic. In this system, statements can be much more than 
simply true or false: they can be, say, necessarily true, pos-
sibly true, or eventually true. This flexible logic is at the 
heart of basic software engineering and the commercial 
program and chip verification industry. Modal logic is 
interdisciplinary, overlapping mathematics, philosophy, 
linguistics, and computer science.” 
—From a Royal Society of New Zealand announcement
Bondarenko Awarded Popov 
Prize 2013
Andriy Bondarenko of Kiev University has been awarded 
the 2013 Vasil A. Popov Prize. According to the prize cita-
tion, he was honored “for his outstanding contributions 
to approximation theory. He along with Radchenko and 
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