Table Of ContentSpringer Proceedings in Mathematics & Statistics
David H. Bailey · Naomi Simone Borwein ·
Richard P. Brent · Regina S. Burachik ·
Judy-anne Heather Osborn · Brailey Sims ·
Qiji J. Zhu Editors
From Analysis
to Visualization
A Celebration of the Life and Legacy
of Jonathan M. Borwein, Callaghan,
Australia, September 2017
Springer Proceedings in Mathematics
& Statistics
Volume 313
Springer Proceedings in Mathematics & Statistics
This book series features volumes composed of selected contributions from
workshops and conferences in all areas of current research in mathematics and
statistics, including operation research and optimization. In addition to an overall
evaluation of the interest, scientific quality, and timeliness of each proposal at the
hands of the publisher, individual contributions are all refereed to the high quality
standards of leading journals in the field. Thus, this series provides the research
community with well-edited, authoritative reports on developments in the most
exciting areas of mathematical and statistical research today.
More information about this series at http://www.springer.com/series/10533
David H. Bailey Naomi Simone Borwein
(cid:129) (cid:129)
Richard P. Brent Regina S. Burachik
(cid:129) (cid:129)
Judy-anne Heather Osborn
(cid:129)
Brailey Sims Qiji J. Zhu
(cid:129)
Editors
From Analysis
to Visualization
A Celebration of the Life and Legacy
of Jonathan M. Borwein, Callaghan, Australia,
September 2017
123
Editors
DavidH.Bailey NaomiSimone Borwein
Lawrence BerkeleyNational Laboratory Western University
Berkeley, CA, USA London,ON, Canada
Richard P.Brent ReginaS. Burachik
Mathematical SciencesInstitute Schoolof ITandMathematical Sciences
Australian National University University of SouthAustralia
Canberra,ACT, Australia Mawson Lakes,SA,Australia
Judy-anneHeather Osborn Brailey Sims
Schoolof Mathematical andPhysical Schoolof Mathematical andPhysical
Sciences Sciences
University of Newcastle University of Newcastle
Callaghan, NSW,Australia Callaghan, NSW,Australia
Qiji J.Zhu
Department ofMathematics
Western Michigan University
Kalamazoo,MI, USA
ISSN 2194-1009 ISSN 2194-1017 (electronic)
SpringerProceedings in Mathematics& Statistics
ISBN978-3-030-36567-7 ISBN978-3-030-36568-4 (eBook)
https://doi.org/10.1007/978-3-030-36568-4
MathematicsSubjectClassification(2010): 00B20,11-06,26-06,33-06,47-06,49-06,52-06,62P05,
91G99,97-06
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Preface
Jonathan Borwein: Mathematician Extraordinaire
Many of us were shocked when our dear colleague Jonathan Michael Borwein
of the University of Newcastle, Australia, died in August 2016. Jonathan ranked
among the most wide ranging and influential mathematicians of the last
half-century. He made significant contributions to a diversity of areas, in the pro-
cess of which he exploited and greatly expanded the methods of experimental
mathematics. In the course of this, he wove a network of colleagues and collabo-
rators that spanned six continents and numbered well into the hundreds. After his
passing, one immediate priority was to gather together as many of his works as
possible. Accordingly, David H. Bailey and Nelson H. F. Beebe of the University
of Utah began collecting as many of Borwein’s published papers, books, reports
and talks as possible, together with book reviews and articles written by others
about Jonathan and his work. The current catalogue [1] lists nearly 2000 items.
Even if one focuses only on formal, published, peer-reviewed articles, there are
over 500 such items. These works are heavily cited—the Google citation tracker
finds over 22,000 citations.
Whatismoststrikingaboutthiscatalogueisthewiderangeoftopics.Onebane
of modern academic research, in general, and of the field of mathematics, in par-
ticular, is that most researchers today focus on a single specialized niche, seldom
attemptingtobranchoutintootherspecialtiesanddisciplinesortoforgepotentially
fruitfulcollaborationswithresearchersinotherfields.Incontrast,Borweinnotonly
learnedaboutnumerousdifferentspecialities,but,infact,didsignificantresearchin
a wide range offields, including experimental mathematics, optimization, convex
analysis, applied mathematics, computer science, scientific visualization, biomed-
icalimagingandmathematicalfinance.Itishardtothinkofasinglemathematician
of themodern era who has published notable research in so many different arenas.
ix
x Preface
A Portrait of the Man as a Mathematician
Jonathanwasapolymath,byitsverydefinition,andatruerenaissancescholar.His
knowledgebasewasasexpansiveasitwasdetailed.Letustakeamomenttopainta
fullerpictureofthismanandhisengagementwithmathematics,technologyandthe
worldaroundhim.BorninStAndrews,Scotlandon20May1951,Jonattendedthe
Madras College in Fife as a child, and went to university at 15, becoming at 23 a
ratheryoung Postdoctoral Fellow at DalhousieUniversity wherehe remained until
1991.
Alwayssteepedinthemathematicalworld,thankstohisfather,DavidBorwein,
Jon starteddoing AMS Math Monthlyproblems with his father from an early age.
TheonlytimeJondidn’thaveamathbookunderhisarm,apenleakinginkinhis
pocketdesperatetobeetchedacrossasheetofcrispwhitepaper—andlateraniPad
toworkon—wasthe3monthshetravelledalongtherouteofXenophon’sAnabasis
through Turkey and Greece in the summer of 1973.
Jon won a 1971 Rhodes Scholarship and settled into life at Oxford. His classes
allowed him to rub shoulders with the likes of Michael Atiyah, Professor of
Geometry, who actually attended a class on mathematical Linguistics with Jon.
Atiyahoftensatunheedingandwouldthenasktheprofessordumbbasicquestions
aboutthelecture.Atamuchlatertime,ataconference,Atiyahlaughedandsaidthat
Jon had certainly gotten more from the class than he did. Such interactions rein-
forcedthehumanityofthegreatprofessorsandinmanywaysbecameatemplatefor
his interactions with students, accepting ofdifferencesand ready toteach all.
Jon was a member of ‘Professors for Peace for the Middle East’, a Canadian
organizationwithverydedicatedpeoplewhowentontobeinfluentialinCanadian
society. In 1967, a group went to Israel to discuss the problems with both
Palestinians and Israelis, from the Mufti of Gaza to Teddy Kollek, the Mayor of
Jerusalem.TheyarrivedinMay,daysaftertheelectionthatheraldedthestartofthe
tenure of Menachem Begin. The authorities they had arranged to meet were so
rattledbytheresultoftheelectionthattheyactuallyreportedthetruthaboutmany
things ‘Middle East’, while filling boxes to depart their offices. In some cases, the
groupwasalsoabletoaccessthenewcomers.Thisorganizationstillexistsdespitea
name change and continues to press for a peaceful resolution.
In 1985, while on sabbatical, Jon went to Cambridge, England and then
Limoges, France. While in Cambridge Jon received a redirected Christmas card
from Yasumasa Kanada, a Professor in the Department of Information Science at
theUniversityofTokyo.Helookedatthereturnaddressandwasastonishedtosee
thatKanadawasinCambridgeaswell.Therewasameetingandthisledtofruitful
discussionsaboutcomputermodellingalgorithmsandp.Thisfriendshiplasteduntil
Kanada’sretirementin2015.Whenaskedwhyacomputerscientistwouldcometo
such a place as Cambridge, Kanada replied that he was looking to imbibe the
theoretical underpinnings and classical view of his work. This was something he
couldnotgetathome.NextinthesabbaticalwasastayinFrance.Jonandhiswife,
Judi, spent an idyllic time in a gîte rural on the grounds of a Chateau near Rilhac
Preface xi
Rancon. This was a perfect place to ruminate on the mysteries of math. The time
spent here led to a very prolific association with Michel Thera and the French
mathematics community, leading eventually to an honorary Doctorate at the
University of Limoges.
At this same time, Jon was reunited with Ephraim J. Borowski, an old friend
from Oxford, who joined Jon for a while at the gîte while working on a Collins
Dictionary. The two sat on the grass outside, or around the table in the
fifteenth-century stone cottage with file cards, filling in definitions. This delightful
interlude led to the Collins Dictionary of Mathematics. Later, Ephraim, burdened
down with file cards, came to work with Jon in Halifax, Nova Scotia. They set up
shop in Jon’s office, situated in the old Halifax Archives, and had a very strict
protocol: nothing was tobechanged on theLisa computer unlessit was first listed
and dated on the white boards. They never misplaced a letter because of this, but
even with five levels of certainty, they almost lost an entire section. Jon had a
lifelong interest in utilizing technology and pushing its limits in the pursuit of a
plethora of academic interests.
Therearenumerous BiographiesofJon,someofwhicharealsoobituaries(see,
for instance, [2] and others at [1]). However, these often glom to certain details
about his life, influence and output. Citing his own writing about ‘The Best
Teacher I Ever Had was …’, these include his childhood experience of teaching
anotherboyatwo-by-twosimultaneousequationattheageof6,andhowonarrival
atWesternUniversity,inhissecondyear,heverynearlydecidedtomajorinhistory
—which would have been a loss to the mathematical community. These biogra-
phies often unevenly focus on the breadth of his contributions, containing them
within the lens of the journal or researcher-author penning the biography. It is
pertinent tostatethathe wasso accomplishedandhad expertise insomany fields,
that the editors at Springer could not find an appropriate replacement for him as
Editor of the SUMAT Series. (Indeed, he was a founding Co-Editor in Chief of
Springer-Verlag’s SUMAT Series of Springer Undergraduate Mathematics and
Technology books.) Apparently, it normally would have required four editors to
cover the fields he knew so intimately.
Overview of this Proceedings
It is the intention of this volume to commemorate Jonathan’s remarkable
achievements and legacies that were explored at his Commemorative Conference
held on 25–29 September 2017, at Noah’s On The Beach, Newcastle, NSW—one
of Jonathan’s favourite spots. Associated events included the Sunday, 24th
September Satellite meeting on Mathematics and Education; the Tuesday, 26th
SeptemberPublicLecturegivenbyKeithDevlin,entitled‘FindingFibonacci—The
QuesttoRediscovertheForgottenMathematicalGeniusWhoChangedtheWorld’
