Peter Benjamin Borwein (born St. Andrews,

Scotland Scotland is a Countries of the United Kingdom, country that is part of the United Kingdom. It contains nearly one-third of the United Kingdom's land area, consisting of the northern part of the island of Great Britain and more than 790 adjac ...

, May 10, 1953 – 23 August 2020) was a

Canadian Canadians () are people identified with the country of Canada. This connection may be residential, legal, historical or cultural. For most Canadians, many (or all) of these connections exist and are collectively the source of their being ''C ...

mathematician A mathematician is someone who uses an extensive knowledge of mathematics in their work, typically to solve mathematical problems. Mathematicians are concerned with numbers, data, quantity, mathematical structure, structure, space, Mathematica ...

and a professor at

Simon Fraser University Simon Fraser University (SFU) is a Public university, public research university in British Columbia, Canada. It maintains three campuses in Greater Vancouver, respectively located in Burnaby (main campus), Surrey, British Columbia, Surrey, and ...

. He is known as a co-author of the paper which presented the Bailey–Borwein–Plouffe algorithm (discovered by

Simon Plouffe Simon Plouffe (born June 11, 1956) is a Canadian mathematician who discovered the Bailey–Borwein–Plouffe formula (BBP algorithm) which permits the computation of the ''n''th binary number, binary digit of pi, π, in 1995. His other 2022 formul ...

) for computing π.

First interest in mathematics

Borwein was born into a Jewish family. He became interested in

number theory Number theory is a branch of pure mathematics devoted primarily to the study of the integers and arithmetic functions. Number theorists study prime numbers as well as the properties of mathematical objects constructed from integers (for example ...

and classical analysis during his second year of university. He had not previously been interested in math, although his father was the head of the

University of Western Ontario The University of Western Ontario (UWO; branded as Western University) is a Public university, public research university in London, Ontario, Canada. The main campus is located on of land, surrounded by residential neighbourhoods and the Thame ...

's mathematics department and his mother is associate dean of medicine there. Borwein and his two siblings majored in mathematics.

Academic career

After completing a Bachelor of Science in Honours Math at the University of Western Ontario in 1974, he went on to complete an MSc and

Ph.D. A Doctor of Philosophy (PhD, DPhil; or ) is a terminal degree that usually denotes the highest level of academic achievement in a given discipline and is awarded following a course of graduate study and original research. The name of the deg ...

at the

University of British Columbia The University of British Columbia (UBC) is a Public university, public research university with campuses near University of British Columbia Vancouver, Vancouver and University of British Columbia Okanagan, Kelowna, in British Columbia, Canada ...

. He joined the Department of Mathematics at

Dalhousie University Dalhousie University (commonly known as Dal) is a large public research university in Nova Scotia, Canada, with three campuses in Halifax, Nova Scotia, Halifax, a fourth in Bible Hill, Nova Scotia, Bible Hill, and a second medical school campus ...

. While he was there, he, his brother

Jonathan Borwein Jonathan Michael Borwein (20 May 1951 – 2 August 2016) was a Scottish mathematician who held an appointment as Laureate Professor of mathematics at the University of Newcastle, Australia. He was a close associate of David H. Bailey, and they ...

and David H. Bailey of

NASA The National Aeronautics and Space Administration (NASA ) is an independent agencies of the United States government, independent agency of the federal government of the United States, US federal government responsible for the United States ...

wrote the 1989 paper that outlined and popularized a proof for computing one billion digits of π. The authors won the 1993

Chauvenet Prize The Chauvenet Prize is an annual award given by the Mathematical Association of America in recognition of an outstanding expository article on a mathematical topic. It consists of a prize of $1,000 and a certificate. The Chauvenet Prize was the ...

and

Merten M. Hasse Prize The Merten M. Hasse Prize is awarded every two years by the Mathematical Association of America (MAA) to recognize an exceptional expository paper appearing in an MAA publication, at least one of whose authors is a younger mathematician, generally ...

for this paper. In 1993, he moved to Simon Fraser University, joining his brother Jonathan in establishing the Centre for Experimental and Constructive Mathematics (CECM) where he developed the

Inverse Symbolic Calculator __NOTOC__ The Inverse Symbolic Calculator is an online number checker established July 18, 1995 by Peter Benjamin Borwein, Jonathan Michael Borwein and Simon Plouffe of the Canadian Centre for Experimental and Constructive Mathematics (Burnaby, Ca ...

Research

In 1995, the Borweins collaborated with

Yasumasa Kanada was a Japanese computer scientist most known for his numerous world records over the past three decades for calculating digits of . He set the record 11 of the past 21 times. Career Kanada was a professor in the Department of Information S ...

of the

University of Tokyo The University of Tokyo (, abbreviated as in Japanese and UTokyo in English) is a public research university in Bunkyō, Tokyo, Japan. Founded in 1877 as the nation's first modern university by the merger of several pre-westernisation era ins ...

to compute π to more than four billion digits. Borwein has developed an algorithm that applies

Chebyshev polynomial The Chebyshev polynomials are two sequences of orthogonal polynomials related to the trigonometric functions, cosine and sine functions, notated as T_n(x) and U_n(x). They can be defined in several equivalent ways, one of which starts with tr ...

s to the

Dirichlet eta function In mathematics, in the area of analytic number theory, the Dirichlet eta function is defined by the following Dirichlet series, which converges for any complex number having real part > 0: \eta(s) = \sum_^ = \frac - \frac + \frac - \frac + \cdo ...

to produce a very rapidly convergent series suitable for high precision numerical calculations, which he published on the occasion of the awarding of an honorary doctorate to his brother, Jonathan. Peter Borwein also collaborated with

's David Bailey and the

Université du Québec The Université du Québec () is a system of ten provincially-run public universities in Quebec, Canada. Its headquarters are in Quebec City. The university coordinates 1400 programs for over 100,000 students. The government of Quebec founded ...

to calculate the individual

hexadecimal Hexadecimal (also known as base-16 or simply hex) is a Numeral system#Positional systems in detail, positional numeral system that represents numbers using a radix (base) of sixteen. Unlike the decimal system representing numbers using ten symbo ...

digits of π. This provided a way for mathematicians to determine the ''n''th digit of π without calculating preceding digits. In 2007 with Tamás Erdélyi, Ronald Ferguson, and Richard Lockhart he settled Littlewood's Problem 22.

Affiliations

A former professor at

, Peter Borwein was affiliated with Interdisciplinary Research in the Mathematical and Computational Sciences (IRMACS), Centre for Experimental and Constructive Mathematics (CECM), Mathematics of Information Technology and Complex Systems (MITACS), and Pacific Institute for the Mathematical Sciences (PIMS).

Personal life and death

Borwein was diagnosed with

multiple sclerosis Multiple sclerosis (MS) is an autoimmune disease resulting in damage to myelinthe insulating covers of nerve cellsin the brain and spinal cord. As a demyelinating disease, MS disrupts the nervous system's ability to Action potential, transmit ...

prior to 2000. He died on 23 August 2020 of

pneumonia Pneumonia is an Inflammation, inflammatory condition of the lung primarily affecting the small air sacs known as Pulmonary alveolus, alveoli. Symptoms typically include some combination of Cough#Classification, productive or dry cough, ches ...

as a result of his MS.

Publications

As a co-author, Borwein has written ''Pi: A Source Book'' (with Lennart Berggren and Jonathan Borwein, 2000), ''Polynomials and Polynomial Inequalities'' (with Tamas Erdelyi, 1998), ''Pi and the AGM'' (1987; reprinted in 1998), ''A Dictionary of Real Numbers'' (with Jonathan Borwein), ''Computational Excursions in Analysis and Number Theory'' (2002), ''The Riemann Hypothesis: A Resource for the Afficionado and Virtuoso Alike'' (with Stephen Choi, Brendan Rooney, and Andrea Weirathmueller, 2007). He and his brother, Jonathan, co-edited the

Canadian Mathematical Society The Canadian Mathematical Society (CMS; French: ''Société mathématique du Canada'') is an association of professional mathematicians dedicated to advancing mathematical research, outreach, scholarship and education in Canada. The Society se ...

Springer-Verlag Springer Science+Business Media, commonly known as Springer, is a German multinational publishing company of books, e-books and peer-reviewed journals in science, humanities, technical and medical (STM) publishing. Originally founded in 1842 in ...

series of ''Books in Mathematics''. In 2002 Peter Borwein, with Loki Jorgenson, won a

Lester R. Ford Award ''The American Mathematical Monthly'' is a peer-reviewed scientific journal of mathematics. It was established by Benjamin Finkel in 1894 and is published by Taylor & Francis on behalf of the Mathematical Association of America. It is an expositor ...

for their expository article ''Visible Structures in Number Theory''.

References

External links

Science.ca profile

Peter Borwein's research interests

Simon Fraser University Centre for Systems Science bio
*

Borwein's website
*
Tamas Erdelyi's website
{{DEFAULTSORT:Borwein, Peter 1953 births 2020 deaths Canadian mathematicians Jewish Canadian scientists Canadian people of Lithuanian-Jewish descent Academic staff of Dalhousie University Pi-related people University of British Columbia Faculty of Science alumni University of Western Ontario alumni Academic staff of Simon Fraser University Deaths from multiple sclerosis People with multiple sclerosis Deaths from pneumonia in Canada Neurological disease deaths in Canada