Peter Benjamin Borwein (born St. Andrews,

Scotland Scotland (, ) is a country that is part of the United Kingdom. Covering the northern third of the island of Great Britain, mainland Scotland has a border with England to the southeast and is otherwise surrounded by the Atlantic Ocean to the ...

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

Canadian Canadians (french: Canadiens) 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 ...

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, structure, space, models, and change. History On ...

and a professor at

Simon Fraser University Simon Fraser University (SFU) is a public research university in British Columbia, Canada, with three campuses, all in Greater Vancouver: Burnaby (main campus), Surrey, and Vancouver. The main Burnaby campus on Burnaby Mountain, located from ...

. 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 mathematician who discovered the Bailey–Borwein–Plouffe formula (BBP algorithm) which permits the computation of the ''n''th binary digit of π, in 1995. His other 2022 formula allows extracting the '' ...

) for computing π.

First interest in mathematics

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

number theory Number theory (or arithmetic or higher arithmetic in older usage) is a branch of pure mathematics devoted primarily to the study of the integers and arithmetic function, integer-valued functions. German mathematician Carl Friedrich Gauss (1777� ...

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), also known as Western University or Western, is a Public university, public research university in London, Ontario, London, Ontario, Canada. The main campus is located on of land, surrounded by resident ...

'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, Ph.D., or DPhil; Latin: or ') is the most common degree at the highest academic level awarded following a course of study. PhDs are awarded for programs across the whole breadth of academic fields. Because it is ...

at the

University of British Columbia The University of British Columbia (UBC) is a public university, public research university with campuses near Vancouver and in Kelowna, British Columbia. Established in 1908, it is British Columbia's oldest university. The university ranks a ...

. He joined the Department of Mathematics at

Dalhousie University Dalhousie University (commonly known as Dal) is a large public research university in Nova Scotia Nova Scotia ( ; ; ) is one of the thirteen provinces and territories of Canada. It is one of the three Maritime provinces and one of the fou ...

. 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 agency of the US federal government responsible for the civil space program, aeronautics research, and space research. NASA was established in 1958, succeeding t ...

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 the highest award for mathematical expository writing. It consists of a prize of $1,000 and a certificate, and is awarded yearly by the Mathematical Association of America in recognition of an outstanding expository article ...

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 Center or centre may refer to: Mathematics *Center (geometry), the middle of an object * Center (algebra), used in various contexts ** Center (group theory) ** Center (ring theory) * Graph center, the set of all vertices of minimum eccentricity ...

(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, ...

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. Kanada was a professor in the Department of Information Science at ...

of the

University of Tokyo , abbreviated as or UTokyo, is a public research university located in Bunkyō, Tokyo, Japan. Established in 1877, the university was the first Imperial University and is currently a Top Type university of the Top Global University Project by ...

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 polynomials related to the 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 trigonometric functions: The Chebyshe ...

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 University of Quebec (French: ''Université du Québec'') is a system of ten provincially run public universities in Quebec, Canada. Its headquarters are in Quebec City. The university coordinates 300 programs for over 87,000 students. The ...

to calculate the individual

hexadecimal In mathematics and computing, the hexadecimal (also base-16 or simply hex) numeral system is a positional numeral system that represents numbers using a radix (base) of 16. Unlike the decimal system representing numbers using 10 symbols, hexa ...

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 Interdisciplinarity or interdisciplinary studies involves the combination of multiple academic disciplines into one activity (e.g., a research project). It draws knowledge from several other fields like sociology, anthropology, psychology, ec ...

(IRMACS), Centre for Experimental and Constructive Mathematics (CECM), Mathematics of Information Technology and Complex Systems (MITACS), and

Pacific Institute for the Mathematical Sciences The Pacific Institute for the Mathematical Sciences (PIMS) is a mathematical institute created in 1996 by universities in Western Canada and the Northwestern United States to promote research and excellence in all areas of the mathematical science ...

(PIMS).

Personal life

Borwein was diagnosed with

multiple sclerosis Multiple (cerebral) sclerosis (MS), also known as encephalomyelitis disseminata or disseminated sclerosis, is the most common demyelinating disease, in which the insulating covers of nerve cells in the brain and spinal cord are damaged. This d ...

prior to 2000. He died on 23 August 2020 of

pneumonia Pneumonia is an inflammatory condition of the lung primarily affecting the small air sacs known as alveoli. Symptoms typically include some combination of productive or dry cough, chest pain, fever, and difficulty breathing. The severity ...

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 the interests of mathematical research, outreach, scholarship and education in Canada. It serves the ...

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 Lester is an ancient Anglo-Saxon surname and given name. Notable people and characters with the name include: People Given name * Lester Bangs (1948–1982), American music critic * Lester W. Bentley (1908–1972), American artist from Wisc ...

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 scientists Canadian people of Lithuanian-Jewish descent Dalhousie University faculty Pi-related people University of British Columbia Faculty of Science alumni University of Western Ontario alumni Simon Fraser University faculty Deaths from multiple sclerosis Deaths from pneumonia in Canada Neurological disease deaths in Canada