Peter Borwein
Encyclopedia
Peter Benjamin Borwein is a Canadian
mathematician
and a professor at Simon Fraser University
. He is known as a co-discoverer of the Bailey-Borwein-Plouffe algorithm
for computing π.
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
's mathematics department
and his mother is associate dean of medicine there. Borwein and his two siblings majored in mathematics.
and Ph.D.
at the University of British Columbia
. He joined the Department of Mathematics at Dalhousie University
. While he was there, he, his brother Jonathan Borwein
and David H. Bailey
of NASA
wrote the 1989 paper that showed a proof for computing one billion digits of π. They won the 1993 Chauvent prize and Hasse prize.
In 1993, he moved to Simon Fraser University, joining his brother Jonathan in
establishing the Centre for Experimental and Constructive Mathematics (CECM).
of the University of Tokyo
to compute π
to more than four billion digits.
Peter Borwein also collaborated with NASA
's David Bailey and the University of Quebec's Simon Plouffe
to calculate the individual hexadecimal
digits of π. This provided a way for mathematicians to determine the nth digit of π without calculating preceding digits. In 2007 with Tamas Erdelyi
, Ferguson, and Lockhart he settled Littlewood's Problem 22.
Polynomials and Polynomial Inequalities (with Tamas Erdelyi
, 1998), Pi and the AGM (1987; reprinted in 1998) and A Dictionary of Real Numbers. He and his brother, Jonathan, co-edit the Canadian Mathematical Society
/Springer-Verlag
series of Books in Mathematics.
, Peter Borwein is 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).
Canada
Canada is a North American country consisting of ten provinces and three territories. Located in the northern part of the continent, it extends from the Atlantic Ocean in the east to the Pacific Ocean in the west, and northward into the Arctic Ocean...
mathematician
Mathematician
A mathematician is a person whose primary area of study is the field of mathematics. Mathematicians are concerned with quantity, structure, space, and change....
and a professor at Simon Fraser University
Simon Fraser University
Simon Fraser University is a Canadian public research university in British Columbia with its main campus on Burnaby Mountain in Burnaby, and satellite campuses in Vancouver and Surrey. The main campus in Burnaby, located from downtown Vancouver, was established in 1965 and has more than 34,000...
. He is known as a co-discoverer of the Bailey-Borwein-Plouffe algorithm
Bailey–Borwein–Plouffe formula
The Bailey–Borwein–Plouffe formula provides a spigot algorithm for the computation of the nth binary digit of π. This summation formula was discovered in 1995 by Simon Plouffe. The formula is named after the authors of the paper in which the formula was published, David H. Bailey, Peter Borwein,...
for computing π.
First interest in mathematics
Borwein became interested in number theoryNumber theory
Number theory is a branch of pure mathematics devoted primarily to the study of the integers. Number theorists study prime numbers as well...
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
University of Western Ontario
The University of Western Ontario is a public research university located in London, Ontario, Canada. The university's main campus covers of land, with the Thames River cutting through the eastern portion of the main campus. Western administers its programs through 12 different faculties and...
'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 MScMaster's degree
A master's is an academic degree granted to individuals who have undergone study demonstrating a mastery or high-order overview of a specific field of study or area of professional practice...
and Ph.D.
Doctor of Philosophy
Doctor of Philosophy, abbreviated as Ph.D., PhD, D.Phil., or DPhil , in English-speaking countries, is a postgraduate academic degree awarded by universities...
at the University of British Columbia
University of British Columbia
The University of British Columbia is a public research university. UBC’s two main campuses are situated in Vancouver and in Kelowna in the Okanagan Valley...
. He joined the Department of Mathematics at Dalhousie University
Dalhousie University
Dalhousie University is a public research university located in Halifax, Nova Scotia, Canada. The university comprises eleven faculties including Schulich School of Law and Dalhousie University Faculty of Medicine. It also includes the faculties of architecture, planning and engineering located at...
. While he was there, he, his brother Jonathan Borwein
Jonathan Borwein
Jonathan Michael Borwein is a Scottish mathematician who holds an appointment as Laureate Professor of mathematics at the University of Newcastle, Australia. Noted for his prolific and creative work throughout the international mathematical community, he is a close associate of David H...
and David H. Bailey
David H. Bailey
David Harold Bailey is a mathematician and computer scientist. He received his B.S. in mathematics from Brigham Young University in 1972 and his Ph.D. in mathematics from Stanford University in 1976...
of NASA
NASA
The National Aeronautics and Space Administration is the agency of the United States government that is responsible for the nation's civilian space program and for aeronautics and aerospace research...
wrote the 1989 paper that showed a proof for computing one billion digits of π. They won the 1993 Chauvent prize and Hasse prize.
In 1993, he moved to Simon Fraser University, joining his brother Jonathan in
establishing the Centre for Experimental and Constructive Mathematics (CECM).
Research
In 1995, the Borweins collaborated with Yasumasa KanadaYasumasa Kanada
is a Japanese mathematician most known for his numerous world records over the past three decades for calculating digits of π. He has set the record 11 of the past 21 times....
of the University of Tokyo
University of Tokyo
, abbreviated as , is a major research university located in Tokyo, Japan. The University has 10 faculties with a total of around 30,000 students, 2,100 of whom are foreign. Its five campuses are in Hongō, Komaba, Kashiwa, Shirokane and Nakano. It is considered to be the most prestigious university...
to compute π
Pi
' is a mathematical constant that is the ratio of any circle's circumference to its diameter. is approximately equal to 3.14. Many formulae in mathematics, science, and engineering involve , which makes it one of the most important mathematical constants...
to more than four billion digits.
Peter Borwein also collaborated with NASA
NASA
The National Aeronautics and Space Administration is the agency of the United States government that is responsible for the nation's civilian space program and for aeronautics and aerospace research...
's David Bailey and the University of Quebec's Simon Plouffe
Simon Plouffe
Simon Plouffe is a Quebec mathematician born on June 11, 1956 in Saint-Jovite, Quebec. He discovered the formula for the BBP algorithm which permits the computation of the nth binary digit of π, in 1995...
to calculate the individual hexadecimal
Hexadecimal
In mathematics and computer science, hexadecimal is a positional numeral system with a radix, or base, of 16. It uses sixteen distinct symbols, most often the symbols 0–9 to represent values zero to nine, and A, B, C, D, E, F to represent values ten to fifteen...
digits of π. This provided a way for mathematicians to determine the nth digit of π without calculating preceding digits. In 2007 with Tamas Erdelyi
Tamas Erdelyi (mathematician)
Tamás Erdélyi is a Hungarian born mathematician, currentlyworking at Texas A&M University. His main areas of research are related to polynomials and their approximations, although he also works in other areas of applied mathematics....
, Ferguson, and Lockhart he settled Littlewood's Problem 22.
Publications
As a co-author, Borwein has written Pi: A Source Book (1999),Polynomials and Polynomial Inequalities (with Tamas Erdelyi
Tamas Erdelyi (mathematician)
Tamás Erdélyi is a Hungarian born mathematician, currentlyworking at Texas A&M University. His main areas of research are related to polynomials and their approximations, although he also works in other areas of applied mathematics....
, 1998), Pi and the AGM (1987; reprinted in 1998) and A Dictionary of Real Numbers. He and his brother, Jonathan, co-edit the Canadian Mathematical Society
Canadian Mathematical Society
The Canadian Mathematical Society is an association of professional mathematicians dedicated to the interests of mathematical research and education in Canada.It was originally conceived in June 1945 as the Canadian Mathematical Congress...
/Springer-Verlag
Springer Science+Business Media
- Selected publications :* Encyclopaedia of Mathematics* Ergebnisse der Mathematik und ihrer Grenzgebiete * Graduate Texts in Mathematics * Grothendieck's Séminaire de géométrie algébrique...
series of Books in Mathematics.
Affiliations
A professor at Simon Fraser UniversitySimon Fraser University
Simon Fraser University is a Canadian public research university in British Columbia with its main campus on Burnaby Mountain in Burnaby, and satellite campuses in Vancouver and Surrey. The main campus in Burnaby, located from downtown Vancouver, was established in 1965 and has more than 34,000...
, Peter Borwein is 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).
See also
- Bailey–Borwein–Plouffe formulaBailey–Borwein–Plouffe formulaThe Bailey–Borwein–Plouffe formula provides a spigot algorithm for the computation of the nth binary digit of π. This summation formula was discovered in 1995 by Simon Plouffe. The formula is named after the authors of the paper in which the formula was published, David H. Bailey, Peter Borwein,...
- David BorweinDavid BorweinDavid Borwein is a Canadian mathematician of Ashkenazi Jewish ancestry, known for his research in the summability theory of series and integrals. He has also done work in measure theory and probability theory, number theory, and approximate subgradients and coderivatives. He has recently...
(father and mathematician) - Jonathan BorweinJonathan BorweinJonathan Michael Borwein is a Scottish mathematician who holds an appointment as Laureate Professor of mathematics at the University of Newcastle, Australia. Noted for his prolific and creative work throughout the international mathematical community, he is a close associate of David H...
(brother and mathematician)