biology

Peter Borwein

Peter Borwein is a biology topic covered in the lgStudy science library. This page brings together a partial reference excerpt, illustrations, worked examples, real-world applications and a short study plan, so you can understand Peter Borwein rather than just read about it. In short: Peter Benjamin Borwein (born St. Andrews, Scotland, May 10, 1953 – 23 August 2020) was a Canadian mathematician and a professor at Simon Fraser University.

Key takeaways

Peter Borwein belongs to biology; place it in that map before memorising details.
Learn the definition first, then one example that makes the definition concrete.
Connect Peter Borwein to a quantity you can measure, compute or draw — that is where exam questions come from.
Reproduce the core statement of Peter Borwein from memory before moving on to harder problems.

Reference excerpt

Peter Benjamin Borwein (born St. Andrews, Scotland, May 10, 1953 – 23 August 2020) was a Canadian mathematician and a professor at Simon Fraser University. He is known as a co-author of the paper which presented the Bailey–Borwein–Plouffe algorithm (discovered by Simon Plouffe) for computing π.

First interest in mathematics Borwein was born into a Jewish family. He became interested in number theory 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.

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. 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 outlined and popularized a proof for computing one billion digits of π. The authors won the 1993 Chauvenet Prize and Merten M. Hasse Prize 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.

Research In 1995, the Borweins collaborated with Yasumasa Kanada of the University of Tokyo to compute π to more than four billion digits. Borwein has developed an algorithm that applies Chebyshev polynomials to the Dirichlet eta function 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 NASA's David Bailey and the Université du Québec'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 Tamás Erdélyi, Ronald Ferguson, and Richard Lockhart he settled Littlewood's Problem 22.

Affiliations A former professor at Simon Fraser University, 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 prior to 2000. He died on 23 August 2020 of pneumonia 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/Springer-Verlag series of Books in Mathematics. In 2002 Peter Borwein, with Loki Jorgenson, won a Lester R. Ford Award for their expository article Visible Structures in Number Theory.

See also Bailey–Borwein–Plouffe formula Erdős–Borwein constant David Borwein (father and mathematician) Jonathan Borwein (brother and mathematician)

References

External links Science.ca profile Peter Borwein's research interests Simon Fraser University Centre for Systems Science bio Bailey, David H. (April 2023). "Peter Borwein: A Visionary Mathematician" (PDF). Notices of the American Mathematical Society. 70 (4): 610–613. doi:10.1090/noti2675. SFU news release on Borwein siblings Borwein's website Peter Borwein at the Mathematics Genealogy Project Tamas Erdelyi's website

Worked examples

Example 1 — a first encounter with Peter Borwein

Start with the simplest possible case. Write down what Peter Borwein claims or describes in one sentence, then invent the smallest concrete situation in which that sentence is true. In biology, the smallest case is usually a single object, a single equation or a single measurement. Check that every symbol or term in your sentence has a meaning in that case.

Example 2 — changing one variable

Take the situation from Example 1 and change exactly one quantity: double it, halve it, or set it to zero. Predict what should happen to Peter Borwein before you calculate. Comparing your prediction with the result is the fastest way to find out whether you understand the idea or only the words.

Example 3 — an exam-style question

Typical questions about Peter Borwein ask you to (a) state it precisely, (b) apply it to given data, and (c) explain a limitation. Practise writing all three answers in under five minutes; the third part is what separates a full-mark answer from an average one.

Applications of Peter Borwein

In research: Peter Borwein appears in biology research whenever the underlying quantities have to be modelled precisely. Papers usually cite it as a starting assumption and then explore where it breaks down.
In technology and industry: Engineering practice reuses Peter Borwein in design rules, simulations and safety margins. Knowing the idea lets you read a specification sheet and understand why the numbers look the way they do.
In the classroom: Peter Borwein is common in secondary-school and first-year university syllabi. It links to neighbouring topics 1953 births, 2020 deaths, Academic staff of Dalhousie University, so understanding it makes those chapters shorter.
In everyday life: Look for Peter Borwein outside the textbook — in sport, cooking, traffic, electronics or the sky above you. An example you found yourself is remembered far longer than one you were given.

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How to study Peter Borwein in 20 minutes

Read the reference excerpt below once, without taking notes.
Close the page and write down what Peter Borwein means in your own words.
Compare your version with the excerpt and mark what you missed.
Work through the three examples above with pen and paper.
Explain Peter Borwein out loud to somebody else — or to Teacher Smith in the lgStudy chat.

Frequently asked questions

What is Peter Borwein in simple terms?

Peter Benjamin Borwein (born St. Andrews, Scotland, May 10, 1953 – 23 August 2020) was a Canadian mathematician and a professor at Simon Fraser University.

Why does Peter Borwein matter?

Because it connects several biology ideas at once: it gives you a definition you can apply, a quantity you can calculate, and a way to check whether a result is plausible.

How should I study Peter Borwein?

Read the excerpt, restate it from memory, then work through the examples and applications listed on this page. The five-step study plan above takes about twenty minutes.

What does this page cover?

It gives you a compact reference excerpt plus original lgStudy explanations, examples, applications and study material on Peter Borwein.