Talks on experimental mathematics

On 3 October 2017 I presented six talks at a seminar on experimental mathematics at the University of Newcastle, in Newcastle, NSW Australia.

Here are the titles and abstracts of these talks, plus URLs for the complete PDF viewgraph files:

1. What is experimental mathematics? (15 minutes)

This overview briefly summarizes what is meant by “experimental mathematics”, as pioneered in large part by the late Jonathan Borwein. We also explain why experimental mathematics offers a unique opportunity to involve a much broader community in the process of mathematical discovery and proof — high school students, undergraduate students, computer scientists,

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Origin of decimal arithmetic with zero pushed back to 3rd century CE

The Bakhshali manuscript

The Bakhshali manuscript is an ancient mathematical treatise that was found in 1881 in the village of Bakhshali, approximately 80 kilometers northeast of Peshawar (then in India, now in Pakistan). Among the topics covered in this document, at least in the fragments that have been recovered, are solutions of systems of linear equations, indeterminate (Diophantine) equations of the second degree, arithmetic progressions of various types, and rational approximations of square roots (more on this below).

The manuscript features an extensive usage of decimal arithmetic — the same full-fledged positional decimal arithmetic with zero system that we

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Bailey to speak Friday March 15 at Worcester Polytechnic Institute

If any of you are in the Boston area, Bailey will be giving the Levi Conant Prize lecture this Friday (Sep 15) at Worcester Polytechnic Institute. The title of the talk is “Computation and analysis of arbitrary digits of Pi and other mathematical constants”. It summarizes some of the recent discoveries about Pi, including formulas that permit one to calculate digits of Pi (or Pi^2 or numerous other constants), beginning at an arbitrary starting point, without needing to compute any of the previous digits.

Here are the details of the talk, including the Abstract:

Conant Prize lecture

Does mathematical training pay off in the long run?

The California Community College mathematics controversy

Eloy Ortiz Oakley, the Chancellor of the California Community College system, recently recommended that intermediate algebra should no longer be required to earn an associate degree, excerpt for students majoring in some field of mathematics, science or engineering (see also this Physics Today report):

College-level algebra is probably the greatest barrier for students — particularly first-generation students, students of color — obtaining a credential. … [I]f we know we’re disadvantaging large swaths of students who we need in the workforce, we have to question why. And is algebra really the only means we have

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Pi and the collapse of peer review

The 1897 Indiana pi episode

Many of us have heard of the Indiana pi episode, where a bill submitted to the Indiana legislature, written by one Edward J. Goodwin, claimed to have squared the circle, yielding a value of pi = 3.2. Although the bill passed the Indiana House, it narrowly failed in the Senate and never became law, due largely to the intervention of Prof. C.A. Waldo of Purdue University, who happened to be at the Indiana legislature on other business. The story is always good for a laugh to lighten up a dull mathematics lecture.

It is worth

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French mathematician completes proof of tessellation conjecture

We have all seen interesting patterns of tiling the plane with interlocking shapes, known as a tessellation. The process of producing a complete inventory of all possible tessellation has resisted solution for over a century, until now.

The honor goes to Michael Rao of the Ecole Normale Superieure de Lyon in France. He has completed a computer-assisted proof to complete the inventory of pentagonal shapes, the last remaining holdout. He identified 371 scenarios for how corners of pentagons might fit together, and then checked, by means of an algorithm, each scenario. In the end, his computer program determined that the

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Are Hollywood stars qualified to comment on science?

Hollywood stars as public spokespersons

Nowadays it is not at all unusual for Hollywood stars to lend their public celebrity status to endorse or promote some cause. For example, Angelina Jolie has lent her name and support to international efforts dealing with the refugee crisis. Sean Penn personally assisted efforts to deal with the Haiti earthquake crisis.

What’s more, some Hollywood stars and celebrities have bona fide scientific credentials and achievements. Perhaps the most notable example is Hedy Lamarr, an Austrian-American actress who starred in movies such as the 1938 film Algiers, directed by John Cromwell, and the 1949 film

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Carlos Rovelli’s “Reality Is Not What It Seems”

C.P. Snow’s “Two Cultures”

Back in 1959, the influential British scholar C. P. Snow gave a lecture entitled The two cultures and the scientific revolution. In this discourse Snow warned of a widening divide between the scientific world on one hand and the humanities on the other: “This polarization is a sheer loss to us all.” Snow wrote,

A good many times I have been present at gatherings of people who, by the standards of the traditional culture, are thought highly educated and who have with considerable gusto been expressing their incredulity at the illiteracy of scientists. Once or twice

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Jonathan Borwein Commemorative Conference

We are pleased to announce the Jonathan M. Borwein Commemorative Conference, which will be held 25-29 September 2017 in Newcastle, Australia.

The conference will focus on the five areas of Jonathan’s Borwein’s research:

Applied analysis, optimisation and convex functions. Chairs: Regina Burachik and Guolin Li. Education. Chairs: Judy-anne Osborn and Namoi Borwein. Experimental mathematics and visualization. Chair: David H. Bailey. Financial mathematics. Chair: Qiji (Jim) Zhu. Number theory, special functions and pi. Chair: Richard Brent.

A total of 36 speakers will give presentations.

The meeting will be held at Noah’s on the Beach in Newcastle, New South Wales, Australia, which

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Is the universe fine-tuned for intelligent life?


Is the universe fine-tuned for intelligent life? Astrophysicist Geraint Lewis and cosmologist Luke Barnes, both at the University of Sydney, Australia, wade into this perplexing and controversial arena in a new book, published by Cambridge University Press, entitled A Fortunate Universe: Life in a Finely Tuned Cosmos.

The book presents a comprehensive analysis of the issue, delving into nuclear physics, astrophysics, cosmology, biology and philosophy. It is entertainingly written, yet does not compromise in detail. The authors mercifully relegate some of the more technical material to footnotes, but even the footnotes are remarkably useful and well documented. The book

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