The future of artificial intelligence: Utopia or dystopia?

MIT cosmologist Max Tegmark is no stranger to controversy. In his 2014 book Our Mathematical Universe, Tegmark proposed that our universe and everything in it are merely mathematical structures operating according to certain rules of logic. He argued that this hypothesis answers Stephen Hawking’s question “What breathes fire into the equations?” — there is no need for anything breathing fire into mathematical equations to create the universe, because the universe is a set of mathematical equations.

In his latest book, Life 3.0: Being Human in the Age of Artificial Intelligence, Tegmark surveys some of the recent advances of the AI

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Fine tuning and Fermi’s paradox

A “freakishly” fine-tuned universe

Ever since the time of Copernicus, the overriding worldview of scientific discovery has been that there is nothing special about Earth and humanity: the Earth is not the center of the solar system — we are merely one of several planets orbiting the Sun; the Sun is not the center of the Milky Way — it is merely one of over 100 billion stars in the galaxy; the Milky Way is not the center of the universe — it is merely one of over 100 billion galaxies in the universe; etc. Indeed, this “Copernican principle” has

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New Go-playing program teaches itself, beating previous program 100-0

A potentially momentous milestone has been reached in the decades-old battle between human intelligence and artificial intelligence.

Go playing board

Until 18 months ago ago, the ancient Chinese game of Go had firmly resisted attempts to apply computer technology — the best human players were substantially better than the best computer programs. This changed abruptly in March 2016, when a Google computer program named “AlphaGo” defeated the reigning world champion 4-1, a defeat that shocked many observers, who had not expected to see this for many years.

Now a new computer program, called “AlphaGo Zero,” which literally taught itself

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Fibonacci: A man of numbers

Keith Devlin, well-known mathematician and author, has published two books on Leonardo Pisano (Leonardo of Pisa), better known to many today as “Fibonacci,” short for “filius Bonacci” (son of the Bonacci family), a name ascribed to Leonardo by the 19th century French historian Guillaume Libri. Devlin argues that Leonardo deserves to be ranked among the all-time most influential scientists and mathematicians, mainly for his key role in popularizing the Hindu-Arabic decimal system to Western Europe during the early Renaissance.

Devlin’s books are:

The Man of Numbers: Fibonacci’s Arithmetic Revolution Finding Fibonacci: The Quest to Rediscover the Forgotten Mathematical Genius Who

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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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