
Introduction
Both traditional creationists and intelligent design writers have invoked probability arguments in criticisms of biological evolution. They argue that certain features of biology are so fantastically improbable that they could never have been produced by a purely natural, “random” process, even assuming the billions of years of history asserted by geologists and astronomers. They often equate the hypothesis of evolution to the absurd suggestion that monkeys randomly typing at a typewriter could compose a selection from the works of Shakepeare, or that an explosion in an aerospace equipment yard could produce a working 747 airliner [Dembski1998; Foster1991; Hoyle1981;
Continue reading Do probability arguments refute evolution?
Courtesy Ahmed Medhat Othman
Evolutionary computing
Evolution has been studied mathematically since the early 1900s, with works by D’Arcy Thompson, Ronald Fisher and others. Among other things, these analyses quantified estimates of how many generations of a given species would be required to achieve a certain level of observed change. With the rise of computer technology in the 1960s, computational simulations were devised to study evolution.
From here is was a relatively straightforward step to apply these same evolutionmimicking simulations to other applications as well, an approach originally termed genetic algorithms. In a typical application, potential engineering design parameters
Continue reading Evolutionary computing and artificial intelligence
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
Continue reading The future of artificial intelligence: Utopia or dystopia?
A “freakishly” finetuned 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
Continue reading Fine tuning and Fermi’s paradox
A potentially momentous milestone has been reached in the decadesold 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 41, 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
Continue reading New Goplaying program teaches itself, beating previous program 1000
Keith Devlin, wellknown 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 alltime most influential scientists and mathematicians, mainly for his key role in popularizing the HinduArabic 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
Continue reading Fibonacci: A man of numbers
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,
Continue reading Talks on experimental mathematics
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 fullfledged positional decimal arithmetic with zero system that we
Continue reading Origin of decimal arithmetic with zero pushed back to 3rd century CE
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
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):
Collegelevel algebra is probably the greatest barrier for students — particularly firstgeneration 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
Continue reading Does mathematical training pay off in the long run?

