Amateur mathematician makes key advance in classic graph theory problem

Introduction

In a curious turn of events, British biogerontologist Aubrey de Grey, a well-known author and Chief Science Officer of the SENS Research Foundation, which is devoted to “reversing the negative effects of aging” and “significantly extending the human lifespan,” has made a significant advance in a 60-year-old graph theory problem.

Needless to say, in this day and age when almost all frontier-level mathematical research requires substantial training and, regrettably, specialization, it is not very often that an person without graduate-level formal training in mathematics, and whose professional life is focused almost entirely in a completely different field, makes a

Continue reading Amateur mathematician makes key advance in classic graph theory problem

Noted mathematician and two computer scientists win prestigious awards

Introduction

The Norwegian Academy of Science and Letters has announced it coveted 2018 Abel Prize, which is named after 19th century mathematician Niels Henrik Abel. This year’s award is Robert P. Langlands of the Institute for Advanced Study, Princeton, USA, for his “visionary program connecting representation theory to number theory.”

Separately, the Association for Computing Machinery announced today that its Turing Award will be given to John L. Hennessy (until recently the President of Stanford University) and David A. Patterson (University of California, Berkeley) for their work in designing “a systematic and quantitative approach to designing faster, lower power, and

Continue reading Noted mathematician and two computer scientists win prestigious awards

Has cosmic fine-tuning been refuted?

Introduction

Is the universe fine-tuned for intelligent life? In 2016, astrophysicist Geraint Lewis and cosmologist Luke Barnes, both at the University of Sydney, Australia, waded into this perplexing and controversial arena in a new book entitled A Fortunate Universe: Life in a Finely Tuned Cosmos [Lewis2016]. The core of the Lewis-Barnes book and an accompanying technical paper by Luke Barnes [Barnes2012] is their review of the “cosmic coincidences”:

Carbon resonance and the strong force. If the strong force were slightly stronger or slightly weaker (by just 1% in either direction), there would be no carbon or any heavier elements anywhere

Continue reading Has cosmic fine-tuning been refuted?

Pinker’s “Enlightenment Now”: Humanism and scientific progress

Introduction

Many have read books and articles by renowned Harvard social scientist Steven Pinker. In his 2011 book The Better Angels of Our Nature: Why Violence Has Declined, Pinker cited a huge amount of historical and sociological data to conclude, counter-intuitively to many, that violence has declined “at the scale of millennia, centuries, decades, and years”, “over several orders of magnitude of violence, from genocide to war to rioting to homicide to the treatment of children and animals.”

Pinker pointed out, for example, that while WWI and WWII had the most wartime fatalities in history, when normalized by world

Continue reading Pinker’s “Enlightenment Now”: Humanism and scientific progress

Do probability arguments refute evolution?

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?

Evolutionary computing and artificial intelligence

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 evolution-mimicking 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

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

Continue reading The future of artificial intelligence: Utopia or dystopia?

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

Continue reading Fine tuning and Fermi’s paradox

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

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

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

Continue reading Fibonacci: A man of numbers