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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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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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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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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Exoplanets, 4 billion-year-old life, Fermi’s paradox and zero-one laws

What do exoplanets, four-billion-year-old life, Fermi’s paradox and zero-one laws of probability theory have to do with each other? Quite a bit, actually. Let us review these developments, one by one:

New exoplanet discoveries

Depiction of the seven exoplanets of the TRAPPIST-1 system. Courtesy NASA.

On 22 February 2017, a consortium of NASA and European astronomers announced that there are not just one but seven planets that potentially could harbor life, all orbiting a yellow dwarf star named TRAPPIST-1, about 40 light-years (235 trillion miles or 378 trillion km) from earth. This is clearly a remarkable discovery, adding seven to

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Asian tigers roar in the latest TIMSS math-science rankings

The latest international results comparing Grade 4 and Grade 8 students in mathematics and science are in, and, once again, the Asian tigers (China, Korea, Japan, and Singapore) are roaring, significantly leading major first-world nations such as the United States, England and Australia.

TIMSS results

The Trends in International Mathematics and Science Study (TIMSS) is an international test to compare the achievement of fourth and eighth grade students in mathematics and science. It has been administered every four years since 1995, thus providing a 20-year period for study of educational trends around the world.

In November 2016, results for the

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Are humans or computers better at mathematics?

Computer proofs

Considerable attention has been drawn to the discovery and proof of mathematical theorems by computer.

Perhaps the first major result by a computer came in 1976, with a proof of four-color theorem, namely the assertion that any map (with certain reasonable conditions) can be colored with just four distinct colors for individual states. This was first proved by computer in 1976, although flaws were later found, and a corrected proof was not completed until 1995.

In 2003, Thomas Hales of the University of Pittsburgh published a computer-based proof of Kepler’s conjecture, namely the assertion that the familiar method

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Why science needs the humanities


Foster in Contact, saying “They should have sent a poet”

Earlier this year, Kentucky governor Matt Bevin declared that state colleges and universities should educate more electrical engineers and fewer French literature majors: “All the people in the world that want to study French literature can do so, they are just not going to be subsidized by the taxpayer.”

Other politicians have sounded a similar refrain. Governor Patrick McCroy of North Carolina suggested basing funding on post-graduate employment rather than enrollment, or, as he put it rather crudely, “It’s not based on butts in seats but on how

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