Computer theorem prover verifies sophisticated new result

Courtesy Maria Nguyen, Quanta Magazine

Computer discovery of mathematical theorems

In 1983 the present author recalls discussing the future of mathematics with Paul Cohen, who in 1963 proved that the continuum hypothesis is independent from the axioms of Zermelo-Fraenkel set theory. Cohen was convinced that the future of mathematics, and much more, lies in artificial intelligence. Reuben Hersch recalls Cohen saying specifically that at some point in the future mathematicians would be replaced by computers. So how close are we to Cohen’s vision?

In fact, computer programs that discover new mathematical identities and theorems are already a staple

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Bach as mathematician

Johann Sebastian Bach; credit Wikimedia

OK. Johann Sebastian Bach (1685-1750) was not a mathematician in a strict sense of the word. There is no “Bach convergence theorem” in real analysis, nor is there a “Bach isomorphism theorem” in algebra. Bach had no formal training in mathematics beyond elementary arithmetic.

But, as we will see, Bach was definitely a mathematician in a more general sense, as a composer whose works are replete with patterns, structures, recursions and other precisely crafted features. There are even hints of Fibonacci numbers and the golden ratio in Bach’s music (see below). Indeed, in this larger

AI system finds counterexamples to graph theory conjectures

Courtesy: towardsdatascience.com

AI comes of age

After several decades of disappointment, effective artificial intelligence (AI) systems emerged in the late 1990s and early 2000s, with the emergence of Bayes-theorem-based methods, combined with steadily advancing computer technology.

One notable milestone came in March 2016, when a computer program named “AlphaGo,” developed by researchers at DeepMind, a subsidiary of Alphabet (Google’s parent company), defeated champion Go master Lee Se-dol, an achievement that many observers had not expected to occur for decades. Then in October 2017, Deep Mind researchers announced a new program, AlphaGo Zero, which was programmed only with the rules

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Muon result may rewrite standard model of physics

Muon g-2 experiment (courtesy Fermilab)

A new measurement of the magnetic moment of the muon may draw into question the standard model of physics, the reigning theoretical construct describing all known fundamental forces and particles of physics. The new result was released in a paper dated today (7 April 2021) with 240 authors, led by researchers at Fermilab in the U.S., but also including researchers from Italy, Germany, United Kingdom, Russia, South Korea, China and Croatia.

The standard model of physics is arguably is the most successful physical theory ever devised, explaining all known fundamental particles and all known forces

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Aho and Ullman receive the ACM Turing Award

Alfred V. Aho (courtesy ACM)

Jeffrey D. Ullman (courtesy ACM)

The 2020 Alan M. Turing Award, bestowed by the Association for Computing Machinery, has been granted to Alfred V. Aho, Professor Emeritus at Columbia University, and Jeffrey D. Ullman, Professor Emeritus at Stanford University. The ACM Turing Award, which is named after computing pioneer Alan Turing, is widely considered to be the most prestigious award in the field of computer science. Past recipients include many of the most accomplished figures in the field, including Richard Hamming, Donald Knuth, William Kahan, Edward Feigenbaum, Jim Gray, Tim Berners-Lee, John Hennessy and David

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