Jonathan Borwein dies at 65

It is my sad duty to report that our colleague Jonathan Borwein, Laureate Professor of Mathematics at the University of Newcastle, Australia, has passed away at the age of 65. He is survived by his wife Judith and three daughters. For details on his funeral and for making donations to a scholarship fund in his name, see the obituary below.

Jonathan M. Borwein

What can one say about Jon’s professional accomplishments? Adjectives such as “profound,” “vast” and “far-ranging” don’t really do justice to his work, the sheer volume of which is astounding: 388 published journal articles, plus another 103

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Sphere packing problem solved in 8 and 24 dimensions

Optimal stacking of oranges

In the 17th century, Johannes Kepler conjectured that the most space-efficient way to pack spheres is to arrange them in the usual way that we see oranges stacked in the grocery store. However, this conjecture stubbornly resisted proof until 1998, when University of Pittsburgh mathematician Thomas Hales, assisted by Samuel Ferguson (son of mathematician-sculptor Helaman Ferguson), completed a 250-page proof, supplemented by 3 Gbyte of computer output.

However, some mathematicians were not satisfied with Hales’ proof, as it relied so heavily on computation. So Hales embarked on project Flyspeck, which was to construct a

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Andrew Wiles wins the Abel Prize

In a certainly well-deserved recognition, the Norwegian Academy of Science and Letters has awarded the 2016 Abel Prize to Andrew Wiles of the University of Oxford, who in 1995 published a proof of Fermat’s Last Theorem, that centuries-old, maddening conjecture that an + bn = cn has no nontrivial integer solutions except for n = 2.

Fermat’s Last Theorem was first conjectured in 1637 by Pierre de Fermat in 1637, in a cryptic annotated marginal note that Fermat wrote in his copy of Diophantus’ Arithmetica. For 358 years, the problem tantalized generations of mathematicians, who sought in vain for a

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Big brother is watching, with new image-recognition techniques

On 17 November 2014, research groups at Google and Stanford University jointly announced significant advances in image recognition software.

Image recognition has been pursued for many years. One of the first and still most widely deployed applications is to recognize faces. Indeed, facial recognition systems have been employed in numerous settings:

In numerous U.S. locations, such as airports; in fact, many presume that such cameras are ubiquitous, as in TV police dramas, although this is not the case. In London, as part of their closed-circuit TV camera crime monitoring system. In various casinos, to recognize “card counters” and other unwanted

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2014 Fields Medals announced

On 13 August 2014, at the quadrennial meeting of the International Congress of Mathematicians, this year held in Seoul, Korea, the four winners of the 2014 Fields Medals were announced by the International Mathematics Union, which administers the awards.

This year’s awardees are:

Artur Avila, a Brazilian mathematician (the first Brazilian mathematician to win the prize) has done notable research in the study of chaos theory and dynamical systems. These areas seek to understand the behavior of systems that evolve over time in which very small changes in the initial conditions can lead to wildly varying outcomes. One well-known example

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New York Times features story on James Simons

On 7 July 2014, the New York Times ran a feature story on James H. Simons, the well-known geometer, hedge fund founder, billionaire and philanthropist. Here are some of the fascinating facts uncovered in the Times story and elsewhere:

Simons was born in 1938 in Newton, Massachusetts, the son of a shoe factory owner. Simons graduated from the Massachusetts Institute of Technology in three years, then received his Ph.D. in mathematics from U.C. Berkeley in three more years, finishing at the age of 23. Simons worked on cryptographic mathematics at the Institute for Defense Analyses in Princeton, New Jersey, but

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Inaugural Breakthrough Prizes in Mathematics announced

June 23, 2014 was a nice day for mathematicians Simon Donaldson, Maxim Kontsevich, Jacob Lurie, Terence Tao and Richard Taylor. They were informed that they will be receiving the inaugural Breakthrough Prizes in Mathematics, each with a cash award of USD$3,000,000.

The Breakthrough Prizes in Mathematics complement the Breakthrough Prizes in Fundamental Physics, which were inaugurated in 2012, and the Breakthrough Prizes in Life Sciences, which were inaugurated in 2013.

In future years, there will be one award in mathematics, one award in physics, and six in life sciences. Each of the eight annual awardees will receive USD$3,000,000, as

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Sinai receives 2014 Abel Prize

Yakov Sinai, Professor of Mathematics at Princeton University since 1993, has been awarded the 2014 Abel Prize for his groundbreaking research in dynamical systems, ergodic theory and mathematical physics. A stipend of approximately USD $1,000,000 accompanies the prize, which is often referred to as the “Nobel Prize” of mathematics.

The Abel Prize is named after Niels Henrik Abel, a Norwegian mathematician of the early 19th century who laid the foundation for group theory. “Abelian groups” are named after Abel. The awarding of the Abel Prize to Sinai strikes close to home for one of the present bloggers (DHB), since ergodic

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Doron Zeilberger comments on experimental mathematics in AMS Notices

In the latest issue (December 2013) of the Notices of the American Society, noted mathematician Doron Zeilberger has published an Opinion piece on the state of pure mathematics, and then contrasts this with experimental mathematics. His article, entitled “[Contemporary Pure] Math Is Far Less Than the Sum of Its [Too Numerous] Parts,” is available here.

Doron Zeilberger is perhaps best known for his work with Herbert Wilf in developing the Wilf-Zeilberger method for computer-based proving of combinatorial identities, a problem that mathematician-computer scientist Donald Knuth once rated as “50” (meaning of the greatest difficulty) in his book The Art of

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Jeopardy! features a category on pi

Jeopardy! is arguably the most popular North American trivia quiz show. Traditionally the show has shied away from mathematical topics, but, in the past year or two, it has featured some interesting and relatively sophisticated mathematical categories.

For example, on 9 May 2013, Jeopardy! featured an entire category on the Abel Prize of mathematics. A listing of the individual questions, together with some background on the Abel Prize, is available in a previous Math Drudge blog.

And, lest we forget, in February 2011 Jeopardy! featured a three-day competition between IBM’s “Watson” computer system and the two best human contestants, Ken

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