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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Why are so many mathematicians also musicians?


As the present authors will readily attest, introducing oneself as a mathematician is generally not an effective way to start a social conversation. But, as Cambridge mathematician Tim Gowers explains, there is a “miracle cure”: just explain that you, as well as many other mathematicians, are also a musician or at least are deeply interested in music.

The present authors are not the best examples of this, because neither is very good at musical performance, although both have an abiding interest in listening to music. One of us listens to an eclectic collection of mostly modern music while he

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Space exploration: The future is now


From the dawn of civilization, humans have dreamed of exploring the cosmos. To date, we have launched over 60 successful missions to the Moon (including six that landed on the Moon with humans), 17 successful missions to Mars, 13 missions to the outer solar system, and five that have left the solar system.

However, many have been concerned lately that the glory days of space exploration are behind us. The Apollo missions ended 44 years ago, and still we have not returned to the Moon. Our current Mars missions are only modestly more sophisticated than earlier missions. And

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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 completely

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New book on the ontology of mathematics

Springer has published a new collection on the ontology of mathematics, edited by son and father Ernest and Philip Davis. According to the publisher’s website,

The seventeen thought-provoking and engaging essays in this collection present readers with a wide range of diverse perspectives on the ontology of mathematics. The essays address such questions as: What kind of things are mathematical objects? What kinds of assertions do mathematical statements make? How do people think and speak about mathematics? How does society use mathematics? How have our answers to these questions changed over the last two millennia, and how might they change

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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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Unexpected pattern found in prime number digits

In a startling new discovery, mathematicians Robert Lemke Oliver and Kannan Soundararajan of Stanford University have found a pattern in the trailing digits of prime numbers, long thought to be paragons of randomness. They first discovered their result by examining base-3 digits, but their result appears to hold for any number base.

In base ten digits, for example, all primes greater than 5 end in 1, 3, 7 or 9, since otherwise they would be divisible by 2 or 5. Under the common assumption that prime numbers resemble good pseudorandom number generators, a prime ending in 1, for instance, should

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Pi Day 2016

Pi Day is here again

Once again Pi Day (March 14, or 3/14 in United States notation) is here, when both professional mathematicians and students in school celebrate this most famous of mathematical numbers. Last year was a particularly memorable Pi Day, since 3/14/15 gets two more digits correct, although some would argue that this year’s Pi Day is also memorable, since 3/14/16 is pi rounded to four digits after the decimal point (the actual value is 3.14159265358979323846…).

Numerous celebrations are scheduled for Pi Day 2016. San Francisco’s Exploratorium features several events, culminating with a “Pi Procession” at 1:59pm Pacific

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New compendium of Pi papers

To celebrate Pi Day 2016, we have prepared a collection of key technical papers that have appeared in the past half century on topics related to Pi and its compution. The collection, entitled Pi the Next Generation: A Selection, is soon to be published by Springer, with ISBN 978-3-319-32377-0. Details are available at the Springer site.

Here is a synopsis of the book, as taken from the Springer site:

This book contains compendium of 25 papers published since the 1970s dealing with pi and associated topics of mathematics and computer science. The collection begins with a Foreword by Bruce Berndt.

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Gravitational waves detected, as predicted by Einstein’s mathematics

In what has to be one of most poorly kept secrets of modern science, on 11 February 2016 a team of over 1000 scientists working on the Laser Interferometer Gravitational-Wave Observatory (LIGO) project announced that they had indeed detected gravitational waves, as predicted 100 years ago as a consequence of Einstein’s general theory of relativity.

The LIGO project

The LIGO project is a large physics experiment to detect gravitational waves, namely ripples in space that are generated by distant cataclysmic events such as the explosive merger of two black holes. LIGO was founded by famed physicist Kip Thorne (who consulted

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