
Readers are welcome to read the new Math Scholar blog, which is available HERE.
For over 7 years, mathematicians David H. Bailey and Jonathan M. Borwein have published essays, new items, quotations and book reviews (236 posts in total). Our posts have included:
Notices of new mathematical discoveries: see Sphere packing problem solved in 8 and 24 dimensions and Unexpected pattern found in prime number digits. Descriptions of new developments in the larger arena of modern science: see Space exploration: The future is now and Gravitational waves detected, as predicted by Einsteinâ€™s mathematics. Discussions of scientific controversies: see How likely
Continue reading Introducing the Math Scholar blog
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 “farranging” don’t really do justice to his work, the sheer volume of which is astounding: 388 published journal articles, plus another 103
Continue reading Jonathan Borwein dies at 65
Introduction
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
Continue reading Why are so many mathematicians also musicians?
Introduction
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
Continue reading Space exploration: The future is now
Optimal stacking of oranges
In the 17th century, Johannes Kepler conjectured that the most spaceefficient 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 mathematiciansculptor Helaman Ferguson), completed a 250page 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
Continue reading Sphere packing problem solved in 8 and 24 dimensions
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 thoughtprovoking 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
Continue reading New book on the ontology of mathematics
In a certainly welldeserved 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 centuriesold, 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
Continue reading Andrew Wiles wins the Abel Prize
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 base3 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
Continue reading Unexpected pattern found in prime number digits
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
Continue reading Pi Day 2016
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 9783319323770. 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.
Continue reading New compendium of Pi papers

