Introducing the Math Scholar blog

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 Einstein’s mathematics. Discussions of scientific controversies: see How likely

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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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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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How likely is it that scientists are engaged in a conspiracy?

Frauds in scientific research

From time to time, the scientific community is rocked by cases of scientific fraud. Needless to say, such incidents do not help instill confidence in the public mind that is already predisposed to be skeptical of inconvenient scientific findings. Some notable cases include: (a) a series of papers in nanoelectronics by a Bell Labs researcher, (b) two papers claiming that electromagnetic fields from cell phones can cause DNA damage, and several dozen articles by Netherlands social scientist Derek Stapel.

How could such frauds have happened? Jonathan Schooler of the University of California, Santa Barbara explains that

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Data vs theory: the mathematical battle for the soul of physics


These are exciting times for the field of physics. In 2012, researchers announced the discovery of the Higgs boson, a discovery four decades in the making, costing billions of dollars (and euros, pounds, yen and yuan) and involving some of the best minds on the planet. And in December 2015, researchers at the Large Hadron Collider in Europe reported that two separate experiments have reported possible traces of a new particle, one that might lie outside the Standard Model, although much more data and scrutiny will be required before anything definite can be said.

Yet behind the scenes a

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More mathematics (and Pi) in the media

The present authors never cease to be amazed at the amount of material on mathematics in general, and mentions of Pi in particular, that have been appearing in the popular media in recent years. We hope this is evidence of a resurgence in both interest in and knowledge of mathematics, although only time will tell if this has any lasting impact.

Mathematics in the movies

A remarkable number of recent movies have dealt with mathematics and mathematicians. The 2001 movie A Beautiful Mind featured the life of mathematician John Nash. In the 2005 movie Proof, Gwyneth Paltrow plays the daughter

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