
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
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.
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
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
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 =
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
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
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
Continue reading New compendium of Pi papers
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 GravitationalWave 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.
Continue reading Gravitational waves detected, as predicted by Einstein’s mathematics
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
Continue reading How likely is it that scientists are engaged in a conspiracy?

