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New results on the prime gap conjecture

The twin prime and prime gap conjectures

Paul Erdos, one of the 20th century’s most famed mathematicians (1913-1996) was well-known for offering prizes for the solution of various mathematical problems. Although most of these prizes were a token USD$25 or the like, he did offer a UDS$10,000 prize for the solution to a certain conjecture

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Low energy nuclear reactions: Papers and patents

Introduction

The world community is truly at a crossroads like never before faced in the history of our civilization. If we continue business-as-usual with the consumption of fossil fuels, then, according to the 2014 edition of the Intergovernmental Panel on Climate Change (IPCC)’s climate change report, grave consequences will almost surely ensue, including rising sea

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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,

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Big Bucks for Big Breakthroughs: Prize recipients give three million dollar maths talks

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

The international, if still Euro-centric,

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Dubious digits: Is this data really that accurate?

When numbers of any sort are presented, whether in mathematics, science, business, government or finance, the default assumption is that the data presented are reasonably reliable to the last digit presented. Thus, if a light bulb is listed as using 3.14 watts, then its actual usage is presumably between 3.13 and 3.15 watts, and certainly

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Fusion energy: Hope or hype?

The IPCC report’s warning

The latest draft edition of the UN’s Intergovernmental Panel on Climate Change (IPCC) bluntly warns that business-as-usual increases in greenhouse gas emissions will cause “further warming and long-lasting changes” in the earth’s the climate system, with increasing likelihood of “severe, pervasive and irreversible impacts for people and ecosystems.” Specific dangers include

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Tilting at windmills

Don Quixote

September 29, 2014 is the 467th birthday of Spanish author Miguel de Cervantes, whose immortal Don Quixote is widely regarded as one of the greatest works of literature in any language. In fact, in 2002 the Norwegian Book Club named Don Quixote as “best literary work ever written” in their listing of the

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To frack or not to frack: That’s not the question

The latest IPCC report

The latest draft edition of the UN’s Intergovernmental Panel on Climate Change (IPCC) report includes some rather stark language:

Continued emission of greenhouse gases will cause further warming and long-lasting changes in all components of the climate system, increasing the likelihood of severe, pervasive and irreversible impacts for people and ecosystems.

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Opportunities and challenges in experimental mathematics

“Experimental mathematics” has emerged in the past 25 years or so to become a competing paradigm for research in the mathematical sciences. An exciting workshop entitled Challenges in 21st Century Experimental Mathematical Computation was held at the Institute for Computational and Experimental Research in Mathematics (ICERM), July 21-25, 2014, which explored emerging challenges of experimental

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Formal proof completed for Kepler’s conjecture on sphere packing

Introduction

On 10 August 2014, a team led by Thomas Hales of the University of Pittsburgh, USA, announced that their decade-long effort to construct a computer-verified formal proof of the Kepler conjecture was now complete. The project was known as Flyspeck, a rough acronym for “Formal Proof of Kepler.”

The Kepler conjecture is the assertion

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