## Two researchers share Abel prize for work in discrete mathematics and computer science

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The Abel Prize

The 2021 Abel Prize, arguably the closest equivalent in mathematics to the Nobel prize, has been awarded jointly to Avi Widgerson of the Institute for Advanced Study in Princeton, and László Lovász of the Eötvös Loránd University in Budapest, for their research linking discrete mathematics and computer science. The recipients will split the award, which is approximately USD$880,000. According to Hanz Munthe-Kaas of the University of Bergen in Norway, who chaired the Abel Prize committee, Widgerson and Lovász “really opened up the landscape ## Pandemics, misinformation and pseudoscience Credit: U.S. Center for Disease Control and Prevention Covid-19 and the misinformation pandemic The Covid-19 pandemic has disrupted human life like no other event of modern history. As of the present date (1 Mar 2021), over 114,000,000 confirmed cases and 2.5 million deaths have been recorded worldwide, according to the Johns Hopkins University database. The U.S. has recorded over 514,000 deaths, and the U.K. has recorded over 123,000. The U.S. death toll, for instance, exceeds the combined combat death toll of all wars fought in its 245-year history (save only the civil war). And for every death there are Continue reading Pandemics, misinformation and pseudoscience ## PiDay 2021 crossword puzzle Yes, it is that time of year — Pi Day (March 14, or 3/14 in North American month/day date notation) is approaching. So in honor of the occasion, I have constructed a new crossword puzzle — see below. This puzzle employs a certain pi-related feature that will become evident as you solve it. This puzzle conforms to the New York Times crossword conventions. As far as difficulty level, it would be comparable to the NYT Tuesday or Wednesday puzzles (the NYT puzzles are graded each week from Monday [easiest] to Saturday [most difficult]). If you would like a full-page version Continue reading PiDay 2021 crossword puzzle ## Machine-learning breakthrough in protein folding Structure of the Nsp 15 hexamer, a component of Covid-19 (Courtesy Argonne Natl Lab) Protein folding Proteins are the workhorses of biology. A few examples in human biology include actin and myosin, the proteins that enable muscles to work; keratin, which is the basis of skin and hair; hemoglobin, the basis of red blood that carries oxygen to cells throughout the body; pepsin, an enzyme that breaks down food for digestion; and insulin, which controls metabolism. A protein known as “spike” is the key for the coronavirus to invade healthy cells. And for every protein in human biology, there Continue reading Machine-learning breakthrough in protein folding ## Do odd perfect numbers exist? New results on an old problem Euclid, from Rafael’s “School of Athens”, Vatican Museum, Rome, photo courtesy Clay Mathematics Institute MathJax.Hub.Config({tex2jax: {inlineMath: [[‘$’,’$’], [‘\$$‘,’\$$’]]}}); Perfect numbers A perfect number is a positive integer whose divisors (not including itself) add up to the integer. The smallest perfect number is$6$, since$6 = 1 + 2 + 3$. The next is$28 = 1 + 2 + 4 + 7 + 14$, followed by$496 = 1 + 2 + 4 + 8 + 16 + 31 + 62 + 124 + 248$and$8128 = 1 + 2 + 4 + 8 + 16 + 32

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## Can computers do mathematical research?

AI comes of age

The modern field of artificial intelligence (AI) began in 1950 with Alan Turing’s landmark paper Computing machinery and intelligence, which outlined the principles of AI and proposed the Turing test. Although early researchers were confident that AI systems would soon be a reality, inflated promises and expectations led to disappointment in the 1970s and again in the 1980s.

A breakthrough of sorts came in the late 1990s and early 2000s with the emergence of Bayes-theorem-based methods, which quickly displaced the older methods based mostly on formal reasoning. When combined with steadily advancing

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## Peter Borwein dies at 67

Peter Borwein (sitting), with his brother Jonathan Borwein (courtesy Canada Foundation for Innovation)

Peter Borwein, retired Professor of Mathematics at Simon Fraser University (British Columbia, Canada) and former Director of SFU’s Centre for Interdisciplinary Research in the Mathematical and Computational Sciences (IRMACS), died on August 23, 2020, at the age of 67, of pneumonia, after courageously battling multiple sclerosis for over 20 years.

Peter was a prolific mathematician, with over 200 publications, including several books. His research included works in classical analysis, computational number theory, Diophantine number theory and symbolic computing. Many of these papers were co-authored with his brother

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## Two mathematicians’ triple play

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The Erdős-Turán conjecture

Paul Erdős, one of the twentieth century’s most unique mathematicians, was known to travel from colleague to colleague, often arriving unannounced, and to immediately delve into some particularly intriguing research problem. See this article and this book for some additional background on this influential mathematician.

One of his more interesting conjectures is his “conjecture on arithmetic progressions,” sometimes referred to as the “Erdős-Turán conjecture.” It can be simply stated as follows: If $A$ is a set of positive integers such that $$\sum_{k \in A} \frac{1}{k} = \infty,$$ then $A$ contains arithmetic progressions of

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## How old is the universe? New results clash

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The standard model

The standard model of physics, namely the framework of laws at the foundation of modern physics, has reigned supreme since the 1970s, confirmed to great precision in a vast array of experimental tests. Among other things, the standard model predicted the existence of the Higgs boson, which was experimentally discovered in 2012, nearly 50 years after it was first predicted.

Yet physicists have recognized for many years that the standard model cannot be the final answer. For example, quantum theory and general relativity are known to be mathematically incompatible. String theory and

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## Covid-19 and the worth of a human life

The scales of justice (courtesy Wikimedia)

Covid-19’s grim toll

The statistics are staggering: As of 1 June 2020, according to the Johns Hopkins University database, the U.S. had logged over 1.811 million confirmed cases of Covid-19 and over 105,000 deaths. The U.K. was next, with over 277,000 confirmed cases and over 38,000 deaths. Worldwide, over 6.3 million cases had been confirmed, with more than 376,000 deaths. If current trends continue, the U.S. death toll alone will soon exceed that of all wars in its history except for the Civil War and World War II.

The economic costs have been

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