An article co-authored by Jonathan M. Borwein and the late Richard E. Crandall on closed forms has appeared in the January 2013 issue of the Notices of the American Mathematical Society. This article tries to answer the question “What is a closed form,” and then explains why obtaining a closed-form expression for a mathematical entity (as opposed, say, to a numerical value) is so important.
The full PDF of the article is available Here.
Here is the introductory paragraph of the article:
Mathematics abounds in terms that are in frequent use yet are rarely made precise. Two such are rigorous
Continue reading Borwein-Crandall article on closed forms appears
Scientists are sometimes pictured by the media, or even by antagonists such as creationists, as completely resolute and inflexible with regards to their theories and assertions. But this is really not an accurate picture. Real scientists do change their minds, particularly when the underlying facts change. As economist John Maynard Keyes is reputed once to have said, “When the facts change, I change my mind. What do you do?” (Actually, according to a columnist in the Wall Street Journal, the Keynes quote may be apocryphal, but it well illustrates our point).
An interesting illustration of a good scholar’s willingness to
Continue reading An opponent of genetically modified crops changes his mind
It is with great sadness that the present bloggers announce the passing of their dear colleague Richard Crandall, who died Thursday December 20, 2012, after a brief bout with acute leukaemia—the week before his 65th birthday on December 29.
Crandall had a long and colorful career. He was a physicist by training, studying with Richard Feynman as an undergrad at the California Institute of Technology, and receiving his Ph.D. in physics at MIT, under the tutelage of Victor Weisskopf, the Austrian-American physicist who discovered what is now known as the Lamb Shift and who was one of the most influential
Continue reading Mathematician/physicist/inventor Richard Crandall dies at 64
In a previous Math Drudge blog, on the growth in scientific fraud, we described the case of Netherlands social psychologist Diederik Stapel, who, based on an initial investigation, had been accused of serious and serial fraud in his work in the field of social psychology.
Now a more detailed report has been released on the affair. As summarized in a November 29, 2012 article in Science, the report paints a picture not only of widespread fraud, but more generally asserts that “from the bottom to the top there was a general neglect of fundamental scientific standards and methodological requirements.”
Some
Continue reading Study released on Dutch researcher’s “culture of fraud”
A fascinating posthumous autobiography of famed mathematician Benoit Mandelbrot has just been published by Pantheon Books.
The book includes a fascinating account of his youth growing up as a Jew in the war-torn years of the 1930s and 1940s. Born in Warsaw in 1924 and raised in a well-educated household whose Lithuanian roots were said to have produced “men of great learning.” His uncle, Szolem Mandelbrojt, was a star among French mathematicians in the early 20th century. In 1931 his father emigrated to Paris, to be joined by Benoit and the rest of the family in 1936. It was a
Continue reading Benoit Mandelbrot’s memoir is published
It a ruling that has drawn international attention (and outrage), a judge in L’Aquila, Italy ruled that seven scientists and seismology experts were guilty of “manslaughter,” because on 31 Mar 2009 they assured local residents that there did not seem any imminent risk of danger from an earthquake, yet an earthquake struck a few days later, tragically killing 300 persons.
But as anyone familiar with earthquake science will attest, there is no known technology for predicting earthquakes, except in a general sense to warn that certain regions, based on regional geology and past patterns of earthquakes, appear to be more
Continue reading Italian judge rules scientists guilty of “manslaughter” for failing to predict earthquake
In an era when many critics of the scientific “establishment” claim that scientists are mostly concerned about circling the wagons to protect funding of their existing pet projects, and in the wake of the battle brewing in the U.S. over the funding of nuclear fusion research in particular, it is interesting to read comments by Robert Hirsch, a senior researcher in the fusion science field, in a speech he recently gave at a fusion workshop.
Here is a brief summary:
After decades of effort, and although a great deal has been learned and accomplished, the stark fact is no
Continue reading Fusion scientist suggests new direction for the field
Many of us were disappointed not to see any serious mention of scientific issues in the recent U.S. presidential debates. Global warming, for example, was never discussed at all, even in the last debate on foreign policy, where it would have naturally fit.
After all, even the U.S. military has now recognized the reality of global warming, and is preparing for a world where climate changes alter the geopolitical landscape in new and potentially very dangerous ways. Among the perils are increasing droughts and crop failures, as well as rising sea levels that render uninhabitable large swaths of currently
Continue reading Antiscience beliefs and U.S. politics
Shinichi Mochizuki, a mathematician at Kyoto University in Japan, has released a 500-page proof of the “abc” conjecture, a celebrated unsolved problem originally posed in 1985.
Let sqp(n) denote the square-free part of an integer n, or in other words the product of the prime factors of n. For example, sqp(18) = 2 * 3 = 6 (here * denotes multiplication). The abc conjecture asserts that for integers a, b and c, where a + b = c, the ratio sqp(a*b*c)r/c always has some minimum value greater than zero for any value of r greater than 1. For example, if
Continue reading Japanese mathematician claims proof of “abc” conjecture
A new book on mathematical computing with Mathematica, co-authored by one of the present bloggers, has been published by Springer. It is a counterpart to a corresponding book with Maple. Here is a synopsis, taken from the book’s Springer website:
Thirty years ago, mathematical computation was difficult to perform and thus used sparingly. However, mathematical computation has become far more accessible due to the emergence of the personal computer, the discovery of fiber-optics and the consequent development of the modern internet, and the creation of Maple™, Mathematica®, and Matlab®.
An Introduction to Modern Mathematical Computing: With Mathematica® looks beyond teaching
Continue reading New book on mathematical computing
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