|
|
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
Most fairly well educated people recognize pseudoscience as bunkum when they see it — astrology, young-earth creationism, alien abduction, pyramid power, etc. Yet some of these same people are now being sucked into a movement that is, according to all rigorous scientific analysis, equally without foundation as the ones listed above: the anti-smart meter movement.
“Smart meters” are devices now being installed by electric and gas utilities in millions of homes and apartments, both in the U.S. and internationally, which a few times per day briefly send a report on usage by a wireless system entirely similar to that used
Continue reading Smart meters for dummies
My brother, Peter Borwein, is a distinguished Canadian mathematician who has something intimate in common with Ann Romney. They both have multiple sclerosis. But as you will see from the following letter that he just wrote to me, the differences outweigh their similarities.
Ann Romney was diagnosed with multiple sclerosis (MS) in 1998. She was born in 1949. I was diagnosed with MS in 1996. I was born in 1953. Exact dates of diagnosis are inexact. MS rarely has an exact starting date. But we were both in our mid-to-late forties: a little atypically-late onset but not extreme.
Continue reading Ann Romney and my Brother
Famed mathematician William Thurston died Tuesday 21 Aug 2012, at his home in Rochester, New York, from cancer. He was arguably one of the handful of 20th century mathematicians — pure or applied — who will be discussed in some detail in 22nd century histories of mathematics and science. As Edward Tenner wrote in the Atlantic Even as he contributed to theoretical physics, Bill’s work was proof that the most abstract math can have gorgeous practical applications.
Although he did work in several areas, the majority of Thurston’s research work was in geometry and topology, namely the branch of mathematics
Continue reading Mathematician William Thurston dies at 65
The political world is seldom a source of high scholarship, but the current U.S. presidential campaign sets new lows. In addition to the worse-than-normal avoidance of substantive issues, and a very unpleasant level of mudslinging, numerical literacy has hit a new low. Here are some telling examples:
Republican presidential hopeful Mitt Romney, during a July 2012 trip to the Middle East, compared the per-capita Gross Domestic Product (GDP) of Israel, which he says is “about $21,000,” to that of Palestinian areas, which is “more like $10,000.” But as the U.K. Guardian notes, Israel’s per-capita GDP was $31,000 in 2011, while
Continue reading Numerical nonsense in the U.S. presidential campaign
In the wake of our previous article “Algebra is essential in a 21st century economy” (see Math Drudge blog and Huffington Post article), one of the present bloggers (DHB) participated in a “televised” interview with Andrew Hacker, the author of the New York Times article in question, together with several other respondents, organized by the Huffington Post. This transcript will be made available here when ready.
Here are some other “talking points” to consider on this issue:
Our economy is moving inexorably to information-age, high-technology careers, many of which require mathematics backgrounds. In a ranking of the top jobs published
Continue reading Talking points for “Algebra is essential in a 21st century economy”
Andrew Hacker’s New York Times Op-Ed
A few days ago, Andrew Hacker, an author and former Professor of political science at Queens College in New York City, created quite a stir with a New York Times Op-Ed entitled Is Algebra Necessary, where he argues that it is no longer necessary to expect the vast majority of K-12 students to study algebra, geometry or calculus.
Hacker argues that the teaching of mathematics takes a toll beginning with students in junior high or middle school. “Algebra is an onerous stumbling block for all kinds of students,” ranging from the disadvantaged to the
Continue reading Algebra is essential in a 21st century economy
In a remarkable New York Times Op-Ed, former climate change skeptic Richard Muller of the University of California, Berkeley, declares not only that global warming is real, but also that “humans are almost entirely the cause.” This is an even stronger statement than that of the Intergovernmental Panel on Climate Change, which in its 2007 report concluded only that “most” of the warming during the past half-century was attributable to human causes.
Muller’s Berkeley Earth group approached the problem by rigorously analyzing historic temperature reports. As he described their efforts,
We carefully studied issues raised by skeptics: biases from
Continue reading A former climate-change skeptic now agrees most warming is caused by humans
Mathematicians and parents
We, the present authors (DHB, from USA, and JMB, from Australia) are research mathematicians/ computer scientists. We are also the proud fathers of seven adult daughters, and a gamut of grandchildren of whom the the oldest is starting school.
Together with our spouses, we have attended a multitude of PTA meetings, sports games, concerts and science fairs. We have read almost as many report cards (and not all of them have been glowing). At the end of the day, our daughters include PhDs, veterinary doctors, lawyers, teachers, web designers, postgraduate students and one senior undergraduate. We have
Continue reading The uneven preparation of K-12 math teachers
|
|