Space, Time and the Limits of Human Understanding

Springer has just published the book Space, Time and the Limits of Human Understanding. The book consists of 39 chapters, each written by a leading figure in one of the six general areas covered in the volume (philosophy, physics, mathematics, biology and cognitive science, logic and computer science, and miscellaneous). The present author has an article, co-authored with the late Jonathan Borwein, entitled “A computational mathematics view of space, time and complexity.” The book is targeted to a technical reader, but a first-year college calculus and physics background suffices for at least 90% of the material.

Here is a sample

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“My Search for Ramanujan”

Recently Ken Ono, a renowned mathematician at Emory University in Atlanta, Georgia, published an autobiography entitled My Search for Ramanujan: How I Learned to Count. It is co-authored with Amir Aczel, who, among other things, wrote the book Finding Zero, but sadly Aczel passed away before the book was completed.

Ken Ono was the son of Takashi Ono, a Japanese mathematician who taught at the University of Pennsylvania. Ono’s field of research has closely paralleled the writings of famed Inidian mathematician Srinivasa Ramanujan. Among other things, Ono significantly extended Ramanujan’s work on partition congruences and mock theta functions, and, with

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Scientific qualifications of Trump’s appointees


NASA image of hurricane Sandy

Donald Trump’s recent naming of key cabinet and agency appointees (which still must be approved by Congress) raises the question of the scientific qualifications for persons serving in high-level public office.

Some say that scientific qualifications are only important for positions directly relevant to scientific research, such as NASA, the National Science Foundation, and their equivalents in other nations. But this is very short-sighted. After all, science and technology are increasingly central to:

Energy: Finding practical and economically viable alternatives to fossil fuels, which involves research in mathematics, high-energy physics and materials science,

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Enhancing reproducibility in mathematical and scientific computing

Victoria Stodden, Marcia McNutt (President of the American Association for the Advancement of Science), David H. Bailey, Ewa Deelman, Yolanda Gil, Brooks Hanson, Michael Heroux, John Ioannidis and Michela Taufer have published an article in Science (the principal journal of the AAAS) entitled Enhancing reproducibility in computational methods.

In this article we argue that the field of mathematical and scientific computing lags behind other fields in establishing a culture and tools to ensure reproducibility. All too often, the authors of computations, even those that are published in peer-reviewed conferences and journals, have not fully documented their algorithms, code, input data

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Breakthrough Foundation announces 2017 prizes in math, physics and life sciences

The Breakthrough Foundation has announced a new set of winners of their awards, including recipients in mathematics, physics and life sciences. The founders of the Breakthrough Prize are Sergey Brin (co-founder of Google) and Anne Wojcicki (co-founder of 23andme), Mark Zuckerberg and Priscilla Chan (founder of Facebook and his spouse), Yuri Milner and Julia Milner (Russian venture capitalist and his spouse), and Jack Ma and Cathy Zhang (founder of Alibaba and his spouse).

Mathematics prize

The Breakthrough Prize in mathematics (USD$3 million) was awarded to Jean Bourgain of the Institute for Advanced Study in Princeton, New Jersey. Bourgain’s work

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Asian tigers roar in the latest TIMSS math-science rankings

The latest international results comparing Grade 4 and Grade 8 students in mathematics and science are in, and, once again, the Asian tigers (China, Korea, Japan, and Singapore) are roaring, significantly leading major first-world nations such as the United States, England and Australia.

TIMSS results

The Trends in International Mathematics and Science Study (TIMSS) is an international test to compare the achievement of fourth and eighth grade students in mathematics and science. It has been administered every four years since 1995, thus providing a 20-year period for study of educational trends around the world.

In November 2016, results for the

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Bailey, Borwein, Mattingly and Wightwick to receive the Levi L. Conant Prize from AMS

The American Mathematical Society has announced that David H. Bailey, Jonathan Borwein, Andrew Mattingly and Glenn Wightwick will receive the 2017 Levi L. Conant Prize. Bailey is a retired senior scientist at the Lawrence Berkeley National Laboratory, and a research associate at the University of California, Davis. Borwein (deceased 2 August 2016) was a Laureate Professor of Mathematics at the University of Newcastle, Australia. Mattingly is senior information technology architect at IBM Australia. Wightwick is deputy vice-chancellor and vice-president (Research) at the University of Technology Sydney.

This year’s prize was awarded for the recipients’ 2013 article The Computation of Previously

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Are humans or computers better at mathematics?

Computer proofs

Considerable attention has been drawn to the discovery and proof of mathematical theorems by computer.

Perhaps the first major result by a computer came in 1976, with a proof of four-color theorem, namely the assertion that any map (with certain reasonable conditions) can be colored with just four distinct colors for individual states. This was first proved by computer in 1976, although flaws were later found, and a corrected proof was not completed until 1995.

In 2003, Thomas Hales of the University of Pittsburgh published a computer-based proof of Kepler’s conjecture, namely the assertion that the familiar method

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Shawn Otto’s “The War on Science”

Shawn Otto has written a new book on science denialism, entitled The War on Science: Who’s Waging It, Why It Matters, What We Can Do About it.

Otto argues that modern science is under attack from three directions: (a) the academic left, which has asserted that science has no claim to objective truth, (b) the religious right, which has fought evolution and more under the banner of biblical literalism, and (c) the industrial world, which has fought scientific findings in the area of health and environmental protection.

Otto observes that science denialism is rooted, surprisingly enough, in the academic left.

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Why science needs the humanities


Foster in Contact, saying “They should have sent a poet”

Earlier this year, Kentucky governor Matt Bevin declared that state colleges and universities should educate more electrical engineers and fewer French literature majors: “All the people in the world that want to study French literature can do so, they are just not going to be subsidized by the taxpayer.”

Other politicians have sounded a similar refrain. Governor Patrick McCroy of North Carolina suggested basing funding on post-graduate employment rather than enrollment, or, as he put it rather crudely, “It’s not based on butts in seats but on how

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