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Essays « Math Scholar

Exoplanets, 4 billion-year-old life, Fermi’s paradox and zero-one laws

What do exoplanets, four-billion-year-old life, Fermi’s paradox and zero-one laws of probability theory have to do with each other? Quite a bit, actually. Let us review these developments, one by one:

New exoplanet discoveries

Depiction of the seven exoplanets of the TRAPPIST-1 system. Courtesy NASA.

On 22 February 2017, a consortium of NASA and European astronomers announced that there are not just one but seven planets that potentially could harbor life, all orbiting a yellow dwarf star named TRAPPIST-1, about 40 light-years (235 trillion miles or 378 trillion km) from earth. This is clearly a remarkable discovery, adding seven to

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Reproducibility: Principles, Problems, Practices, and Prospects

The book Reproducibility: Principles, Problems, Practices, and Prospects, which contains a chapter co-authored by the late Jonathan Borwein and the present authors (Victoria Stodden and David H. Bailey), has won a 2017 Prose Award (“Honorable Mention”) in the category “Textbook/Best in Physical Sciences and Mathematics.” These prizes are awarded annually in 53 categories by the Professional and Scholarly Publishing division of the Association of American Publishers.

This volume consists of 27 chapters, grouped into six sections, which collectively address questions of reproducibility in a broad range of scientific disciplines, ranging from medicine, physical sciences, life sciences, social sciences and even

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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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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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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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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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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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Remembrances of Jon Borwein

In the wake of Jon Borwein’s passing, I have constructed the Jonathan Borwein Memorial website.

This site features a collection of over 30 tributes to Jon’s life and work. These range from recollections of time spent visiting and working with Jon to detailed assessments of his prodigious professional output. Many of these contain touching comments of the anguish and consternation of his passing and how much we will all miss his leadership.

One described Jon as “a force of nature, uncontainable and omnipresent. His passion for knowledge was insatiable and drove him to a breadth of research that is extremely

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