Top 500 supercomputer performance (orange = #1, blue = #500, green = sum)
Postmodern critiques of scientific progress
The fact that scientific research has made immense progress over the past years, decades and centuries is taken for granted among professional scientists and most of the lay public as well. But there are others, from both the left wing and the right wing of society, who question, dismiss or even reject the notion that science progresses. One group, which is mostly rooted in the right wing of society, rejects the scientific consensus on evolution, as with the creationism and intelligent
Continue reading Is scientific progress real?
AI’s tortuous history
The field of artificial intelligence (AI) is actually rather old. Ancient Greek, Chinese and Indian philosophers developed principles of formal reasoning several centuries before Christ. In 1651, British philosopher Thomas Hobbes wrote in Leviathan that “reason … is nothing but reckoning (that is, adding and subtracting).” In 1843 century Ada Lovelace, widely considered to be the first computer programmer, ventured that machines such as Babbage’s analytical engine “might compose elaborate and scientific pieces of music of any degree of complexity or extent.”
In 1950 Alan Turing’s landmark paper Computing machinery and intelligence outlined the principles of AI
Continue reading 2018: The year that artificial intelligence came of age
This annual Supercomputing conference is a showcase for the field of highperformance scientific and mathematical computing, featuring a firstrate peerreviewed technical program, tutorials, workshops, and a massive exhibit hall where universities, national laboratories and computer vendors from around the world exhibit their research, hardware and software. This year’s conference, SC18, which is being held in Dallas, Texas, has attracted well over 10,000 attendees. The conference is cosponsored by the Association for Computing Machinery (ACM) and the Computer Society of the Institute of Electrical and Electronic Engineers (IEEE).
Awards
Four prestigious professional society awards are presented at the SC18 conference. This
Continue reading US leads but China rises in latest Top500 supercomputer list
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Credit: Vatican Museum
Introduction: Ancient Greek mathematicians developed the methodology of “rulerandcompass” constructions: if one is given only a ruler (without marks) and a compass, what objects can be constructed as a result of a finite set of operations? While they achieved many successes, three problems confounded their efforts: (1) squaring the circle; (2) trisecting an angle; and (3) duplicating a cube (i.e., constructing a cube whose volume is twice that of a given cube). Indeed, countless mathematicians through the ages have attempted to solve these problems, and countless incorrect “proofs” have been
Continue reading Simple proofs: The impossibility of trisection
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Credit: MathIsFun.com
The fundamental theorem of algebra is the assertion that every polynomial with real or complex coefficients has at least one complex root. An immediate extension of this result is that every polynomial of degree $n$ with real or complex coefficients has exactly $n$ complex roots, when counting individually any repeated roots.
This theorem has a long, tortuous history. In 1608, Peter Roth wrote that a polynomial equation of degree $n$ with real coefficients may have $n$ solutions, but offered no proof. Leibniz and Nikolaus Bernoulli both asserted that quartic polynomials of
Continue reading Simple proofs: The fundamental theorem of algebra
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Credit: fjordstone.com
Mankind has been fascinated with $\pi$, the ratio between the circumference of a circle and its diameter, for at least 2500 years. Ancient Hebrews used the approximation 3 (see 1 Kings 7:23 and 2 Chron. 4:2). Babylonians used the approximation 3 1/8. Archimedes, in the first rigorous analysis of $\pi$, proved that 3 10/71 < $\pi$ < 3 1/7, by means of a sequence of inscribed and circumscribed triangles. Later scholars in India (where decimal arithmetic was first developed, at least by 300 CE), China and the Middle East computed $\pi$
Continue reading Simple proofs: The irrationality of pi
Euler’s identity Credit: Redbubble.com
Mathematics and beauty
Modern mathematics is one of the most enduring edifices created by humankind, a magnificent form of art and science that all too few have the opportunity of appreciating. The great British mathematician G.H. Hardy wrote, “Beauty is the first test; there is no permanent place in the world for ugly mathematics.” Mathematicianphilosopher Bertrand Russell added: “Mathematics, rightly viewed, possesses not only truth, but supreme beauty — a beauty cold and austere, like that of sculpture, without appeal to any part of our weaker nature, without the gorgeous trappings of painting or music,
Continue reading Simple proofs of great theorems
Credit: Berkeley Center for Cosmological Physics
String theory, fine tuning and the multiverse
String theory is the name for the theory of mathematical physics which proposes that physical reality is based on exceedingly small “strings” and “branes,” embedded in 10 or 11dimensional space. String theory has been proposed as the longsought “theory of everything,” because it appears to unite relativity and quantum theory, and also because it is so “beautiful.”
Yet in spite of decades of effort, by thousands of brilliant mathematical physicists, the field has yet to produce specific experimentally testable predictions. What’s more, hopes that string theory
Continue reading Does the string theory multiverse really exist?
Pi nonsense in peerreviewed journals
In a previous Math Scholar blog, we lamented the decline of peer review, as evidenced by the surprising number of papers, published in supposedly professional, peerreviewed journals, claiming that Pi is not the traditional value 3.1415926535…, but instead is some other value. In the 12 months since that blog was published, other papers of this most regrettable genre have appeared.
As a single example of this genre, the author of a 2015 paper, which appeared in the International Journal of Engineering Sciences and Research Technology, states, “The area and circumference of circle has been
Continue reading The rise of paytopublish journals and the decline of peer review
Introduction
In a new book, Lost in Math: How Beauty Leads Physics Astray, Sabine Hossenfelder reflects on her career as a theoretical physicist. She acknowledges that her colleagues have produced “mindboggling” new theories. But she is deeply troubled by the fact that so much work in theoretical physics today is disconnected from empirical reality, yet is excused because the theories themselves, and the mathematics behind them, are “too beautiful not to be true.”
Hossenfelder notes that there have been numerous instances in the past when scientists’ overreliance on “beauty” has led it astray. Newton’s clockwork universe, with seemingly selfevident
Continue reading Does beautiful mathematics lead physics astray?

