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Do probability arguments refute evolution? Updated 20 December 2023 (c) 2023
Introduction
In the past few decades, modern science has uncovered a universe that is far vaster and more awe-inspiring than ever imagined before, together with a set of elegant natural laws that deeply resonate with the idea of a cosmic lawgiver (and isn’t it remarkable that we humans can uncover and understand these laws?). Along this line, 46% of Americans (including 54% of atheists, 55% of agnostics and 43% of nones) say that they experience a “deep sense of wonder about the universe” on at least a weekly basis
Continue reading Do probability arguments refute evolution?
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Factorization and cryptography
Until a few decades ago, number theory, namely the study of prime numbers, factorization and other features of the integers, was widely regarded as the epitome of pure mathematics, completely divorced from considerations of practical utility. This sentiment was expressed most memorably by British mathematician G.H. Hardy (best known for mentoring Ramanujan and results on the Riemann Zeta function), who wrote in his book A Mathematician’s Apology (1941),
I have never done anything “useful”. No discovery of mine has made, or is likely to make, directly or indirectly, for good
Continue reading New factorization advances: Is your bank account safe?
Gregory Zuckerman, author of The Greatest Trade Ever, has published a new book highlighting the life and work of Jim Simons, who, at the age of 40, walked away from a very successful career as a research mathematician and cryptologist to try his hand at the financial markets, and ultimately revolutionized the field. Zuckerman’s new book is titled The Man Who Solved the Market: How Jim Simons Launched the Quant Revolution.
Upbringing and academic career
Simons’ background hardly suggested that he would one day lead one of the most successful, if not the most successful, quantitative hedge fund operation in
Continue reading Jim Simons: The man who solved the market
Credit: IPCC
The facts of climate change
At this point in time, the basic facts of climate change are not disputable in the least. Careful planet-wide observations by NASA and others have confirmed that 2018 was the fourth-warmest year in recorded history. The only warmer years were 2016, 2017 and 2015, respectively, and 18 of the 19 warmest years in history have occurred since 2001. Countless observational studies and supercomputer simulations have confirmed both the fact of warming and the conclusion that this warming is principally due to human activity. These studies and computations have been scrutinized in great
Continue reading The scientific debate is over: it is time to act on climate change
IBM’s “Q” quantum computer; courtesy IBM
Google’s quantum computing achievement
For at least three decades, teams of researchers have been exploring quantum computers for real-world applications in scientific research, engineering and finance. Researchers have dreamed of the day when quantum computers would first achieve “supremacy” over classical computers, in the sense that a quantum computer solving a particular problem faster than any present-day or soon-to-be-produced classical computer system.
In a Nature article dated 23 October 2019, researchers at Google announced that they have achieved exactly this.
Google researchers employed a custom-designed quantum processor, named “Sycamore,” consisting of programmable quantum
Continue reading Quantum supremacy has been achieved; or has it?
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Credit: Ancient Origins
Introduction In a previous Math Scholar blog, we presented Archimedes’ ingenious scheme for approximating $\pi$, based on an analysis of regular circumscribed and inscribed polygons with $3 \cdot 2^k$ sides, using modern mathematical notation and techniques.
One motivation for both the previous blog and this blog is to respond to some recent writers who reject basic mathematical theory and the accepted value of $\pi$, claiming instead that they have found $\pi$ to be a different value. For example, one author asserts that $\pi = 17 – 8 \sqrt{3} =
Continue reading Pi as the limit of n-sided circumscribed and inscribed polygons
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Log_10 of the error of a continued fraction approximation of Pi to k terms
Approximation of real numbers by rationals
The question of finding rational approximations to real numbers was first explored by the Greek scholar Diophantus of Alexandra (c. 201-285 BCE), and continues to fascinate mathematicians today, in a field known as Diophantine approximations.
It is easy to see that any real number can be approximated to any desired accuracy by simply taking the sequence of approximations given by the decimal digits out to some point, divided by the appropriate power
Continue reading New paper proves 80-year-old approximation conjecture
The TRAPPIST-1 system of exoplanets, approximately 40 light-years away
Exoplanets galore
As of the present date (August 2019), more than 4000 exoplanets have been discovered orbiting other stars, and by the time you read this even more will have been logged. Several hundred exoplanets were announced in a July 2019 paper (although these await independent confirmation). All of this is a remarkable advance, given that the first confirmed exoplanet discovery did not occur until 1992.
Most of the discoveries mentioned above are planets that are either too large or too close to their sun to possess liquid water, much
Continue reading How many habitable exoplanets are there, really?
A large cluster galaxy in the center acts as a gravitational lens, splitting the light from a more distant supernova into four yellow images (arrows)
The standard model of physics has reigned supreme since the 1970s, successfully describing experimental physical reality in a vast array of experimental tests. Among other things, the standard model predicted the existence of a particle, now known as the Higgs boson, underlying the phenomenon of mass. This particle was experimentally discovered in 2012, nearly 50 years after it was first predicted.
Yet physicists have known for many years that the standard model cannot be the
Continue reading How fast is the universe expanding? New results deepen the controversy
Complex of bacteria-infecting viral proteins modeled in CASP 13
Introduction
In an advance that may presage a dramatic new era of pharmaceuticals and medicine, DeepMind (a subsidiary of Alphabet, Google’s parent company) recently applied their machine learning software to the challenging problem of protein folding, with remarkable success. In the wake of this success, DeepMind and other private companies are racing to further extend these capabilities and apply them to real-world biology and medicine.
The protein folding problem
Protein folding is the name for the physical process in which a protein chain, defined by a linear sequence of amino
Continue reading Protein folding via machine learning may spawn medical advances
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