## The scientific debate is over: it is time to act on climate change

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

## Quantum supremacy has been achieved; or has it?

IBM’s “Q” quantum computer; courtesy IBM

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

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## Pi as the limit of n-sided circumscribed and inscribed polygons

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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 $\pi = 17 – 8 \sqrt{3} = Continue reading Pi as the limit of n-sided circumscribed and inscribed polygons ## New paper proves 80-year-old approximation conjecture MathJax TeX Test PageMathJax.Hub.Config({tex2jax: {inlineMath: [[‘$’,’$’], [‘\$$‘,’\$$’]]}}); 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 ## How many habitable exoplanets are there, really? 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? ## How fast is the universe expanding? New results deepen the controversy 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 ## Protein folding via machine learning may spawn medical advances 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 ## Mathematicians prove result tied to the Riemann hypothesis MathJax TeX Test PageMathJax.Hub.Config({tex2jax: {inlineMath: [[‘$’,’\$’], [‘\$$‘,’\$$’]]}});

Ken Ono, Emory University

Don Zagier, Max Planck Institute

Michael Griffin, BYU

Larry Rolen, Vanderbilt University

Introduction

Four mathematicians, Michael Griffin of Brigham Young University, Ken Ono of Emory University (now at University of Virginia), Larry Rolen of Vanderbilt University and Don Zagier of the Max Planck Institute, have proven a significant result that is thought to be on the roadmap to a proof of the most celebrated of unsolved mathematical conjecture, namely the Riemann hypothesis. First, here is some background:

The Riemann hypothesis

The Riemann hypothesis was first posed by the German

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## Computational tools help create new living organism

A colony of the new Syn61 bacteria; credit: BBC

Creating life

In a remarkable development with far-reaching consequences, researchers at the Cambridge Laboratory of Molecular Biology have used a computer program to rewrite the DNA of the well-known bacteria Escherichia coli (more commonly known as “E. coli”) to produce a functioning, reproducing species that is far more complex than any previous similar synthetic biology effort.

Venter’s 2010 project

This effort has its roots in a project spearheaded by J. Craig Venter, the well-known maverick biomedical researcher known for the “shotgun” approach to genome sequencing pioneered by his team at

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## Researchers use “magic functions” to prove sphere-packing results

Optimal stacking of oranges.

The sphere-packing problem

The Kepler conjecture is the assertion that the simple scheme of stacking oranges typically seen in a supermarket has the highest possible average density, namely pi/(3 sqrt(2)) = 0.740480489…, for any possible arrangement, regular or irregular. It is named after 17th-century astronomer Johannes Kepler, who first proposed that planets orbited in elliptical paths around the sun.

Hales’ proof of the Kepler conjecture

In the early 1990s, Thomas Hales, following an approach first suggested by Laszlo Fejes Toth in 1953, determined that the maximum density of all possible arrangements could be obtained