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

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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

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Protein folding via machine learning may spawn medical advances

Complex of bacteria-infecting viral proteins modeled in CASP 13


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

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Mathematicians prove result tied to the Riemann hypothesis

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Ken Ono, Emory University

Don Zagier, Max Planck Institute

Michael Griffin, BYU

Larry Rolen, Vanderbilt University


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

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Pi, climate change denial and creationism


Right off, it may not sound like pi, climate change denial and young-Earth creationism have much in common. In fact, there is an important connection. Here is some background.

Credit: Michele Vallisneri, NASA JPL

Computing pi

Pi = 3.1415926535…, namely the ratio between the circumference of a circle and its diameter, has fascinated not only mathematicians and scientists but the public at large for centuries. Archimedes (c.287–212 BCE) was the first to present a scheme for calculating pi as a limit of perimeters of inscribed and circumscribed polygons, as illustrated briefly in the graphic to the right (see

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Google AI system proves over 1200 mathematical theorems

The Chudnovsky formula for Pi (Credit: Craig Wood)

AI’s rocky start

The modern field of artificial intelligence (AI) began in 1950 with Alan Turing’s landmark paper Computing machinery and intelligence, which outlined the principles of AI and proposed a test, now known as the Turing test, for establishing whether AI had been achieved. Although early researchers were confident that AI systems would soon be a reality, inflated promises and expectations led to the “AI Winter” in the 1970s, a phenomenon that sadly was repeated again, in the late 1980s and early 1990s, when a second wave of AI systems

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P-hacking and scientific reproducibility

Credit: Wikimedia

The reproducibility crisis in science

Recent public reports have underscored a crisis of reproducibility in numerous fields of science. Here are just a few of recent cases that have attracted widespread publicity:

In 2012, Amgen researchers reported that they were able to reproduce fewer than 10 of 53 cancer studies. In 2013, in the wake of numerous recent instances of highly touted pharmaceutical products failing or disappointing when fielded, researchers in the field began promoting the All Trials movement, which would require participating firms and researchers to post the results of all trials, successful or not. In

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An n log(n) algorithm for multiplication

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The discovery of decimal arithmetic

The discovery of decimal arithmetic in ancient India, together with the well-known schemes for long multiplication and long division, surely must rank as one of the most important discoveries in the history of science. The date of this discovery, by an unknown Indian mathematician or group of mathematicians, was recently pushed back to the third century CE, based on the recent dating of the Bakhshali manuscript, but it probably happened earlier, perhaps around 0 CE.

Arithmetic on modern computers

Computers, of course, do not use

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