
Homo Deus
In his new book Homo Deus, Israeli scholar Yuval Noah Harari has published one of the most thoughtful and farreaching analyses of humanity’s present and future. Building on his earlier Sapiens, Harari argues that although humanity has made enormous progress across in the past few centuries, the future of our society, and even of our species, is uncertain.
Harari begins with a reprise of human history, from prehistoric times to the present. He then observes that although religious beliefs are much more nuanced and sophisticated than in the past, human society still relies heavily on the narratives
Continue reading Homo Deus: A brief history of tomorrow
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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
Continue reading Mathematicians prove result tied to the Riemann hypothesis
A colony of the new Syn61 bacteria; credit: BBC
Creating life
In a remarkable development with farreaching consequences, researchers at the Cambridge Laboratory of Molecular Biology have used a computer program to rewrite the DNA of the wellknown 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 wellknown maverick biomedical researcher known for the “shotgun” approach to genome sequencing pioneered by his team at
Continue reading Computational tools help create new living organism
Optimal stacking of oranges.
The spherepacking 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 17thcentury 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
Continue reading Researchers use “magic functions” to prove spherepacking results
Introduction
Right off, it may not sound like pi, climate change denial and youngEarth 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
Continue reading Pi, climate change denial and creationism
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
Continue reading Google AI system proves over 1200 mathematical theorems
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
Continue reading Phacking and scientific reproducibility
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Credit: MathIsFun.com
The discovery of decimal arithmetic
The discovery of decimal arithmetic in ancient India, together with the wellknown 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
Continue reading An n log(n) algorithm for multiplication
LENR: Science or pseudoscience?
As chronicled in the earlier Math Scholar blog, a community of researchers has been pursuing a new green energy source, known as “low energy nuclear reaction” (LENR) physics, or, variously, “latticeassisted nuclear reaction” (LANR) physics or “condensed matter nuclear reaction” (CMNR) physics. This work harkens back to 1989, when University of Utah researchers Martin Fleischmann and Stanley Pons that they had achieved desktop “cold fusion,” in a hastily called news conference. After several other laboratories failed to reproduce these findings, the scientific community quickly concluded that the Utah researchers were mistaken, to put it mildly.
But
Continue reading LENR: A skeptical perspective
The Norwegian Academy of Science and Letters has awarded the Abel Prize, a mathematical award often regarded as on a level with the Nobel Prize, to Karen Uhlenbeck of the University of Texas, USA.
The award cited her work in geometric analysis, gauge theory and global analysis, which has application across a broad range of modern mathematics and mathematical physics, including models for particle physics, string theory and general relativity.
Her career began in the mid1960s, under the advisor Richard Palais. Palais had been exploring some connections between analysis (generalizations of calculus) and topology and geometry (the mathematical theory of
Continue reading Karen Uhlenbeck wins the Abel Prize

