A “freakishly” finetuned universe
Ever since the time of Copernicus, the overriding worldview of scientific discovery has been that there is nothing special about Earth and humanity: the Earth is not the center of the solar system — we are merely one of several planets orbiting the Sun; the Sun is not the center of the Milky Way — it is merely one of over 100 billion stars in the galaxy; the Milky Way is not the center of the universe — it is merely one of over 100 billion galaxies in the universe; etc. Indeed, this “Copernican principle” has
Continue reading Fine tuning and Fermi’s paradox
A potentially momentous milestone has been reached in the decadesold battle between human intelligence and artificial intelligence.
Go playing board
Until 18 months ago ago, the ancient Chinese game of Go had firmly resisted attempts to apply computer technology — the best human players were substantially better than the best computer programs. This changed abruptly in March 2016, when a Google computer program named “AlphaGo” defeated the reigning world champion 41, a defeat that shocked many observers, who had not expected to see this for many years.
Now a new computer program, called “AlphaGo Zero,” which literally taught itself
Continue reading New Goplaying program teaches itself, beating previous program 1000
Keith Devlin, wellknown mathematician and author, has published two books on Leonardo Pisano (Leonardo of Pisa), better known to many today as “Fibonacci,” short for “filius Bonacci” (son of the Bonacci family), a name ascribed to Leonardo by the 19th century French historian Guillaume Libri. Devlin argues that Leonardo deserves to be ranked among the alltime most influential scientists and mathematicians, mainly for his key role in popularizing the HinduArabic decimal system to Western Europe during the early Renaissance.
Devlin’s books are:
The Man of Numbers: Fibonacci’s Arithmetic Revolution Finding Fibonacci: The Quest to Rediscover the Forgotten Mathematical Genius Who
Continue reading Fibonacci: A man of numbers
The Bakhshali manuscript
The Bakhshali manuscript is an ancient mathematical treatise that was found in 1881 in the village of Bakhshali, approximately 80 kilometers northeast of Peshawar (then in India, now in Pakistan). Among the topics covered in this document, at least in the fragments that have been recovered, are solutions of systems of linear equations, indeterminate (Diophantine) equations of the second degree, arithmetic progressions of various types, and rational approximations of square roots (more on this below).
The manuscript features an extensive usage of decimal arithmetic — the same fullfledged positional decimal arithmetic with zero system that we
Continue reading Origin of decimal arithmetic with zero pushed back to 3rd century CE
The California Community College mathematics controversy
Eloy Ortiz Oakley, the Chancellor of the California Community College system, recently recommended that intermediate algebra should no longer be required to earn an associate degree, excerpt for students majoring in some field of mathematics, science or engineering (see also this Physics Today report):
Collegelevel algebra is probably the greatest barrier for students — particularly firstgeneration students, students of color — obtaining a credential. … [I]f we know we’re disadvantaging large swaths of students who we need in the workforce, we have to question why. And is algebra really the only means we have
Continue reading Does mathematical training pay off in the long run?
The 1897 Indiana pi episode
Many of us have heard of the Indiana pi episode, where a bill submitted to the Indiana legislature, written by one Edward J. Goodwin, claimed to have squared the circle, yielding a value of pi = 3.2. Although the bill passed the Indiana House, it narrowly failed in the Senate and never became law, due largely to the intervention of Prof. C.A. Waldo of Purdue University, who happened to be at the Indiana legislature on other business. The story is always good for a laugh to lighten up a dull mathematics lecture.
It is worth
Continue reading Pi and the collapse of peer review
Hollywood stars as public spokespersons
Nowadays it is not at all unusual for Hollywood stars to lend their public celebrity status to endorse or promote some cause. For example, Angelina Jolie has lent her name and support to international efforts dealing with the refugee crisis. Sean Penn personally assisted efforts to deal with the Haiti earthquake crisis.
What’s more, some Hollywood stars and celebrities have bona fide scientific credentials and achievements. Perhaps the most notable example is Hedy Lamarr, an AustrianAmerican actress who starred in movies such as the 1938 film Algiers, directed by John Cromwell, and the 1949 film
Continue reading Are Hollywood stars qualified to comment on science?
What do exoplanets, fourbillionyearold life, Fermi’s paradox and zeroone laws of probability theory have to do with each other? Quite a bit, actually. Let us review these developments, one by one:
New exoplanet discoveries
Depiction of the seven exoplanets of the TRAPPIST1 system. Courtesy NASA.
On 22 February 2017, a consortium of NASA and European astronomers announced that there are not just one but seven planets that potentially could harbor life, all orbiting a yellow dwarf star named TRAPPIST1, about 40 lightyears (235 trillion miles or 378 trillion km) from earth. This is clearly a remarkable discovery, adding seven to
Continue reading Exoplanets, 4 billionyearold life, Fermi’s paradox and zeroone laws
The latest international results comparing Grade 4 and Grade 8 students in mathematics and science are in, and, once again, the Asian tigers (China, Korea, Japan, and Singapore) are roaring, significantly leading major firstworld nations such as the United States, England and Australia.
TIMSS results
The Trends in International Mathematics and Science Study (TIMSS) is an international test to compare the achievement of fourth and eighth grade students in mathematics and science. It has been administered every four years since 1995, thus providing a 20year period for study of educational trends around the world.
In November 2016, results for the
Continue reading Asian tigers roar in the latest TIMSS mathscience rankings
Computer proofs
Considerable attention has been drawn to the discovery and proof of mathematical theorems by computer.
Perhaps the first major result by a computer came in 1976, with a proof of fourcolor theorem, namely the assertion that any map (with certain reasonable conditions) can be colored with just four distinct colors for individual states. This was first proved by computer in 1976, although flaws were later found, and a corrected proof was not completed until 1995.
In 2003, Thomas Hales of the University of Pittsburgh published a computerbased proof of Kepler’s conjecture, namely the assertion that the familiar method
Continue reading Are humans or computers better at mathematics?

