2019 April « Math Scholar

Pi, climate change denial and creationism

Introduction

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.

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 this Math Scholar blog for details).

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Google AI system proves over 1200 mathematical theorems

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 also disappointed.

A breakthrough of sorts came in the

Continue reading Google AI system proves over 1200 mathematical theorems

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

MathJax TeX Test PageMathJax.Hub.Config({tex2jax: {inlineMath: [[‘$’,’$’], [‘\$‘,’\$’]]}});

Credit: MathIsFun.com

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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Math Scholar

Pi, climate change denial and creationism

Google AI system proves over 1200 mathematical theorems

P-hacking and scientific reproducibility

An n log(n) algorithm for multiplication

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