Real-world issues about mathematics

A Big Think article, which draws on the ideas of Kurt Gödel, and thinks about whether mathematics is built on unproven foundations.

Mordechai Levy-Eichel in Aeon considers various aspects of mathematics for – its “joyful, beautiful” nature, its role in shaping modern society, and the way in which it often neglected when people consider the history of ideas.

This Medium blog comparing mathematics and the natural sciences, and offers some very useful definitions for both these areas of knowledge. It also considers the role of inference in creating knowledge.

A New York Times article, that explores the reason why the equation 8 ÷ 2(2+2) = ? went viral (and why mathematicians hate it).

This is one of the biggest science stories of the last few years (decades, perhaps) – the images of the M87 Black Hole, created from the data created by various telescopes positioned around the world. Here is the coverage from Time, The The Guardian, Vox, and The Washington Post.

A Conversation article, applying mathematical knowledge to the Euro 2020 Panini sticker album.

This Atlantic story looks at a new algorithm-based tool, COMPAS, that is supposed to be able to calculate (ie predict) a defendant’s risk of committing another crime. However, it seems that the tool is no more accurate than “random volunteers recruited from the internet”.

This Wired article looks at how a ‘predictive policing tool’ – a database created by London’s Metropolitan police – is being used to calculate the risks posed by individuals, and determine the actions taken against them by the authorities.

A Discover Magazine article about the way most people use the word and concept ‘average’ in a misguided way.

A Vox article, showing you the mathematics behind Covid-19, and why this is essential to understanding the pandemic. 

A Discover Magazine article, evaluating what statistics can reveal about the scale of serial killers who were never caught.

This Aeon essay examines how we generate figures of probability, pointing out that there are different possible approaches, suggesting that the concept of probability is not as simple as we think.

This short Aeon video by Cathy O’Neil ponders the nature of algorithms, and challenges the idea that they represent “indisputable mathematical truths”.

A Conversation article, looking at how research in mathematics is a deeply imaginative and intuitive process – aided by AI.

This Smithsonian article considers how the discovery of the Möbius strip in the mid-19th century launched a brand new field of mathematics: topology.

This Science story looks at the claim by Sir Michael Atiyah that he has solved the Riemann hypothesis, a mathematical problem relating to prime numbers that has existed for more than a century and a half. It examines why this solution is unlikely to actually have been discovered.

A Veritasium video, which outlines the Collatz Conjecture – the simplest mathematical problem no one can solve.

This Vox article considers the ‘genius’ of the discovery of the concept of zero, and the implications behind this step forward for mathematicians.

Oliver Roeder at FiveThirtyEight looks at the discovery of the largest ever prime number, and how such discoveries have proceeded over the years. He also considers why we are compelled to continue looking for these special numbers.

An Aeon video, looking at why Bayes’ Theorem has an increasing relevance in the world of ‘big data’, and how it can help us to “reprogramme our intuition”.

A New York Times article that explores the reason why the equation 8 ÷ 2(2+2) = ? went viral (and why mathematicians hate it).