by John Allen Paulos Election season has put an increased focus on the stock market, but little attention is ever paid to the Efficient Market Hypothesis (the EMH, for short). As I’ve written in A Mathematician Plays the Stock Market, it is a fundamental and important notion, but it is also a little weird. Its…
by John Allen Paulos Several years ago the Nobel committee selected two economists, Thomas Schelling of the University of Maryland and Robert Aumann of Hebrew University, to receive the prize for their stellar work on game theory. Aumann has contributed many seminal ideas with real-world applications, one in particular that is especially relevant today. It…
by John Allen Paulos With apologies to Charles Dickens, it will be the best of times, it will be the worst of times. In his recent book, Deep Utopia: Life and Meaning in a Solved World, philosopher Nick Bostrom, the author of Superintelligence, speculates about human and trans-human lives after AI has developed to a kind of…
by John Allen Paulos An abstract paradox discussed by Yale economist Martin Shubik has a logical skeleton that can, perhaps surprisingly, be shrouded in human flesh in various ways. First Shubik’s seductive theoretical game: We imagine an auctioneer with plans to auction off a dollar bill subject to a rule that bidders must adhere to.…
by John Allen Paulos Bertrand Russell’s advice for aging gracefully is rather simple: Broaden your horizons. He recommends that we should try to expand our interests and concerns. Doing so will help us become less focused on ourselves and more open to the world around us. He adds metaphorically, “An individual human existence should be…
by John Allen Paulos Philosopher Daniel Dennett’s new book, I’ve Been Thinking, just came out, and I was reminded of a party game he’s written about. A variant of the child’s game of twenty questions, it is relevant to an increasingly pressing question: How do different social bubbles, media subcultures, or cults develop. Let me…
by John Allen Paulos Over the years I’ve been teaching, many people have asked me about the content of an elementary course I teach. I’m interested in the syllabi and exams of courses in other fields, so this I hope may be of interest to others as well. The survey course on which this exam…
by John Allen Paulos Kurt Gödel was a logician whose work in mathematical logic was seminal and fundamental. His famous incompleteness theorems, in particular, have changed our view of mathematics and computer science. He was born in Austria and lived through political turmoil there before fleeing the country after the Nazis annexed it in 1938.…
by John Allen Paulos Raymond Queneau was a French novelist, poet, mathematician, and co-founder of the Oulipo group about which I wrote last year here. The group is primarily composed of French writers, mathematicians, and academics and explores the use of mathematical and quasi-mathematical techniques in literature. Their work is funny, experimental, weird, and thought-provoking. A reader of…
by John Allen Paulos Despite many people’s apocalyptic response to ChatGPT, a great deal of caution and skepticism is in order. Some of it is philosophical, some of it practical and social. Let me begin with the former. Whatever its usefulness, we naturally wonder whether CharGPT and its near relatives understand language and, more generally,…
Dilip D’Souza in Shaastra: Yet, exactly why is Paulos comparing humour and mathematics? He’s doing what I suspect has become a lifelong pursuit: showing just how ubiquitous mathematics is and how much we lose by being deaf to that truth. He’s doing so by relating mathematics to so much that makes us human. So, there’s…
by John Allen Paulos Intelligibility or precision: to combine the two is impossible. ―Bertrand Russell. Please forgive the long letter; I didn’t have time to write a short one. ―Blaise Pascal I have always resonated with the two quotes above and believe they’re particularly germane to writing popular mathematics. Let me start with Russell. If his…
by John Allen Paulos Numerology can easily result from free association and, given its assertions, it certainly seems like it has been. In any case, I thought I’d try my hand at it. In particular, the date 9-11 and the destruction of the WTC twin towers have together given rise to all sorts of numerological…
by John Allen Paulos I recall a party game I once wrote about. The game, described by philosopher Daniel C. Dennett in his book “Consciousness Explained,” is a variant of the familiar childhood game requiring that one try to determine by means of Yes or No questions a secretly chosen number between one and one…
by John Allen Paulos Herschel Walker claims that we have enough trees already, that we send China our clean air and they return their dirty air to us, that evolution makes no sense since there are still apes around, and freely offers other astute scientific insights. He may be among the least knowledgeable (to put…
by John Allen Paulos The separation of church and state seems to be dissolving. It’s becoming increasingly easy for politicians and other public figures to cross the line between expressing their faith and aggressively proclaiming it and its alleged real-world consequences. Although often leading to social strife and intolerance, such overweening proclamations are growing in…
by John Allen Paulos Lanchester’s square law was formulated during World War I and has been taught in the military ever since. It is marginally relevant to the war in Ukraine, particularly the balance between the quantity and quality of the two armies’ weapon systems. Although more accurately expressed in terms of differential equations, Lanchester’s…
by John Allen Paulos The Ouvroir de Littérature Potentielle (Workshop of Potential Literature), Oulipo for short, is the name of a group of primarily French writers, mathematicians, and academics that explores the use of mathematical and quasi-mathematical techniques in literature. Don’t let this description scare you. The results are often amusing, strange, and thought-provoking. The…
by John Allen Paulos Covid has given rise to a variety of counterintuitive mathematical outcomes. A good example is this recent headline (link below): One third of those hospitalized in Massachusetts are vaccinated. Anti-vaxxers have seized on this and similar such factually accurate headlines to bolster their positions. They, and others as well, interpret them…
by John Allen Paulos In politics, business, and education, the issue of how to ensure proportional representation of groups is often salient. A salient issue, but usually an impossible task. Why? Since group identity and wokeness arouse so much emotion, a “geologic upheaval of thought” as Proust characterized it, it’s probably best to discuss a…