by Ashutosh Jogalekar Considered the epitome of genius, Albert Einstein appears like a wellspring of intellect gushing forth fully formed from the ground, without precedents or process. There was little in his lineage to suggest genius; his parents Hermann and Pauline, while having a pronounced aptitude for mathematics and music, gave no inkling of the…
by John Allen Paulos The well-known counterintuitive Monty Hall problem continues to baffle people if the emails I receive are any indication. A meta-problem is to understand why so many people are unconvinced by the various solutions. Sometimes people even cite the large number of the unconvinced as proof that the solution is a matter…
by John Allen Paulos I’ve always liked stories that depended on mistaken identity, a very old theme in general. Having a degree in mathematical logic, I was also drawn to the subject on a more theoretical level, on which lies Gettier’s Paradox. Since Plato and the ancient Greeks, knowledge has been taken by many philosophers…
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John Allen Paulos in Slate: Imagine there are 100 toy blocks in front of a toddler. Each of the blocks costs $1, 50 of them are red, 50 blue, and to build a sturdy little house requires about 75 or so blocks. By necessity the house will contain blocks of both colors—even if the child…
John Allen Paulos at ABC News: Here's the situation. Three people enter a room sequentially and a red or a blue hat is placed on each of their heads depending upon whether a coin lands heads or tails. Once in the room, they can see the hat color of each of the other two people…
by Jonathan Kujawa On “Things to Make and Do in the Fourth Dimension” by Matt Parker. I came dangerously close to not becoming a mathematician. Like many people my experiences with math in school left me irritated and bored. I have a poor memory and I'm not a detail oriented person [1]. The arbitrary rules…
John Allen Paulos in Slate: The present political and cultural climate seems to have led to an intensifying of the natural human tendency to hurl charges of hypocrisy at one another. Rather than partaking in this pleasant activity and pointing to the many current instances of political or personal hypocrisy, I’d like here to offer…
John Allen Paulos responds to the question, “What insight or idea has thrilled or excited you?” in The Atlantic: I could mention my first introduction to Godel’s theorem about the essential incompleteness of mathematics; or my first encounter with the Banach-Tarski theorem in topology showing that a sphere the size of a pea can be…
John Allen Paulos in The New York Times: The essayist Alain de Botton has been writing a great deal lately about crushes, those sudden infatuations aroused by the merest of stimuli — the way she subtly rolls her eyes at a blowhard’s pronouncements, her intentional dropping of a glass to attract a waiter’s attention, the…
John Allen Paulos in the New York Times: Bertrand Russell once wrote that mathematics had a “beauty cold and austere.” In this new book, the historian Amir Alexander shows that mathematics can also become entangled in ugliness hot and messy. The time was the late 16th and 17th centuries, and the mathematics in question was…
Transcript from NPR: IRA FLATOW, HOST: This is SCIENCE FRIDAY. I'm Ira Flatow. Every member of the House of Representatives and a few from the Senate, about a third of the Senate, I believe, is up for re-election this year. There will be hundreds of debates, local and national. Candidates will be asked questions about…
John Allen Paulos in the New York Times: I’ve visited Singapore a few times in recent years and been impressed with its wealth and modernity. I was also quite aware of its world-leading programs in mathematics education and naturally noted that one of the candidates for president was Tony Tan, who has a Ph.D. in…
John Allen Paulos in the New York Times: One way to get a clearer picture of an electorate’s preferences is to ask prospective voters to rank the candidates and not merely say which one is their first choice. Who is their second choice, third, fourth, fifth? Doing this allows us to get a better overall…
John Allen Paulos in the New York Times Book Review: Sharon Bertsch McGrayne introduces Bayes’s theorem in her new book with a remark by John Maynard Keynes: “When the facts change, I change my opinion. What do you do, sir?” Bayes’s theorem, named after the 18th-century Presbyterian minister Thomas Bayes, addresses this selfsame essential task:…
Sharon Bertsch McGrayne introduces Bayes’s theorem in her new book with a remark by John Maynard Keynes: “When the facts change, I change my opinion. What do you do, sir?” Bayes’s theorem, named after the 18th-century Presbyterian minister Thomas Bayes, addresses this selfsame essential task: How should we modify our beliefs in the light of…
John Allen Paulos in his Who's Counting column at ABC News: A claim of prejudicial treatment is the basis for many news stories. The percentage of African-American students at elite universities, the ratio of Hispanic representatives in legislatures, and, just recently, the proportion of women among Wikipedia contributors have all been written about extensively. Oddly…
John Allen Paulos in Scientific American: The number of friends we have is typical of many situations in which the average deviates from individuals’ experience. Another is class size. Let’s imagine a small department offering three courses for the semester. One is a survey course with 80 students, one an upper-level course with 15 students,…
John Allen Paulos in his Who's Counting column at ABC News: To obtain a fair result from a biased coin, the mathematician John von Neumann devised the following trick. He advised the two parties involved to flip the coin twice. If it comes up heads both times or tails both times, they are to flip…
John Allen Paulos in the New York Times: Half a century ago the British scientist and novelist C. P. Snow bemoaned the estrangement of what he termed the “two cultures” in modern society — the literary and the scientific. These days, there is some reason to celebrate better communication between these domains, if only because…