Book review: The Best Writing on Mathematics, 2018 by Mircea Pitici
The Best Writing on Mathematics is an annual collection of essays about mathematics. These are not the sort of pieces you would see in scholarly journals of mathematics. Not only are they not about new mathematical results, but the intended audience is much broader. None of these essays require advanced training in mathematics; for nearly all of them, secondary school math would be plenty. Rather, these are the sorts of articles you might find in a mainstream journal such as The New Yorker or Harpers, but with a focus on some aspect of math.
This collection, published in 2019, contains 18 essays that were published in 2017. They range from “tightly argued theoretical positions to bold speculations on the limits of the applicability of mathematics”. In this edition, my favorite pieces included:
• Francis Su on Mathmatics for Human Flourishing. Su reports that he got a letter from a man who was in prison for a series of armed robberies, was addicted to drugs and did not graduate from high school. The man wrote to Su for help in learning advanced calculus. From this, Su goes on to lamen the poor perception of mathematics and to offer some remedies, The subsections of this essay are titled
Su appears to be aiming primarily at math teachers and professors; the piece first appeared in The American Mathematical Monthly. But anyone who believes that math is important, and particularly anyone who teaches or helps anyone learn mathematics (even if you are just helping your kids with their homework) will appreciate this piece.
• The Bizarre World of Nontransitive Dice by James Grime. Grime investigates sets of three or more dice that have a very odd property: They are non-transitive. In other words, if you have three dice (A, B and C) and roll A and B, A is more likely to win; if you roll B and C, B is more likely to win, but if you roll A and C, C is more likely to win.
. This is deeply weird and Grimes explains it well.
• The Bingo Paradox by Arthur Benjamin, Joseph Kisenwether, and Ben Weiss. In an ordinary game of Bingo, if you have a lot of players, it is much more likely that the first “Bingo!” will be from a horizontal row than a vertical column. Another very counterintuitive result and another good explanation.
• The Sleeping Beauty Controversy by Peter Winkler.
Sleeping Beauty agrees to the following experiment. On Sunday, she is put to sleep and a fair coin is flipped. If it comes up heads, she is awakened on Monday morning; if tails, she is awakened on Monday and again on Tuesday morning. In all cases, she is not told the day of the week, is put back to sleep shortly after, and will have no memory of any Monday or Tuesday awakenings.
When Sleeping Beauty is awakened on Monday or Tuesday, what is the probability — to her — that the coin came up heads?
This question has spawned an incredibly large literature and consensus on the answer has not been reached. Winkler guides us through that literature.
• Written in Stone: The World’s First Trigonometry Revealed in an Ancient Babylonian Tablet by Daniel Mansfield and N. J. Wildberger. It turns out that the Babylonians knew a lot of trigonometry and, thanks to their base 60 number system, could get exact results for many cases where the later Greeks could not.