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The Best Writing on Mathematics 2017

Mircea Pitici, editor
Princeton University Press
Publication Date: 
Number of Pages: 
[Reviewed by
Allen Stenger
, on

The most striking thing about this collection is how beautiful the writing is. The articles cover a wide variety of topics, with some biographical sketches, some math education, some philosophy, and a moderate amount of actual mathematics. I think there’s something here for everyone, but no one will like all the articles. There are nineteen articles, of which about fourteen (depending on how you categorize) appeared in scholarly journals or collections. So while most of them can be understood and enjoyed by the intelligent lay reader, that was usually not the original audience. This is the eighth annual edition in the series, all with the same editor.

My favorite articles: a sketch of Richard K. Guy’s life on the occasion of his hundredth birthday; an article encouraging children to count on their fingers (I still do this, I didn’t realize it was out of fashion); a very interesting speculation by Jeremy Gray on what would have happened if the Fields Medal had started 150 years ago instead of 80 (he thinks math was much poorer in talent back then, and it would have been hard to line up both judges and prizewinners); a thought-provoking article on using the catenary to find logarithms (this goes back to Leibniz), which leads to a consideration of why we consider some functions fundamental and others not; an interesting although inconclusive look at whether the human brain is Bayesian; and a wide-ranging look at how the science of prediction has changed over the years (how impressive are those political predictions, really?).

In addition to the articles, which are the main content, there are also 20 pages of citations for additional interesting articles, and a two-page survey of additional interesting books.

Allen Stenger is a math hobbyist and retired software developer. He is an editor of the Missouri Journal of Mathematical Sciences. His personal web page is His mathematical interests are number theory and classical analysis.

Mircea Pitici ix
Mathematical Products Philip J. Davis 1
The Largest Known Prime Number Evelyn Lamb 7
A Unified Theory of Randomness Kevin Hartnett 10
An “Infinitely Rich” Mathematician Turns 100
Siobhan Roberts 24
Inverse Yogiisms Lloyd N. Trefethen 28
Ramanujan in Bronze Gerald L. Alexanderson 37
Creating Symmetric Fractals Larry Riddle 45
Projective Geometry in the Moon Tilt Illusion Marc Frantz 54
Girih for Domes: Analysis of Three Iranian Domes Mohamm adhossein Kasraei, Yahya Nourian, and Mohamm adjavad Mahdavinejad 64
Why Kids Should Use Their Fingers in Math Class Jo Boaler and Lang Chen 76
Threshold Concepts and Undergraduate Mathematics Teaching Sinéad Breen and Ann O’Shea 82
Rising above a Cause-and-Effect Stance in Mathematics Education Research John Mason 93
How to Find the Logarithm of Any Number Using Nothing but a Piece of String Viktor Blåsjö 99
Rendering Pacioli’s Rhombicuboctahedron Carlo H. Séquin and Raymond Shiau 106
Who Would Have Won the Fields Medal 150 Years Ago? Jeremy Gray 121
Paradoxes, Contradictions, and the Limits of Science Noson S. Yanofsky 130
Stairway to Heaven: The Abstract Method and Levels of Abstraction in Mathematics Jean-Pierre Marquis 145
Are Our Brains Bayesian? Robert Bain 172
Great Expectations: The Past, Present, and Future of Prediction Graham Southorn 182
Contributors 193
Notable Writings 199
Acknowledgments 221
Credits 223