CTK Insights

23 Oct

The Best Writing on Mathematics

I could not agree more with David Mumford's introduction to the latest anthology edited by Mircea Pitici for the Princeton University Press:

If we learn to say things simply and build up slowly from the concrete to the abstract, we may be able to build many bridges among our various specialties. For me, this style will always be The Best Writing on Mathematics, and this book is full of excellent examples of it.

During the past year I had a chance to read some of the included articles. I may only applaud their selection into the anthology. Terence Tao gave a lecture " Structure and Randomness in the Prime Numbers" at the 50th International Mathematical Olympiad. "How to Be a Good Teacher Is Undecidable Problem" by Erica Flapan, "How Your Philosophy of Mathematics Impacts Your Teaching" by Bonnie Gold,"Augustus De Morgan Behind the Scenes" by Charlotte Simmons were plucked from The College Mathematics Journal, "Was Cantor Surprised?" by Fernando GouvÍa from The American Mathematical Monthly, while "Mathematics Meets Photography" by David Swart and Bruce Torrence from Math Horizons; "Bottom Line in Mathematics Education" by David Mumford and Sol Grafunkel was originally written for the Huffington Post; "Why Math Works?" by Mario Livio and "The Strangest Numbers in String Theory" by John Baez and John Huerta were published in Scientific American, "The Unplanned Impact of Mathematics" by Peter Rowlett in Nature.

The rest of the chapters are new to me. Timothy Gowers in "Is Mathematics Discovered or Invented?" expresses a belief that the question does not have a satisfactory answer and proceeds with illuminating analysis and examples from (and outside of) mathematics some of which are better characterized as discovered (or observed) while others as invented (or created). The mathematician Gowers' view is only partially in agreement with that of the astrophysicist Mario Livio. According to Livio,

... humans invent mathematical concepts by way of abstracting elements from the world around them - shapes, lines, sets, groups, and so forth - either for some specific purpose or simply for fun. They then go on to discover the connections among those concepts.

I have not yet had the time to read all of the book. One thing I noticed, though, is that of the three volumes of "The Best Writings" the latest is the shortest. Indeed, the 2010 volume claimed 408 pages, the next one was 382 pages long, while in the 2012 anthology there are only 288 pages. The material selected by the editor is of highest quality, making the books a delightful and engaging read. Hopefully, the diminishing size of the books is not an indication of the publisher's intent to eventually discontinue the series.

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