...a companion blog to "Math-Frolic," specifically for interviews, book reviews, weekly-linkfests, and longer posts or commentary than usually found at the Math-Frolic site.

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"Mathematics, rightly viewed, possesses not only truth, but supreme beauty – a beauty cold and austere, like that of sculpture, without appeal to any part of our weaker nature, without the gorgeous trappings of painting or music, yet sublimely pure, and capable of a stern perfection such as only the greatest art can show." ---Bertrand Russell (1907) Rob Gluck

"I have come to believe, though very reluctantly, that it [mathematics] consists of tautologies. I fear that, to a mind of sufficient intellectual power, the whole of mathematics would appear trivial, as trivial as the statement that a four-legged animal is an animal." ---Bertrand Russell (1957)

******************************************************************** Rob Gluck

Tuesday, June 20, 2017

Ed Scheinerman.... Seeing Masterpieces In Mathematics

Math-Frolic Interview #42


I fear that too many people’s mathematics education is devoid of joy. Imagine if children’s reading education focused primarily on  spelling and punctuation, but not on delights such as Harry Potter or creating stories of one’s own; that approach would hardly instill students with a love of literature.
-- Ed Scheinerman


Thus far, Dr. Ed Scheinerman's "The Mathematics Lover's Companion" is my favorite popular math book of this year. It's a buffet of somewhat typical math topics that are well-worn in other volumes, but Ed's specific mix and engaging writing style about what he views as "masterpieces" of math-thought, help raise the volume above most of its counterparts. The 23 chapter headings from the Table of Contents give you a hint of the content, but not of Ed's fresh, clear writing style (he has previously won awards from MAA for his expository writing):  
https://www.ams.jhu.edu/ers/books/math-lovers-companion/

I definitely recommend the volume to budding math enthusiasts, and seasoned ones as well!
I was happy to get Dr. Scheinerman's responses to a few questions:

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1) Just by way of introduction can you briefly recount your own path to becoming a professional mathematician?

From about grade 7 on I was very fortunate to have had excellent mathematics teachers. Geometry was almost entirely doing proofs; proof was a wholly unexpected concept for me and greatly sparked my interest. Of particular importance though was my 10th grade mathematics teacher, John Wells, who emphasized mathematics as a creative subject. He encouraged and supported my mathematical interests, including advocating my application to the Hampshire College Summer Studies in Mathematics led by David Kelly. Attending that program was undoubtedly the most important catalyst in my path to becoming a mathematician.

[...currently, Dr. Scheinerman is a mathematics professor at Johns Hopkins University]

2)  Your prior writing seems to be mostly technical or academic in nature… what made you decide to write a “popular” math book, and who would you say the book is primarily written for?

I find that most people do not have a good sense of what mathematics is about. It seems to me that all the “good stuff” is left out of a typical high school curriculum. It is not unusual for me to meet people that know what a prime number is, but have no idea (and likely never considered) that there are infinitely many or how one can prove this. Showing that there are infinitely many primes is certainly accessible to high school students. 

We don’t teach English to students just so they can read instructions and write advertising copy. Were we to teach English the way we teach mathematics, we’d omit reading any Shakespeare and students would conflate spelling and literature, just as most people conflate arithmetic and mathematics. I recall (with horror) attending a presentation by a highly distinguished journalist who quipped that he “could never understand what an isosceles triangle was” and the audience laughed in agreement. 

My goal therefore is to provide a bit of an antidote: to present exciting mathematical topics that are accessible at the high school level that readers can enjoy.

3)  What might you say sets your book apart from many other volumes that cover similar topics… or why might someone familiar with these topics still enjoy reading your volume?

I tried in this book to “get to the point” for my reader. One can purchase entire books on (say) the number π but I sought to give my reader a “tasting menu” of great mathematics in which each chapter stands independent of the others. That way the reader can skip around, or put the book aside for a while to return later for another round of fun.

4)  What were some other subjects you considered for inclusion in the book, but in the end didn’t make the cut as math "masterpieces”?

I struggled mightily to write a chapter about the Axiom of Choice. I was not able to present it in a way that I thought my readers would find intelligible and interesting. I think it’s just too technical and the path to interesting consequences (e.g., nonmeasurable sets) too difficult for my intended audience.

5)  Who have been some of your own favorite “popularizers” of math over the years?

Without doubt one name stands above all others: Martin Gardner. I avidly read his Scientific American column and his many books.

[...Martin, a non-professional-mathematician, would no doubt be heartened, yet surprised, at how often his name comes up in this context!]

6)  The first two parts of the book essentially cover elements of algebra and geometry, fitting topics for a math volume, while Part 3 is about “Uncertainty” (a favorite topic of mine). Can you say a little about how that came to be the third big subject area of the book?

I must admit that the organization of the book arose after the chapters were written. I had (nearly) two dozen independent chapters and sought a way to arrange them. The broad headings of number, shape, and uncertainty worked.

7)  Do you have any further “popular” math books in mind to write?

Both I and my editor are encouraged by the positive reception this book has been getting (including a shout-out in the New York Times Review of Books) so I’m working on a Mathematics Lover’s Companion, Volume 2. My first chapter is written and it’s a “do it yourself” introduction about mathematical research that will demonstrate the process (including some of the frustration and then the joy) of mathematical discovery. It should be widely accessible even to folks whose algebra has completely rusted.

[...this is great to hear about!]

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Thanks for the answers here Dr. Scheinerman; very much looking forward to your next volume (and hoping you find a way to include the Axiom of Choice! ;)




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