Recent expository Articles

January 11, 2008: the article "Mathematical Platonism and its Opposites" is available here as a [PDF] file.

I wrote a "math news" article for the journal Nature ([NATURE Vol 443, 7 September 2006) [PDF] about the recent work on the Sato-Tate Conjecture. (Also, for this article, William Stein did some beautiful calculations. A more complete account of them is available on William Stein's website.) Here is a longer version of this, entitled finding meaning in error terms which started as the text of a lecture I gave in the Current Developments in Mathematics section of the AMS winter meeting in New Orleans in January 2007, but in its present form is now an expository article that I am submitting to the Bulletin of the American Mathematical Society."

I wrote a short piece "About the cover: Diophantus's Arithmetica" [PDF 10 Meg] that appears in the July 2006 issue of the Bulletin of the American Mathematical Society, for which I want to mention an erratum: I erroneously identified the figure on the cover as Erato, muse of erotic poetry, but it seems, rather, to be Orpheus."

I wrote a few words [PDF] in the memory of Serge Lang, a part of which will be published in the "Notices".

I was asked by the french journal "Les Dossiers de la Recherche" to write an expository article, intelligible to a general audience, hinting why prime numbers are exciting and important. The article "Pourquoi les nombres premiers?" appeared in the August-October 2005 issue of that journal. [PDF]

I had a conversation with Peter Pesic about "imagination and mathematics" has appeared in the Spring 2005 issue of the journal "Daedalus" (pp. 124-130). Here is a provisional version of the text as a [PDF]. Here, also, are some notes about Imagination and Mathematics: The Geometry of Thought, a conversation with Eva Brann [PDF] that I wrote to prepare myself for a public event at the Philoctetes Center in New York City on May 13, 2008.

I have recently written an expository article on the theme of deformations entitled "Perturbations, deformations, and variations (and 'near-misses') in geometry, physics, and number theory" for the issue of the Bulletin of the A.M.S. in honor of René Thom (Bull. Amer. Math. Soc. 41 (2004), 307-336). [PDF].

A short article I wrote entitled 'What is a Motive?' [PDF] appeared in the Notices: Notices of the AMS 51, no 10, (2004)1214-1216).

The journal "For the learning of Mathematics" reprinted a section of my book Imagining numbers (particularly the square root of minus fifteen) that dealt with the concept of time in mathematics, and asked me to write an article expanding on that theme. My article, 'On the absence of time in mathematics', [PDF] was published in the November 2004 issue of that journal.

I wrote an expository article for the French journal 'Pour la Science' entitled 'Plus symétrique que la sphere' (Pour la Science Oct/Dec (2003) 78-85), [PDF].

Forewords to Books

I wrote four forewords to books for general audiences. The classic expository text "Number: The Language of Science" by Tobias Dantzig has been republished by pi-Press. It is edited by my brother Joseph Mazur who also wrote an afterword for this republication, and I wrote a foreword for it. Download it as a file: [PDF].

I wrote a foreword for "Fearless Symmetry: Exposing the Hidden Patterns of Numbers" by Avner Ash & Robert Gross. It was published this past year by Princeton University Press. Download it as a file: [PDF].

I wrote forewords for two classic popular books on mathematics written by Lillian R. Lieber, with drawings by Hugh Gray Lieber . These are "The Education of T.C. MITS" published last year by Paul Dry Books [PDF] and "Infinity:Beyond the beyond the beyond" to be published shortly by Paul Dry Books. [PDF].

I wrote a foreword to a book of poems by Emily Galvin ("Do the Math" to be published shortly by Tupelo Press). Download it here [PDF].

Provisional and not yet published

My article "How did Theaetetus prove his Theorem?" has now been published in "The Envisoned Life: Essays in honor of Eva Brann" (eds: P. Kalkavage, E. Salem) Paul Dry Books, Philadelphia, 2007. [PDF] The article discusses the curious fact that although Theaetetus' Theorem is beautifully formulated in Plato's dialogue ("The Theaetetus"), no proof of it seems to have been preserved in what has come down to us from the ancient literature, nor does there seem to be much discussion (in the secondary literature) of what Theaetetus' proof might have looked like.

I am writing an expository piece about Algebraic Numbers as a chapter of a book the Princeton Companion for Mathematics edited by Timothy Gowers, which is to appear soon.