Recent Expository Articles
- February 2013: Here Here [PDF] is the write-up the lecture History of Mathematics as a tool I gave in the History of Mathematics seminar organized this semester by Anthony Liu and Lucia Mocz.
- August 2012: Here are notes to my lecture " A brief introduction to the work of Haruzo Hida for the conference in celebration of the 60th birthday of Haruzo Hida, held at UCLA, June 18-23, 2012
([PDF])
- Here are notes to my lecture "Primes, knots and Po" for the conference in celebration of the 80th birthday of Valentin Poenaru, held in Autrans, France July 1-6, 2012
([PDF])
- Visions, Dreams, and Mathematics
[PDF] was published in the Spring of 2012 by Princeton University Press in a collection of essays ( Circles Disturbed: The interplay of Mathematics and Narrative) that I coedited with Apostolos Doxiadis. Here is an interview I gave to the journal NATURE about this volume: [PDF] and here is a link to brief description I gave of this volume to the online journal Berfrois.
- Here are rough notes entitled
"Is it Plausible?"
([PDF]) related to a talk I gave at the JMM Conference, January 5, 2012
- Here are rough notes entitled
"What is the surface area of a hedgehog?"
([PDF]) related to the Steiner Lecture I gave at St. Johns College in Annapolis, in the Fall of 2012.
- Here [PDF] are the notes for a joint MSRI-UC Berkeley colloquium for
graduate students entitled "Elliptic curves, their companions, and
their statistics" given in the winter of 2011 in conjunction with the MSRI program "Arithmetic Statistics."
- June 17 2010: The Language of Explanation notes [PDF]is an essay I wrote for the University of Utah Symposium in Science and Literature (November, 2009) and in anticipation of a panel discussion on Mathematics,
Language, and Imagination with Alice Fulton and Fred Lerdahl.
- Here are some notes [PDF]
on my Number Theory Seminar lecture "Ranks of twists of elliptic curves" on Feb. 3, 2010.
- Here are the notes [PDF]
to my Basic Notions Talk (Feb 1, 2010) on Hilbert's Tenth Problem and Elliptic Curves.
- I wrote a brief response [PDF]
to a question posed by Phil Davis and David Mumford:
"What should a professional mathematician know?"
- I participated in a panel on Number Theory and Logic at the
MAMLS@Harvard conference (May 9 2009).
Here are my notes [PDF], entitled:
Connections between Logic and Number Theory.
- I gave a brief talk Arithmetic and some of its aspirations
to the "Friends of Harvard Mathematics" on May 5 2009 about Number Theory.
Here are my notes [PDF] for that talk.
- I was asked to give a short (twenty-five minute) talk on the subject
of "Time" in an up-coming conference in Comparative Literature (to be
held at Harvard, March 2009). Here
is a first draft [PDF] of my text, entitled
"On time (in mathematics and literature)."
- May 16, 2008: Here are some notes [PDF]
about Imagination and Mathematics that I wrote to prepare myself for a
public event
at the Philoctetes Center in New York City on May 13, 2008.
- January 11, 2008: the article "Mathematical Platonism and its Opposites" was published in the June 2008 European Mathematical Newsletter (pp.19-21).
It is is available here as a [PDF] file.
For a discussion of this article and related ones see
this website.
- 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."
- Sep. 17, 2007: A version [PDF],
dated Jul 29, 2006 of the article "When is one thing equal to some other thing?".
It has been published in the volume: Proof and Other Dilemmas: Mathematics and Philosophy
B. Gold and R, Simons, Editors (2008) Series: Spectrum.
-
Sept. 5, 2006: A Nature
article ([NATURE Vol 443, 7 September 2006) [PDF]
about the recent work on the Sato-Tate Conjecture (with
computations by William Stein).
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.'
- 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 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.
- Here is 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].
- 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.
- This expository piece [PDF]
about Algebraic Numbers has appeared as a chapter
in the book The Princeton Companion for Mathematics,
by Timothy Gowers, June Barrow-Green, Imre Leader (Editors),
American Mathematical Society (2008).
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].