Love and Math

Frenkel Edward 2008Talking of his grandfather who had overcome poverty and blindness to become a US Senator, Gore Vidal once wrote that no challenge is finally insurmountable if you mean to prevail.  I was reminded of this in reading Edward Frenkel’s superb memoir, Love and Math.  Frenkel overcame the widespread and systemic anti-semitism in Soviet Mathematics to establish himself as a world-leading mathematician at a very young age.

Denied entry in 1984 because of his ethnicity to Moscow State University’s (MGU’s) Department of Mechanics and Mathematics (Mekh-Mat), the leading undergraduate mathematics programme in the USSR, he entered instead the mathematics program at Kerosinka, the Moscow Institute of Oil and Gas.  Anti-semitism (and anti-Armenianism, anti-Chinese racism, etc) in the admissions process at Mekh-Mat was so widespread, that other Moscow institutions, such as Kerosinka, were able to recruit very good Jewish and minority students.   One theory is that this policy was deliberate, since having all the Jewish mathematicians studying in one or two institutions made their monitoring easier for the KGB.

Frenkel had grown up in Kolomna – only 70 miles from Moscow, but well into the provinces – and had not attended a special mathematics school (as did, for example, Vadim Delone at FizMat #2), nor had an opportunity to participate in the mathematical study circles that were widespread in the larger soviet cities.  He did have the help of a local mathematician, Evgeny Petrov, a professor at a teacher training college in Kolomna.   Frenkel was very fortunate to have such help.   I recall my envy on learning on the first day of lectures in my first year at university that some of my fellow students, who had grown up near to the university, had been meeting our professors for years previously for after-school mentoring and coaching. (On the other hand, even the brightest of my fellow students so mentored ended up winning no Fields Medal, nor even becoming a mathematician.)

Good mathematical undergraduates from Kerosinka and other specialized institutes in Moscow literally scaled the fences at MGU to attend, illegally but often with the encouragement of the teachers, lectures at Mekh-Mat.  Frenkel did this and was again fortunate in being befriended by some very great mentors:  Dmitry Fuchs (now at UC Davis), his student Boris Feigin, and Yakov Khurgin.  Their generous mentoring was unpaid, time-intensive, and often brave, given the society they lived in.   As a result, Frenkel wrote his first research paper in only his second year as an undegraduate, a paper subsequently published in Israel Gelfand’s famous journal, Functional Analysis and Applications.  Gelfand was someone that even my professors, in the 1970s and in faraway Australia, spoke of with awe.

With the opening of perestroika, the Mathematics Department at Harvard University decided to invite some young Soviet mathematicians for research visits, and Frenkel was one of these:  He received his invitation in March 1989, before he had even completed his first degree.  While at Harvard, he had another Russian mentor, Vladimir Drinfeld (now at University of Chicago), and Frenkel completed his PhD there, in 1 year, under the supervision of another Russian, Joseph Bernstein (now at Tel-Aviv).  Frenkel is very generous in his acknowledgement of the support he received from his mentors and from others, and his story warms the heart.  Despite the anti-semitism he experienced, he has prevailed in the end, being now a professor at U-Cal Berkeley (and a film-maker).  Reading his account, I was reminded repeatedly of the ancient spiritual wisdom:  When the disciple is ready, the guru will appear.

Frenkel interleaves his personal story with an account of his changing research focus along the way, a focus which has mostly followed the powerful thread of the Geometric Langlands Programme.   His writing is fluent, wise and witty, and he manages to convey well the excitement and pure, joyous exhilaration that mathematical thinking can provide.  His writing makes most of the underlying mathematical ideas clear to non-experts.  That said, however, the text has a couple of weaknesses, both minor, although both I found irritating.  No one who does not already know something of category theory would understand it, even at a high level, from the single paragraph devoted to it on page 156.   Another minor criticism is that the text does not always adequately explain the diagrams, or what is being done with them.    But then I have particular views about reasoning over diagrams.

In summary, this is a superb book – wise, generous, witty, and heart-warming – and reading it will enlarge your knowledge of mathematics, of the Langlands Program, and of the power of the human spirit.   Everyone in the pure mathematical universe should read it.

An index to posts on the Matherati is here.


Edward Frenkel [2013]:  Love and Math:  The Heart of Hidden Reality. New York, NY:  Basic Books.


Gertrude Stein:

One plunges here and there with energy and misdirection during the storm and stress of the making of a personality until at last we reach the twenty-ninth year the straight and narrow gateway of maturity and life which was all uproar and confusion narrows down to form and purpose and we exchange a great dim possibility for a small hard reality.”

Keeping open a great dim possibility, and thus avoiding a narrowing to a small hard reality, is the main purpose of life.

RIP: Peter Geach

The death has occured of British philosopher and logician Peter Geach (1916-2013).
There is a famous story, perhaps apocryphal, of the logician Alfred Tarski, Polish-born but in American exile from WW II, asking his American City College of New York colleague Emil Post why he, Post, was the only prominent propositional logician who was not Polish.   Post replied that he was not born American, but had come to the USA as a child, and had in fact been born in Poland (although at the time part of the Russian empire).   It has seemed at times that Poland cornered the market in logicians and we find yet another example in Peter Geach.  According to his Guardian obituary, his maternal grandparents were Polish.
Long ago, I wrote an essay, in a logic course taught by Paul Thom and Malcolm Rennie, exploring a system of entailment due to Geach.  Then, as now, pure mathematicians mostly disparaged logic, and my university offered no further courses in the discipline that has since become the single most important to artificial intelligence and automated reasoning.   Universities are very good at preparing their graduates for the past; for the future, not so much.

RIP: Natalia Gorbanevskaya

Natalie Gorbanevska 19677
The death occurred last month of Natalia Gorbanevskaya (1936-2013, pictured in 1967), Russian poet and Soviet dissident, and one of the Moscow Seven, brave opponents of the occupation by forces of the Warsaw Pact of Czechoslovakia in August 1968.  From 1975 she lived in exile, initially in Israel and then in France.  For most of this time she was stateless, and did not have a passport until 2006, when granted Polish citizenship.   As in the 19th century, Russia disowns its best and brightest children.  The Economist has an obituary here.
There was more than this one protest against the invasion, with over 200 people involved in protests elsewhere in the USSR and across the Eastern Bloc.  A list of 160 Soviet protesters against the invasion, prepared by Memorial, is here.  The courage of the Moscow Seven and these others has been recognized by the Czech Republic, but not yet by the Russian Federation.   Indeed, Russia has still to apologize to Czechslovakia for the invasion.
From Gorbanevskaya’s poetry (translation by Daniel Weissbort):

The crime has not yet been expunged,
the hour of truth has not yet struck.
logs in the stove still ticking over,
although the fire’s already out.

Recent Reading 10

The latest in a sequence of lists of recently-read books.
David Eagleman [2010]: Sum: Tales from the Afterlives.  (London, UK:  Canongate).  A superb collection of very short stories, each premised on the assumption that something (our bodies, our souls, our names, our molecules, etc) lives beyond death. Superbly fascinating.  One will blow your mind!  (HT: WPN).
A. C. Grayling [2013]:  Friendship.  (New Haven, CT and London, UK:  Yale University Press).
Andrew Sullivan [1998]:  Love Undetectable:  Reflections on Friendship, Sex and Survival.  (London, UK: Vintage, 1999).
Michael Blakemore [2013]: Stage Blood. (London, UK: Faber & Faber).  A riveting account of Blakemore’s time at the National Theatre in London.
Continue reading ‘Recent Reading 10’


Having created lists of concerts I have attended, bands I have heard, galleries I have visited, etc, I overlooked theatre and dance productions I have seen.  Herewith a list, sometimes annotated, to be updated as and when I remember additional events.

  • The Lieutenant of Inishmore, at the Noel Coward Theatre, St Martin’s Lane, London, August 2018.  Martin McDonagh’s very funny satire on the IRA and the INLA, in a well-acted production.  The production was somewhat gory for my tastes.
  • Continue reading ‘Theatre’