Archive for the 'Matherati' Category

Reg Gilbert RIP

Reg J Gilbert was an Australian statistician who spent much of his career working in developing countries and for international organizations.  His career began in the Australian Bureau of Statistics after which he worked in Papua New Guinea and later in Botswana. In PNG he was Director of Statistics and led the first national population census in 1980 following Independence in 1975. He died between 2001 and 2004 [See footnote 9, page iv, of Anon 2004].  Although we never met, I keep meeting people in the oddest places who knew him, so I feel like my life has shadowed his. Florence Skelly is another person I never met whose circle of influences I keep encountering.



Reginald J Gilbert [1986]:  The first complete enumeration of Papua New Guinea – The 1980 Population Census. Journal of Official Statistics, 2(4): 501–514.

Reginald J Gilbert [2001]: Asking questions on economic characteristics in a population census.  STAT Working Paper 2001-1, ILO Geneva, Switzerland. 2001.

Anon [2004]:  Collection of Economic Characteristics in Population Censuses.  Technical Report, Statistics Division, Department of Social and Economic Affairs, United Nations Secretariat and Bureau of Statistics, International Labour Office. ST/ESA/STAT/119.  Footnote 9, page iv.

Paris life



A salute to Bella Subbotovskaya

Bella Subbotovskaya (1938-1982) was a Russian mathematician who founded an underground university in Moscow to teach mathematics to students, particularly but not only Jewish students, excluded from education by the anti-Semitic policies of Moscow State University and other institutions of higher learning. The unpaid lecturers in this underground university were both Jewish and non-Jewish. The activity came to be called the Jewish People’s University and operated, against strong KGB harassment, from 1978 to 1983. Her death was due to a suspicious car accident that may well have been a KGB assassination.

I never cease to be amazed at the stupidity of racism. Even in a allegedly rationalist state such as the late USSR, the authorities deemed it desirable to exclude the best students from university on the basis of their ethnicity or religion.


G. Szpiro [2007]: Bella Abramovna Subbotovskaya and the Jewish People’s University. Notices of the American Mathematics Society (NAMS), 54 (10): 1326-1330.

The New World versus the Old

Propose to an Englishman any principle, or any instrument, however admirable, and you will observe that the whole effort of the English mind is directed to find a difficulty, defect, or an impossibility in it.  If you speak to him of a machine for peeling a potato, he will pronounce it impossible:  if you peel a potato with it before his eyes, he will declare it useless, because it will not slice a pineapple.  Impart the same principle or show the same machine to an American, or to one of our colonists, and you will observe that the whole effort of his mind is to find some new application of the principle, some new use for the instrument. ”

Charles Babbage, 1852, in a paper on taxation.  Cited on page 132 of Doron Swade [2000]:  The Cogwheel Brain:  Charles Babbage and the Quest to Build the First Computer. London, UK:  Little, Brown and Company.

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.

Influential Books

This is a list of non-fiction books which have greatly influenced me – making me see the world differently or act in it differently.  They are listed chronologically according to when I first encountered them.

  • 2015 – Benedict Taylor [2011]: Mendelssohn, Time and Memory. The Romantic Conception of Cyclic Form. (Cambridge UP)
  • 2010 – Hans Kundnani [2009]: Utopia or Auschwitz: Germany’s 1968 Generation and the Holocaust. (London, UK: Hurst and Company)
  • 2009 – J. Scott Turner [2007]:  The Tinkerer’s Accomplice: How Design Emerges from Life Itself. (Harvard UP) (Mentioned here.)
  • 2008 – Stefan Aust [2008]: The Baader-Meinhof Complex. (Bodley Head)
  • 2008 – Pierre Delattre [1993]:  Episodes. (St. Paul, MN, USA:  Graywolf Press)
  • 2006 – Mark Evan Bonds [2006]: Music as Thought: Listening to the Symphony in the Age of Beethoven. (Princeton UP)
  • 2006 – Kyle Gann [2006]: Music Downtown: Writings from the Village Voice. (UCal Press)
  • 2004 – Igal Halfin [2003]: Terror in My Soul: Communist Autobiographies on Trial. (Cambridge, MA, USA: Harvard UP)
  • 2001 – George Leonard [2000]: The Way of Aikido: Life Lessons from an American Sensei.
  • 2000 – Stephen E. Toulmin [1990]:  Cosmopolis:  The Hidden Agenda of Modernity.  (University of Chicago Press)
  • 1999 – Michel de Montaigne [1580-1595]:  Essays.
  • 1997 – James Pritchett [1993]:  The Music of John Cage.  (Cambridge UP, UK)
  • 1996 – George Fowler [1995]:  Dance of a Fallen Monk: A Journey to Spiritual Enlightenment. (New York:  Doubleday)
  • 1995 – Chungliang Al Huang and Jerry Lynch [1992]:  Thinking Body, Dancing Mind.   (New York: Bantam Books)
  • 1995 – Jon Kabat-Zinn [1994]: Wherever You Go, There You Are.
  • 1995 – Charlotte Joko Beck [1993]: Nothing Special: Living Zen.
  • 1993 – George Leonard [1992]: Mastery: The Keys to Success and Long-Term Fulfillment.
  • 1990 – Trevor Leggett [1987]:  Zen and the Ways.  (Tuttle)
  • 1989 – Grant McCracken [1988]:  Culture and Consumption.
  • 1989 – Teresa Toranska [1988]:  Them:  Stalin’s Polish Puppets.  Translated by Agnieszka Kolakowska.(HarperCollins) (Mentioned here.)
  • 1988 – Henry David Thoreau [1865]:  Cape Cod.
  • 1988 – Rupert Sheldrake [1988]: The Presence of the Past: Morphic Resonance and the Habits of Nature.
  • 1988 – Dan Rose [1987]:  Black American Street Life: South Philadelphia, 1969-1971. (U Penn Press)
  • 1987 – Susan Sontag [1966]: Against Interpretation. (Farrar, Straus and Giroux)
  • 1987 – Gregory Bateson [1972]: Steps to an Ecology of Mind. (U Chicago Press)
  • 1987 – Jay Neugeboren [1968]:  Reflections at Thirty.
  • 1982 – John Miller Chernoff [1979]: African Rhythm and African Sensibility: Aesthetics and Social Action in African Musical Idioms. (University of Chicago Press)
  • 1981 – Walter Rodney [1972]: How Europe Underdeveloped Africa.  (London: Bogle-L’Overture Publications)
  • 1980 – James A. Michener [1971]: Kent State: What happened and Why.
  • 1980 – Andre Gunder Frank [1966]:  The Development of Underdevelopment.  (Monthly Review Press)
  • 1980 – Paul Feyerabend [1975]: Against Method: Outline of an Anarchistic Theory of Knowledge.
  • 1979 – Aldous Huxley [1945]:  The Perennial Philosophy.
  • 1978 – Christmas Humphreys [1949]:  Zen Buddhism.
  • 1977 – Raymond Smullyan [1977]:  The Tao is Silent.
  • 1976 – Bertrand Russell [1951-1969]:  The Autobiography.  (London: George Allen & Unwin)
  • 1975 – Jean-Francois Revel [1972]:  Without Marx or Jesus: The New American Revolution Has Begun.
  • 1974 – Charles Reich [1970]: The Greening of America.
  • 1973 – Selvarajan Yesudian and Elisabeth Haich [1953]:  Yoga and Health. (NY:  Harper)
  • 1972 – Robin Boyd [1960]: The Australian Ugliness.

Mathematicians of the 20th Century

With so many blogs being written by members of the literati, it’s not surprising that a widespread meme involves compiling lists of writers and books.  I’ve even succumbed to it myself.   Lists of mathematicians are not as common, so I thought I’d present a list of the 20th century greats.    Some of these are famous for a small number of contributions, or for work which is only narrow, while others have had impacts across many parts of mathematics.

Each major area of mathematics represented here (eg, category theory, computer science) could equally do with its own list, which perhaps I’ll manage in due course.  I’ve included David Hilbert, Felix Hausdorff and Bertrand Russell because their most influential works were published in the 20th century.  Although Hilbert reached adulthood in the 19th century, his address to the 1900 International Congress of Mathematicians in Paris greatly influenced the research agenda of mathematicians for much of the 20th century, and his 1899 axiomatization of geometry (following the lead of Mario Pieri) influenced the century’s main style of doing mathematics.   For most of the 20th century, mathematics was much more abstract and more general than it had been in the previous two centuries.    This abstract style perhaps reached its zenith in the work of Bourbaki, Grothendieck, Eilenberg and Mac Lane, while the mathematics of Thurston, for example, was a throwback to the particularist, even perhaps anti-abstract, style of 19th century mathematics.  And Perelman’s major contributions have been in this century, of course.

  • David Hilbert (1862-1943)
  • Felix Hausdorff (1868-1942)
  • Bertrand Russell (1872-1970)
  • Henri Lebesgue (1875-1941)
  • Godfrey Hardy (1877-1947)
  • LEJ (“Bertus”) Brouwer (1881-1966)
  • Srinivasa Ramanujan (1887-1920)
  • Alonzo Church (1903-1995)
  • Andrei Kolmogorov (1903-1987)
  • John von Neumann (1903-1957)
  • Henri Cartan (1904-2008)
  • Kurt Gödel (1906-1978)
  • Saunders Mac Lane (1909-2005)
  • Leonid Kantorovich (1912-1986)
  • Alan Turing (1912-1954)
  • Samuel Eilenberg (1913-1998)
  • René Thom (1923-2002)
  • John Forbes Nash (1928-2015)
  • Alexander Grothendieck (1928-2014)
  • Michael Atiyah (1929- )
  • Steven Smale (1930- )
  • Paul Cohen (1934-2007)
  • Nicolas Bourbaki (1935- )
  • Sergei Novikov (1938- )
  • Stephen Cook (1939- )
  • William Thurston (1946-2012)
  • Edward Witten (1951- )
  • Andrew Wiles (1953- )
  • Richard Borcherds (1959- )
  • Grigori Perelman (1966- )
  • Vladimir Voevodsky (1966- )
  • Edward Frenkel (1968- )

And here’s my list of great mathematical ideas.

Our impact on others

JOHN-Fritz 1953

A nice story about the possibly unknown effects of our actions, from a review by mathematician Marjorie Senechal of a book about German Jewish mathematicians:

Fritz John (1910–1994) [pictured in 1953], Jewish on his father’s side, left Germany in 1933 for England; in 1935 he was appointed assistant professor of mathematics at the University of Kentucky in Lexington.  Back in the 1930s, the University of Kentucky was small and isolated but, except for two years of war-related work, John stayed there until 1946, when he moved permanently to New York University.  Surely he was glad to rejoin his mentor, [mathematician Richard] Courant.  But he made a difference in Lexington; I don’t know if he ever knew it.

I grew up near Lexington and took piano lessons from a teacher in town named Helen Lipscomb.  Helen was a polio victim, confined to a wheelchair; her brother, Bill, was a chemist at the University of Minnesota.  I met Bill Lipscomb for the first time in 2009, two years before he died at the age of ninety-two.  By then he’d taught at Harvard for forty years and earned a Nobel prize (1976) [in Chemistry] for his work on boranes.  Unlike me, Bill had attended the University of Kentucky after a Lexington public high school; he’d had a music scholarship and studied chemistry on the side.  “Why did you decide to become a chemist instead of a musician?” I asked him. “What changed your mind?” “A math class,” he told me. “A math class taught by a German named Fritz John.” (page 213)


Marjorie Senechal [2013]:   Review of:   Birgit Bergmann, Moritz Epple, and Ruti Ungar (Editors):  Transcending Tradition: Jewish Mathematicians in German-Speaking Academic Culture.   Springer Verlag, 2012.  Notices of the American Mathematical Society, 60 (2):  209-213.  Available here.

One day in the life . . .

Khan-Tengri Mountain at sunset

. . . of Boris N. Delone (1890-1980), Russian mathematician, moutaineer, and polymath, member of a famous family of mathematicians and physicists, whose grandson was a dissident poet:

July 6, 1975, Delone spends a cold night (-25 degrees C) in a tent on a glacier under the beautiful peak of Khan Tengri (7000 m, the Tien Shan mountain system, Central Asia) [pictured, at sunset] at a height of about 4200 m.  In the morning a helicopter picks him up to take him to Przhevalsk (now Karakol), a Kyrgyz city at the eastern tip of Lake Issyk-Kul.  From Przhevalsk he takes a local flight  to Frunze (now Bishkek), the capital of Kyrgyzstan, where the heat exceeds 40 degrees C.   After queuing up for a few hours and with the help of some “kind people” and the Academy of Sciences membership card he succeeds in purchasing an air ticket to Moscow.   Late at night he arrives at Domodedovo airport in Moscow, from which he still needs to go to his country house near Abramtsevo (Moscow oblast).   Taking the last commuter train, he arrives at the necessary station at around 2 am; from there it is another three kilometers to his house, half of which are in a dark dense forest.  He loses his way and, after roaming around the night forest for a long time, leaves his heavy rucksack in a familiar secluded place.  Only in the morning does Delone succeed in getting home safely.”  (page 13).

In that year, 1975, Boris Delone was 85 years old.



N. P. Dolbilin [2011]: Boris Nikolaevich Delone (Delaunay): Life and Work. Proceedings of the Steklov Institute of Mathematics, 275: 1-14.  Published in Russian in Trudy Matematicheskogo Instituta imeni V. A. Steklov, 2011, 275:  7-21.  A pre-print version of the paper is here.


Thurston on mathematical proof

Bill Thurston

2012 saw the death of Bill Thurston, leading geometer and Fields Medalist.   Learning of his death led me to re-read his famous 1994 AMS paper on the social nature of mathematical proof.   In my opinion, Thurston demolished the views of those who thought mathematics is anything other than socially-constructed.  This post is just to present a couple of long quotes from the paper. 

Continue reading ‘Thurston on mathematical proof’