Posted by: Alexandre Borovik | June 18, 2013

The Faulty Logic of the ‘Math Wars’

A brilliant opinion piece by ALICE CRARY and W. STEPHEN WILSON in the Opinion Pages of the New Your Times. A highlighted message:

Mastering and using algorithms involves a special and important kind of thinking.

Read the whole paper. It also contains a great quote from  John Dewey: the goal of education

“is to enable individuals to continue their education.”


[With thanks to muriel]

Posted by: Alexandre Borovik | June 16, 2013

Comparative linguistics, circa 1860

От того, что так много на французском языке говориться и много было хорошего писано, язык выработался очень хорошо: на нем можно выразить такие мелочные, вежливые и пустые тонкости, каких не скажешь на прямом, строгом, сильном языке, которым говорит вся Русская Земля.

Мир Божий: Руководство по русскому языку для приготовительного класса [военно-учебных заведений] / Сост. А. Разин. Спб., 1860.

Posted by: Alexandre Borovik | June 16, 2013

Mathematics Lecture in Gezi Park

Mathematics Lecture in Gezi Park

Ali Nesin is giving a mathematics lecture in Gezi Park, Monday 10 June 2013. And more photographs from Gezi Park:

Posted by: Alexandre Borovik | June 15, 2013

The origin of the Russian tradition in mathematics education

Surprise surprise, it appears to be Leonard Euler’s “Universal Arithmetic”, written by him in St Petersburg and published there in 1768 in Russian translation produced by his students:


It clearly set out standards of quality of mathematical content and enshrined the propaedeutics principle so visible in the Russian tradition: a textbook was supposed to be a stepping stone to further more advanced study.

Posted by: Alexandre Borovik | June 4, 2013

A professional skill: parsing







I am proud that, after marking 220 examination scripts in first year linear algebra , I was still able to locate, at a glance, an error in this picture — thanks to skills in parsing of meaningless symbolic input developed over many years of teaching mathematics.

Posted by: Alexandre Borovik | April 29, 2013

Andrei Zelevinsky 1/30/1953 – 4/10/2013

Andrei Zelevinsky 1/30/1953 – 4/10/2013

Posted by: Alexandre Borovik | November 25, 2012

Reading and doing arithmetic nonconsciously

Asael Y. SklarNir Levy , Ariel GoldsteinRoi MandelAnat Maril, and Ran R. Hassin, Reading and doing arithmetic nonconsciously, Published online before print November 12, 2012, doi:10.1073/pnas.1211645109,   PNAS November 12, 2012


The modal view in the cognitive and neural sciences holds that consciousness is necessary for abstract, symbolic, and rule-following computations. Hence, semantic processing of multiple-word expressions, and performing of abstract mathematical computations, are widely believed to require consciousness. We report a series of experiments in which we show that multiple-word verbal expressions can be processed outside conscious awareness and that multistep, effortful arithmetic equations can be solved unconsciously. All experiments used Continuous Flash Suppression to render stimuli invisible for relatively long durations (up to 2,000 ms). Where appropriate, unawareness was verified using both objective and subjective measures. The results show that novel word combinations, in the form of expressions that contain semantic violations, become conscious before expressions that do not contain semantic violations, that the more negative a verbal expression is, the more quickly it becomes conscious, and that subliminal arithmetic equations prime their results. These findings call for a significant update of our view of conscious and unconscious processes.

See a popular exposition in New Scientist.

Posted by: Alexandre Borovik | October 13, 2012

Feit-Thompson theorem has been totally checked in Coq

An announcement is here. A quote:

From Laurent Théry
Date: Thursday 20 September 2012, 20:24
Re: [Coqfinitgroup-commits] r4105 – trunk


Just for fun

Feit Thompson statement in Coq:

Theorem Feit_Thompson (gT : finGroupType) (G : {group gT}) : odd #|G| -> solvable G.

How is it proved?

You can see only green lights there:

and the final theory graph at:

How big it is:

Number of lines ~ 170 000
Number of definitions ~15 000
Number of theorems ~ 4 200
Fun ~ enormous!

— Laurent



Posted by: Alexandre Borovik | August 22, 2012

News from Chile re: Boris Weisfeiler’s disappearance

From Olga Weisfeiler:

Today brought big news from Chile regarding my brother’s disappearance. After many many years of frustration, arrest warrants have been issued for 8 police and military officers for the kidnapping and enforced disappearance of my brother, who went missing in 1985.

A briefing should be up on NYT shortly.
For more information on the case itself, please see
For all those who have supported the efforts over the years, a very big thank you!


Posted by: Alexandre Borovik | July 22, 2012

Women in the violent world of mathematics

I refer to my old post Women and mathematics in relation to the caustic comic strip by Zach Weiner. Both my post (which later became a section in my book Mathematics under the Microscope) and Weiner’s cartoons are about the place of a woman in the violent world of mathematics and about men’s perception of women’s place. If you think that this is an exaggeration then read comments to my post, like this one, from a female colleague:

As one of the few female mathematicians in Alexandre’s field I think he is correct.

You probably have to be a research mathematician to understand what he is saying about being bold, needing intellectual independence, the psychologically charged and tense discourse and everyone looking and acting as if they are going to get into a fist fight any moment.

This is typically not how women behave and when a woman does act like this (learned or natural) she gets all sorts of criticism for not being the sweet docile soft person she looks like. And all too often the criticism is from other women, not just from men.

Or this comment, sent to me in response to my book and published in the Addenda and Comments:

Part of my anger and frustration at school was that so much of this subject
that I loved, mathematics, was wasted on what I thought was frivolous or
immoral applications: frivolous because of all those unrealistic puzzles,
and immoral because of the emphasis on competition (Olympiads, chess, card
games, gambling, etc). I had (and retain) a profound dislike of
competition, and I don’t see why one always had to demonstrate one’s
abilities by beating other people, rather than by collaborating with them.
I believed that “playing music together”, rather than “playing sport against
one another”, was a better metaphor for what I wanted to do in life, and as
a mathematician.

Indeed, the macho competitiveness of much of pure mathematics struck me very
strongly when I was an undergraduate student: I switched then to
mathematical statistics because the teachers and students in that discipline
were much less competitive towards one another. For a long time, I thought
I was alone in this view, but I have since heard the same story from other
people, including some prominent mathematicians. I know one famous category
theorist who switched from analysis as a graduate student because the people
there were too competitive, while the category theory people were more

It may be worth mentioning that I am male. In other words, a dislike of competitiveness is not confined to women. The
statistics department I entered as an undergraduate, for example, had no
women in it, yet was much less competitive than the pure mathematics
department (which had once been headed by a woman). I think it is
disciplinary tradition rather than gender that is the key factor here.

I am now a Computer Scientist. I have also found differences in the competitiveness of people in different sub-domains of CS.
To generalize greatly, I have found people in Artificial Intelligence (AI)
much less macho and competitive than those in (say) Algorithm and Complexity
Theory. Within AI, people in (say) Argumentation are generally much less
macho and competitive than those in Game Theory and Mechanism Design. In each
case, the more formal and mathematical the domain, the more competitive it
tends to be. It could be that these domains have acquired their cultures
from mathematicians, while the other domains have been less influenced by
the culture of mathematics.

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