Posted by: Alexandre Borovik | December 15, 2014

Calling a spade a spade: Mathematics in the new pattern of division of labour

This is the last pre-publication version of my paper:

Alexandre V. Borovik, Calling a spade a spade: Mathematics in the new pattern of division of labour, arXiv:1407.1954v3 [math.HO].

The growing disconnection of the majority of population from mathematics is
becoming a phenomenon that is increasingly difficult to ignore. This paper
attempts to point to deeper roots of this cultural and social phenomenon. It
concentrates on mathematics education, as the most important and better
documented area of interaction of mathematics with the rest of human culture.
I argue that new patterns of division of labour have dramatically changed the
nature and role of mathematical skills needed for the labour force and
correspondingly changed the place of mathematics in popular culture and in the
mainstream education. The forces that drive these changes come from the tension
between the ever deepening specialisation of labour and ever increasing length
of specialised training required for jobs at the increasingly sharp cutting
edge of technology.
Unfortunately these deeper socio-economic origins of the current systemic
crisis of mathematics education are not clearly spelt out, neither in cultural
studies nor, even more worryingly, in the education policy discourse; at the
best, they are only euphemistically hinted at.
This paper is an attempt to describe the socio-economic landscape of
mathematics education without resorting to euphemisms.



  1. Very interesting post partly because you mentioned Braverman (who I only recently read partly because a ‘leftist’ reading group affiliated with Jacobin Mag (on the web) of which I am a sort of member was reading it. I have seen your views on the ‘hourglass’ issue before and Braverman’s ideas also occur in various forms in other sources.

    (I am curious about your own views on the 3 alternatives for democratic societies (assuming the oceans and ISIS dont rise) you describe—I think we are heading for 2 (i have a niece who is in her first year at MIT and she and her friends (scattered around at US universities) were at Thanksgiving—interestingly, the 3 women were all in STEM fields, the 2 men were in non- mathematical fields (somewhat standard—the women do the work); the math she was doing in high school, especially using advanced calculators/computers as described in your paper, I never was exposed to until college). Alot of the people I know have little use for math or science—they are into literary theory or service jobs.

    I have been talking a bit with some ‘alternative’ or ‘popular education’ groups about math and science education as well as research. (Some of the people are affiliated in part with an old US group, ‘science for the people’ which basically arose out of anti-vietnam war and and anti-military activism). It is hard to justify learning something abstract like math, or even science—if you are working a cash register you can learn about landing a rocket on a comet by watching TV. Some of these people are of the the type ‘we dont need no math or science, just to get in the street and organize; and besides those things conflict with our spiritual selves’.

    Probably the most applicable part of math in my opinion for a democratic society are things like blog and others—basically arithmatic and a bit of probability. (In the USA a big issue now is ‘ferguson’ (not niall, though thats another issue) —- one group of people say ‘police shootings’ are the issue, others say ‘its black on black crime’. I personally have a hard time finding and crunching the numbers to know the answer if there is one (and where I live both issues arise, but its very political).

    This gets me to my questions, which of course you are not required to respond to.


    1. Are there different kinds of mathematical competency, in the way some people who are good at sports may not be able to actually do equally well at football, soccer, running, basketball, kayaking, etc and people into music may not be equally capable of creating great symphonies, rock, rap, and pop hits, and such?

    I notice there’s very little physics on your site (azimuth blog, john baez, looks at connections between math and biology, etc.; louis kauffman looks at say ‘knots and physics’ (his wife was my sister’s college roomate)). I read a fair amount on the relation between statistical mechanics and economics and biology, but for example the figure 9 problem in your paper stumped me (i couldn’t even remember what ‘oblique’ meant—and I think thats a big problem in math/science education (newton’s laws seem known, but when every theorem is associated with someone’s name that’s a problem, like the cognitive tests when you have people look at the word ‘red’ written in blue colors and ask then what it is. If i were writing a curriculum on that problem—ratios of functions—i would do it quite differently, starting with some really simple examples (in the spirit of ehrenfest’s proof of the second law of thermodynamics (boltzmann)). .

    I was terrible at number theory, but fields like random graphs (erdos-reyni-bollobos), combinatorics, some non-linear dynamics and statistical mechanics I could get some sort of grasp of (partly because I had an objective, via applied math—I was trying to solve problems in biology and economics (though of course fairly limited in scope—i wasn’t trying to solve the issue of mortality or extinction, nor why I am often low on money and people I am around are even lower on it, though also some have more).

    Can you figure out ‘entropic inference’ (caticha) or ‘tsallis entropy’? Are these important, and if so why?


    2. Alot of the people I come across seem to be fairly good at computer programming, though I think alot of it has to do with basically combining existing programs into a larger one (I used to do C language programming to solve equations but have completely forgotten it, like it was a bad experience). However they often seem to have little understanding or interest in math or science. They read Braverman for example and think he is profound and fascinating; I view it as fine, but trivial (or current but known) and of historical interest like Marx.

    Is computer programming math? I knew someone who had a PhD in both theoretical physics and computer science—she told me go into CS since its all the same. But that is only at the theoretical level (p/np etc.); I dont know about the other kinds, like what alot of people i come across do—eg write programs to assign plane seats to people. Most of this seems to be like the math calculators.


    3. The automation of alot of math (hourglass,skilling/deskilling) actually seems to promote current standard consumer democracy.

    Rather than try to think about some abstract idea (what is the cardinality of the continuum? etc.) you just go to the automated checkout line and buy something. Its easy. You can get an ipod and meet someone for a movie, partly created through the use of algebraic geometry.

    Now you can get a 3D printer, and maybe make yourself a handgun (a bit of a problem in my area).

    There are it seems, a relatively small number of people who really are interested in extremely abstract things, most of the rest are happy to experience them vicariously. (My Jacobin magazine reading group is discussing the 2 tier ‘tracked’ education system of Germany (some go to theoretical schools, others go into trades; the people in this group mostly seem to go ‘theoretical schools’ but in the humanities since they want to make a living decrying the ‘social division of labor’ though they dont want to have a trade, or do any dirty work (nor math).

    This almost seems like evolution—-division of labor is similar to speciation and the ‘web of life’ in ecology.

    —————–peace out (thats it). (i see the templeton fund has a ‘spiritual capitalism’ section; its hard to see why people are so against the 1%; andrew carnegie gave alot of his money away (and my dad went to carnegie mellon as well).

  2. p.s. just got back from my jacobin group (joke). i realized, in the mathematical tradition (even fourier needed to be corrected by cantor, in paradise), that in correct grammar one should call a spade a shovel. (I think G Mackey wrote ‘harmonic analyses as the exploitation of symmetry’ (1980 BAMS) (the prof who gave me that article tried to flunk me because i didnt attend class except for exams). all the exploitation, class field theory, color of the character of your group (MLK, hermann weyl, or trace of the matrix), chromatic polynomials (graph theory (bari—one in graph theory, another blown up because she was an EF! activist, and also a NYT’s science journalist in that family). .

  3. A lot of wonderful questions, thanks. I will think.

  4. With thanks to Laurent Duval:

  5. maybe getting off track here, but i’m in america, and there was an american named feynman who had this quote ‘i wonder why i wonder why i wonder…’ (etc iterate into goodstein’s theorem’) (as an aside his ‘lectures in physics’ books i thought were great and informative though some i didnt understand, but the people who were teaching me quantum and statistical mechanics said ‘we dont do it that way—we focus on things like spherical harmonics, bessel functions, etc. even if you dont know what they are—just shut up and calculate’. Of course, americans are descended from the neanderthals, such as they have in europe. So i wonder why i wonder if you think you think etc. Maybe u think think u think but are just confused. (i actually downloaded one of your books which looks quite good but i havent read much of it). V I Arnold (maybe affiliated with KAM theory (ergodicity) has an article on ‘the teaching of mathematics’ in which he slams french math education (though i gather one person whose papers i have won a fields medal (villani, on optimal transport, involving stuff like lagrangians for the fokker-planck equation and ricci flow). Another, Lockhardt’s lament, may have some similar views (see ‘a mathematician’s lament’ on wikipeida or amazon). I also have some historical papers on russian mathematics during the stalin era and they aren’t flattering to many people, even in stochastic processes.

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