Alexandre Borovik on Autodidacticism
Post date: Apr 15, 2014 10:48:52 AM
John Dewey famously said
"The aim of education is to enable individuals to continue their education … the object and reward of learning is continued capacity for growth. Now this idea cannot be applied to all the members of a society except where intercourse of man with man is mutual, and except where there is adequate provision for the reconstruction of social habits and institutions by means of wide stimulation arising from equitably distributed interests. And this means a democratic society."
Theoretically speaking, the best way to enable individuals to continue their education is to turn them into autodidacts. This is what is supposed to happen at the higher levels of education -- part of professional skills of a researcher is to be able to learn, in a selective, systematic and focused way, from the flow of research information, published or otherwise disseminated.
In the Russian mathematics community, there is a jargon use of the verb "vyuchit', which means "to have learned", but in the simplest, primary school meaning, something as "to learn by heart", with emphasis on achieving very sound knowledge. A child can be asked:
"Have you ``vyuchil'' times table by 6?",
In mathematical community it is used in expressions like
"He has ``vyuchil'' etale cohomology''
Of course, statements like that refer to autodidactism as part of professional activity of research mathematicians.
I would suggest to use the word "autodidacity", if it is not used already in some other meaning, to mean "capacity to learn on his/her own". I have the feeling that the traditional meaning of the word "scholar" included something like
"some who learned enough from others to be able to continue to learn on his own".
I can also conjecture that originally, prior to the era of empirical sciences, there were no difference between "learning on his own" and "researching".
Returning to the modernity, I have a feeling that autodidacity is not prominent in graduates of maths departments of British universities; Moreover, I suggest that majority of our PhDs failed to develop autodidactic skills.
So, we have obvious sociological and historical facets of the problem of autodidactism. It also touches, obviously, on education and the IT revolution in education, and on modern-day politics -- the hackers' movement is made of autodidacts.
And, why this problem is interesting to me, there is also a very interesting aspect related to the philosophy of mathematical practice: the relations between learning and research in mathematicians' work.
I have already started to think a bit about the latter problem; see my paper
"Mathematics discovered, invented, and inherited, Selected Passages From Correspondence With Friends", 1 no. 4 (2013), 13-28. arXiv:1309.3073.
published in my own Samizdat journal (ISSN 2054-7145) because I could not imagine it being accepted in any official publication. The paper was written for a handful of my research collaborators and mathematician friends.
As I boldly state in the Abstract,
"The classical platonist/formalist dilemma in philosophy of mathematics can be expressed in lay terms as a deceptively naive question:
Is new mathematics discovered or invented?
Using an example from my own mathematical life, I argue that there is also a third way:
new mathematics can also be inherited"
And I conclude on p. 26:
"This paper documents a convoluted history of a few simple but powerful mathematical ideas and the way they were inherited, or ignored, or re-discovered by new generations of mathematicians.
I was privileged to work with Israel Moiseevich Gelfand. He made a clear distinction between the two modes of work in mathematics expressed by Russian words `prIdumyvanie' and `prOdumyvanie', very similar and almost homophonic. The former means `inventing', the latter `properly thinking through' and was used by Gelfand with the meaning
`systematically thinking through back to the origins, fundamentals, first principles of particular mathematical concepts or problems.'
Gelfand valued `prOdumyvanie' more than `pridumyvanie', he believed that prOdumyvanie yielded deeper results. The stories told here, I hope, support this view."
Gelfand himself was a classical autodidact; I feel that `prOdumyvanie' is closely related to "professional autodidactism" and makes an interesting target for a philosophical study.