Posted by: Alexandre Borovik | March 5, 2009

## A childhood story: Autodidact

I was in elementary-school age (ca. 6-9 years) fascinated by  elementary geometry, in part because a popular TV series on astronomy  and relativity catched my imagination and provided some fascinating  statements, like the usual visualizations of strange non-euclidian  things. I found the possibility to prove “obvious” statements by  general principles absolutely fascinating, much more fascinating than  proving more complicated statements. However, when I asked teachers  about non-euclidian geometry, their negative reaction alienated me  very much. Further I found the way, some geometric objects were  defined, too ugly to accept. E.g. an ugly definition for such a nice  figure as a circle to prove interesting statements appeared to me very  crude. On the other hand, my tries to do it with nicer definitions did  not work.

At age ca. 14 I started learning analysis by myself, because I wanted  to understand relativity, and the book I had proved every statement  twice: first by elementary geometric constructions with help of  problem-specific thought experiments, then by analysis. That the later  proofs were much shorter, more general and looked somehow better, made  me interested in analysis. I had much trouble to understand what  definitions are and to separate the Definition / Statement / Proof parts  of the text. My feeling towards definitions was ca. “Well, that’s O.K.  and obvious, but what are these things really and why one uses this  selection of features for definition?” So, reading the first ca. 20  pages needed several weeks, i.e. ca. the same time as the rest of the  book.

I am Austrian, lack advanced school degrees, and after some years of tutoring  students  I was invited to do an entrance exam. My math education is completely autodidactic, and was from  German books, but shifted — from age ca. 16 on, after I obtained  access to the university library –to English (later to French and  Russian too; unfortunately the library refuses to buy Japanese math  books) ones.

The later had a strange side effect, because I had then acquired from  mathbooks apparently an English with strong traces of Latin grammar  initially, which made people “accuse” me of being some weird  upper class teenager playing the uneducated, but “obviously knows  Latin”.

A side effect of autodidactism may be that my mathematical interests  are still strongly guided by aesthetical impressions, esp. if concepts  allow visualizations. Some theories have very special aesthetical  properties, e.g. class field theory and it’s connection with modular  forms. A negative result of going to a university is that I study in a  much more superficial way than earlier — formerly, I read something  until I could not only solve the exercises, but derive the whole  theory from a handful of basic ideas, which were often helpful in  seemingly different math contexts too. Now I read more and faster, but  restrict usually to understanding the techniques of the proofs.