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.
[For the expalnation of the project, read I need your stories]