spreading mathematics

accessing mathematics and headaches

Studying mathematics and getting a headache need not be cause and effect. However, many times in seminars or reading some papers one gets the impression of being a little dumb. Well, I'm pretty sure you know those seminars in which everybody's constantly nodding or papers with obvious steps (once written they take three sheets, but they are obvious).

At times I think that we need to be admired for something and in mathematics this "something" is intelligence. The less people that understands something, the more difficult it is, the more intelligent the writer is. Something similar applies to speeches. The strange thing is that if you do not understand something in a seminar, you just keep quiet and spend (lose) one or two hours waiting for the storm to pass you by. Well one should stand up and quietly leave the room.

Our life is short. I should be able to quickly decide if something will be of my interest. If so, then I can dedicate time to it. For established theories there are plenty of tutorials on the web (god blesses the web) but not so for recent research papers or new theories. After all, it is not that difficult to include some examples to illustrate the concepts. Even in those papers submitted for publishing.

I agree in that mathematics are not easy, but most times we make them even more difficult. I think that mathematicians should be aware of the necessity of selling the product (I should include myself). The Bourbaki school which has had a big influence on the twentieth century belongs to the past. We should react and go to the opposite - as it is always the case: thesis, antithesis, synthesis - and try to make accessible even state-of-the-art papers. Good ideas are not difficult.

Another point is that technicalities prevail over conceptual research. In a "deep paper" one expects hard-to-follow equations just above obscure paragraphs. With minor exceptions, new approaches and concepts are not normally recognized though they are usually more influential as they allow us to think from a different perspective.

I confess I'm not a fan of B. Mandelbrot at all, but I do mind the importance of his work. Today's quote I agree, first, because it seems to support the thesis of this post and, second, because for me mathematics is nothing more (and nothing less) than a language: being a language, mathematics may be used not only to inform but also, among other things, to seduce.