Notes from a math lecture

Public lectures have a distinguished history going at least as far back as Faraday, but I hardly have any history of attending them. Call it new year fervor that has not subsided yet (or whatever), something did prompt me out of my laziness when I came to know of a public lecture to be given by Prof. Schmid from Harvard last week. My thinking was, more or less, it's a public lecture, How hard can it be?

The topic of the lecture was 'Riemann's continuous, nowhere differentiable function'. As it happens, before Riemann it was thought that a function that is continuous everywhere but differentiable almost nowhere could not exist. Weierstrass was the first to publish such a function, though Riemann (second hand reports claim) gave an example of such a function earlier, but without giving proof. Working that out took a while. G. H. Hardy showed in 1916 that the function is not differentiable at irrational points, while Gerver and Smith showed in 1970s that it is not differentiable at rational points either, except those of the form p/q with p and q relatively prime. Prof. Schmid worked on this function himself, which is intimately related to fractals, a topic which came to prominence much later. The area is important and broad enough to have its own book.

That is the summary, and I am afraid I cannot go in more detail. The lecture was obviously intended for students who are learning related stuff and was full of details and formalism, though the key ideas (like the ones mentioned above) were clearly  brought out. I remember reading John Derbyshire's Prime obsession with great interest, and those who have read it (or are otherwise familiar with the history of Riemann hypothesis) would not fail to notice a parallel here. One minor quibble on the personal front is that I was interested in getting a view on, of the six remaining millennium problems (which include both Riemann hypothesis and P vs NP), which one we are closest to solving, but ended up squandering the opportunity to ask. 

Overall it was a good learning experience, and sitting in a hall surrounded by an overwhelmingly young crowd brought back memories of my own college days, turning it into a refreshing one as well.