Ramanujian's Deathbed Problem Cracked 205
Jake's Mom sends word of the serendipitous solution to a decades-old mathematical mystery. Researchers from the University of Wisconsin have unraveled a major number theory puzzle left at the death of one of the twentieth century's greatest mathematicians, Srinivasa Ramanujan. From the press release: "Mathematicians have finally laid to rest the legendary mystery surrounding an elusive group of numerical expressions known as the 'mock theta functions.' Number theorists have struggled to understand the functions ever since... Ramanujan first alluded to them in a letter written [to G. H. Hardy] on his deathbed, in 1920. Now, using mathematical techniques that emerged well after Ramanujan's death, two number theorists at the University of Wisconsin-Madison have pieced together an explanatory framework that for the first time illustrates what mock theta functions are, and exactly how to derive them."
Re:Ramanujan (Score:5, Interesting)
Math, being theoritical, does not require a lot of external resources (like laboratories etc.)
Re:Ease of understanding & teaching. (Score:5, Interesting)
I can relate to that. I studied math at a famous university for a couple of years before I dropped out. Here are some of the things I remember:
We started with over 100 students in the first year. By the third year, the number had dropped to less than 10 students. Half of those dropped out later. The professors were proud of this fact.
Each lecture took three hours, with one fifteen minute break. You were only allowed to ask questions in the last 15 minutes of the lecture.
Professors only took the trouble to learn students' names when they entered third-year courses.
I once wrote a research paper for one of the professors for a first-year course. In the very last paragraph of the paper I wrote a little joke. The paper was marked "A", then the "A" was crossed out, "C-" written below it, with an arrow pointing to the joke.
Math students had access to the faculty mainframe (this was in the early 1980s), but did not get instruction on how to use it, as opposed to physics students. The reasoning was that math students either should not need computers for their work, or should be smart enough to figure it all out by studying the manuals.
Professors often supplied example excercises. Students were encouraged to make these excercises and supply their answers to the professor. However, these answers were NEVER corrected, so that after a while students simply did not bother anymore.
Professors were notorious for not preparing lectures, and working out examples as they were going along, often failing to prove what they wanted to prove. One particularly telling incident was when a professor was working out a complex proof, starting at the top left of one of the two four-piece blackboards in the hall, and chalking down, very fast, formula after formula. I was trying to follow his proof, but, of course, was always several lines behind. But I thought I did understand it, and was approaching to where he was. When he was at the bottom-right of the second blackboard, he paused, and kept staring at the last line he had written, muttering to himself. While I was approaching this last line (making lots of notes, because OF COURSE these proofs weren't in the textbooks or anything), he started scanning back. After doing this for about five minutes, he suddenly walked over to the first board again, changed a plus into a minus in one of the first lines, then made lots of changes in the rest of what he had written, and finally wrote "Q.E.D." at the bottom-right. Then he closed the blackboards and sent us on our way.
Through this experience I thought I simply was not good enough at math. But when I switched to computer science, where math courses were taught by computer scientists, I passed with flying colours, usually as the best of the class. Not because the courses were easier, but because they were taught better.