Abelian Functions and the Development of Mathematics

Taken from Pi and the AGM:

When I was a student, abelian functions were, as an effect of the Jacobian tradition, considered the uncontested summit of mathematics and each of us was ambitious to make progress in this field. And now? The younger generation hardly knows abelian functions.

How did this happen? In mathematics, as in other sciences, the same processes can be observed again and again. First, new questions arise, for internal or external reasons, and draw researchers away from the old questions. And the old questions, just because they have been worked on so much, need ever more comprehensive study for their mastery. This is unpleasant, and so one is glad to turn to problems that have been less developed and therefore require less foreknowledge – even if it is only a matter of axiomatics, or set theory, or some such thing.

Felix Klein (1849-1925), Development of Mathematics in the 19th Century, 1928

Klein succintly described what is the current state of mathematics (at least in Singapore.) In a typical year, you get 30 students learning algebra, 100 students learning coding theory (90% of whom who think a field is some piece of land with grass on it) and 150 students learning graph theory. While the local arts scene has government support and funding, there is none for pure mathematics. It’s really difficult to see where the next generation of pure mathematicians is going to come from.

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