One million pages of new math every year.
I was in the library today where I read the book 'Letters to a young mathematician' from professor Ian Stewart. Stewart answers questions of his ( hypothetical ) niece Gem who wants to become a mathematician. If you have a question about a career in mathematics it may very well be that you will find the answer in Stewart's book. In the preface he writes that he considers the book an update to Hardy's famous book 'A mathematician's Apology'. Things changed a bit compared to Hardy's days. Where Hardy spent four hours a day on math and the rest of the day in leisure ( i.e. watching cricket ) the research mathematicians of today have 10 to 12 hour workdays doing a lot more than basic research.
Anyway, in one letter Stewart, very much part of the current mathematical elite, explains how the young mathematician should pursue for a career. First he almost apologizes for the fact that her thesis advisor will probably be someone who just got his Ph.D him/herself ( the number of female mathematicians is growing fast as Stewart explains elsewhere ). This remark alone should be red flagged. He then explains in the same apologetical fashion that you can consider yourself lucky if you have a good teacher. Most teachers only teach because it comes with the job of researching. And a good researcher is the one with the most publications. And since there are approximately 500,000 research mathematicians worldwide this explains the creation of one million pages of new math every year. Just imagine the industry behind it.
Attacking a serious mathematical problem like the Poincare conjecture or the Riemann hypothesis may take decades of work with only a small chance of successful completion. I think I am beginning to understand why Grigori Perelman doesn't like the establishment and vice versa.
Something is wrong.
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