In the 3,000 categories of mathematical writing, new mathematics is being created at a constantly increasing rate. The ocean is expanding, both in depth and in breadth.
By multiplying the number of papers per issue and the average number of theorems per paper, their estimate came to nearly two hundred thousand theorems a year. If the number of theorems is larger than one can possibly survey, who can be trusted to judge what is ‘important’? One cannot have survival of the fittest if there is no interaction. It is actually impossible to keep abreast of even the more outstanding and exciting results. How can one reconcile this with the view that mathematics will survive as a single science? In mathematics one becomes married to one’s own little field. [...] The variety of objects worked on by young scientists is growing exponentially. [...] Only within the narrow perspective of a particular speciality can one see a coherent pattern of development.
Peer-review is the predator. But if the prey population is higher than can be sheltered by selection of promising ideas from nonsense, nonsense will prevail. That is, those people producing valuable results won’t be favored over those that come up with marginal or wrong results.
Yes, that’s exactly the kind of stuff I recommended The Mathematical Experience for. It takes a bird’s eye view instead of going for the usual textbook minutiae, but still feels like it’s talking about the actual practice of mathematics instead of something simplified to death for the benefit of popular audiences.
Thanks, I just ordered ‘Darwin’s Dangerous Idea’ and ‘Code: The Hidden Language of Computer Hardware and Software’. I’ve already got the others.
Here a tidbit from ‘The Mathematical Experience’
I’ve ordered a copy, but on a second look, I’m not sure that the argument is sound, or even interesting.
Biological evolution runs on the local non-survival of the least fit (and sometimes the unlucky), not on an overview-based evaluation of the fittest.
Peer-review is the predator. But if the prey population is higher than can be sheltered by selection of promising ideas from nonsense, nonsense will prevail. That is, those people producing valuable results won’t be favored over those that come up with marginal or wrong results.
Yes, that’s exactly the kind of stuff I recommended The Mathematical Experience for. It takes a bird’s eye view instead of going for the usual textbook minutiae, but still feels like it’s talking about the actual practice of mathematics instead of something simplified to death for the benefit of popular audiences.