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I think the last point doesn't really hold its own in any way. Many discoveries throughout history have started from someone just playing around with an idea, t

I think the last point doesn't really hold its own in any way. Many discoveries throughout history have started from someone just playing around with an idea, toying with it at first, but eventually becoming obsessed. The thing is, there's no way to tell beforehand. It might be a toy with no ultimate use or meaning, or it might lead to something entirely novel somewhere down the line. That's why play, in a very broad sense, is a core part of science and invention.

TZubiri 2y ago
If 1 out of 10 chmessicians discover something useful, the discoverer had good taste and deserves credit. There is no insurance redistributing credit amongst all of the pointless searches. The guys who invented imaginary numbers or eigenvectors weren't just throwing darts at a board and got "lucky".
- kevinventullo 2y ago
  It sounds like you have an infallible instinct for exactly which lines of research should be funded and which are useless dead ends. The NSF should hire you immediately!
  - monadINtop 2y ago
    But he's not wrong, research really isn't just random playing (which I think is obviously still good and fun and should be done for it's own sake, of which this blog post is a great example though it probably wouldn't be worth the time of a formal research project). It's the reason why "good questions" and seemingly arbitrary or trivial problems - especially those which motivates the development of much deeper machinery or discovery in order to solve them - is widely appreciated across all fields of math (poincare conjecture, galoi's proof of the unsolvability of the quintic, fermat's last theorem, riemann zeta's zeroes etc.) In all cases those good questions where not randomly cooked up but posed from a previous, more direct line of inquiry, of which the originator usually had a good insight into. Though for the examples I gave the unexpected depth certainly could not have been anticipated beforehand.
  - Viliam1234 2y ago
    People can make a good educated guess without being literally infallible.
  - DiscourseFan 2y ago
    always the problem with scientific research is that we never know why anything actually works the way it does, but we have a lot of ways of talking about it

TZubiri 2y ago

If 1 out of 10 chmessicians discover something useful, the discoverer had good taste and deserves credit. There is no insurance redistributing credit amongst all of the pointless searches. The guys who invented imaginary numbers or eigenvectors weren't just throwing darts at a board and got "lucky".

kevinventullo 2y ago
It sounds like you have an infallible instinct for exactly which lines of research should be funded and which are useless dead ends. The NSF should hire you immediately!
- monadINtop 2y ago
  But he's not wrong, research really isn't just random playing (which I think is obviously still good and fun and should be done for it's own sake, of which this blog post is a great example though it probably wouldn't be worth the time of a formal research project). It's the reason why "good questions" and seemingly arbitrary or trivial problems - especially those which motivates the development of much deeper machinery or discovery in order to solve them - is widely appreciated across all fields of math (poincare conjecture, galoi's proof of the unsolvability of the quintic, fermat's last theorem, riemann zeta's zeroes etc.) In all cases those good questions where not randomly cooked up but posed from a previous, more direct line of inquiry, of which the originator usually had a good insight into. Though for the examples I gave the unexpected depth certainly could not have been anticipated beforehand.
- Viliam1234 2y ago
  People can make a good educated guess without being literally infallible.
- DiscourseFan 2y ago
  always the problem with scientific research is that we never know why anything actually works the way it does, but we have a lot of ways of talking about it