One aspects of fundamental research (and research in general) that I see missing from this post and many other explanations of why it is not the best use of your time, is being incremental. With some very rare exceptions, the maths you actually need, even if developed at the time where it was needed, depend on many things that had to be found prior to that.
The example that comes to mind, and was not mentioned in the post or the comments (as far as I know), is the birth of computer science. You can say: yay, Turing “invented” (with a lot of other people) theoretical computer science to solve concrete problems, when it was needed. But that would completely obstruct the fact that Turing builds heavily on top of Gödel, which solved questions of a purely mathematical nature. Among the ideas Gödel’s work essential to the birth of computer science, diagonalization goes back to Cantor, whose work concerns some of the most pure and abstract maths ever.
That being said, I do agree from experience that many arguments one makes about justifying doing maths or theoretical computer science do not hold under scrutiny. Yet for the reason I give above, I still think pure theoretical research is necessary.
One aspects of fundamental research (and research in general) that I see missing from this post and many other explanations of why it is not the best use of your time, is being incremental. With some very rare exceptions, the maths you actually need, even if developed at the time where it was needed, depend on many things that had to be found prior to that.
The example that comes to mind, and was not mentioned in the post or the comments (as far as I know), is the birth of computer science. You can say: yay, Turing “invented” (with a lot of other people) theoretical computer science to solve concrete problems, when it was needed. But that would completely obstruct the fact that Turing builds heavily on top of Gödel, which solved questions of a purely mathematical nature. Among the ideas Gödel’s work essential to the birth of computer science, diagonalization goes back to Cantor, whose work concerns some of the most pure and abstract maths ever.
That being said, I do agree from experience that many arguments one makes about justifying doing maths or theoretical computer science do not hold under scrutiny. Yet for the reason I give above, I still think pure theoretical research is necessary.