Non-constructive proofs of existence are one of the undesirable features of mainstream or classical mathematics. Some non-mainstream mathematicians have investigated how to modify logic to eliminate non-constructive proofs. For example:
Intuitionism is a broad term for this kind of tendency within mathematics. However, the term seems to mean a lot of different things to different people.
The (original) joke (as opposed to Nesov’s flame) isn’t necessarily ideological. It simply lampoons the general attitude of pure mathematicians, who by nature are typically more interested in the theoretical existence of solutions than in the practicalities of finding them, leaving the latter for scientists, engineers, etc. (Mathematicians, in other words, are very “meta” kind of people.)
I did not understand this joke, assuming it was supposed to be funny.
Non-constructive proofs of existence are one of the undesirable features of mainstream or classical mathematics. Some non-mainstream mathematicians have investigated how to modify logic to eliminate non-constructive proofs. For example:
http://en.wikipedia.org/wiki/Brouwer%E2%80%93Heyting%E2%80%93Kolmogorov_interpretation
Intuitionism is a broad term for this kind of tendency within mathematics. However, the term seems to mean a lot of different things to different people.
http://intuitionism.org/
The (original) joke (as opposed to Nesov’s flame) isn’t necessarily ideological. It simply lampoons the general attitude of pure mathematicians, who by nature are typically more interested in the theoretical existence of solutions than in the practicalities of finding them, leaving the latter for scientists, engineers, etc. (Mathematicians, in other words, are very “meta” kind of people.)