>>10914866Heres the explanation
It does not seem to me that all areas of mathematics are equally valuable; I am sure that mathematics in itself does not have value. Otherwise, mathematics turns out to be a kind of complex intellectual game, and we find ourselves in the area designated by Hermann Hesse ("Bead Game"), where there are no criteria at all - except for the assessment of the professional community. And the professional community, which is to hide, is simultaneously corrupt and fragmented. The professional community of mathematicians does not have a single criterion, and if it had one, it would only be worse, probably because it would be based on slurred power games on the principle that you scratch me, and I scratch you, a la Academy of Sciences.
Nevertheless, some areas of mathematics are undergoing quite obvious flowering. Yu.I. Manin noticed in the late 1980s that the 1960s was the 10th anniversary of prosperity for algebraic topology, the 1970s for algebraic geometry, and the 1980s for mathematical physics. In this sense, the 1980s continue to this day. The mathematical ideas associated with the 1990s (the mirror hypothesis, Gromov-Witten invariants, Seiberg-Witten invariants, quantum cohomology) all come from string geometry.
I think this is no coincidence. Mathematics lost the general criteria, losing the general context; at the moment, far fewer people understand what is happening in science in general than 20 years ago, and even less than 40 years ago. With the loss of abstract criteria, the utilitarian becomes the only effective criterion. Mathematics is only insofar as it is related to string theory; this is a basic assumption that I do not want to discuss now. Relevance for physics is the only criterion that we have left; and almost all mathematics related to physics relates to string geometry. This thesis is well supported by the observation above: (almost) all of the interesting ideas of the last 20 years are related to string physics.
