At least intuitively, it is not clear to me why wisdom as such has value.
For example, I feel that dedicating your life to studying chess is almost valueless (and Bobby Fischer also felt that way at the end of his life). True, it may have entertainment and aesthetic value if someone plays beautiful games, but if we take the entertainment value out of the picture, it is really hard for me to find value in a person sitting in his room and developing the theory of chess.
In the end, how is that different from theoretical mathematics? (Especially since theoretical math does not even have the entertainment value.) Why think that wisdom has value in itself?

Every intellectual development has very considerable value.
Even if at the moment it has no practical value, our world has always been based on progress, and it is only a matter of time, whether long or short, until there will indeed be some use for a theoretical mathematical development.
Thank you

The question is definitely a good one, but it is clear that research and development in every field, including mathematics, when driven by human curiosity, is not only important but constitutes the very essence of the human spirit on this planet. When stardust gathers over the course of 13 billion years into creatures with understanding and consciousness that ask what their source is, that is simply moving, not to say unfathomable. The question is always there, and there are countless examples of theoretical research that over the years became practical and important and interesting early on, and there is simply no force that will stop such research, not even Trump

Theoretical mathematics is simply something that describes nature that we have not yet discovered

It is simply not true that every mathematical discovery becomes useful at some stage. Very far from it. The overwhelming majority have no use at all.

It is also not true that theoretical mathematics is a part of nature that we have not yet discovered. Mathematics does not describe nature at all.

As for the question itself, the practical aspect is a means that allows us to live, and the question is what we live for. Wisdom is one of the goals, and therefore to see usefulness as the purpose of wisdom is to turn things upside down.
A parable: a poor Chinese man received two small coins of charity and bought a slice of bread and a flower. When he was asked why he did not buy two slices, he answered that he bought the bread in order to live and the flower so there would be something to live for.
By the way, in all fields in academia, most work is not useful. That is not a feature unique to mathematics.

Fair enough, let us say that justifies a person engaging in theoretical mathematics for enjoyment in his private time.
But according to your own view, you also admit that it is not appropriate for just anyone to be a kollel fellow and make a living at the state’s expense, unless he contributes something significant to the world of Torah study, and I assume the same would apply to mathematics.
And if a person is engaged in some field that only 8 other people in the world are capable of understanding, how is his contribution different from that of an untalented kollel fellow? After all, I am sure he too has a positive influence on maybe 8 people in his yeshiva and helps them learn a bit.
So my question is this: if contribution has no significance here, why should not a person without talent also be a kollel fellow and receive money like the mathematics professor, when both of them barely contribute to anyone besides themselves? And if contribution does have significance here, in what way does the professor of algebraic topology, whose work is understood by 8 people, contribute more than the failed kollel fellow who helps 8 people?

Indeed, I have no objection at all to funding kollel fellows with proper screening and in reasonable measure.

In 1940 the mathematician Godfrey Harold Hardy, a highly regarded mathematician in the field of number theory, published a book, “Apology,” in which he defended the “uselessness” of the fields he worked in (including number theory).

Decades later, thanks to number theory, the field of cryptography developed (RSA encryption, for example), all thanks to discoveries in number theory.

We never know in advance which knowledge will move humanity forward and which will turn out to be completely irrelevant. Neural networks too were considered for a long time an unnecessary model for artificial intelligence, until our computing power grew by dozens of orders of magnitude and they became the basis for the most advanced AI systems in the world.

These are well-known points. But how do you get from here to the conclusion that every mathematical discovery has a use?

Ignorance. Without pure mathematics, even the theory of relativity would not have come into being. The use of theoretical mathematics in physics and in many other fields often appears long after the theoretical invention. Computing as well developed out of pure theoretical mathematics, and so on.