I only brought up gender because I was clarifying what the quoted author meant because the person I originally replied to found it confusing and spurious. I think the key is that the intersubjective nature of science means that it is open to social analysis, a subset of which is feminist analysis, and basically I've just been giving my interpretation of what the quoted author was saying.

You brought up a lot of interesting points but I only have the energy to respond to one of them given my reception lately :)

> To that point, I would really be interested in hearing a little more about how intersubjectivity plays out in the mathematics research community.

1. What constitutes a correct proof? A proof has to convince other humans. Two mathematicians who work together a lot can sketch out an informal proof that they both agree on, but it's harder to write a proof that is widely considered rigorous enough. A fully formal proof that a computer can verify isn't anywhere near feasible. What constitutes rigor today is different from what constituted rigor for Euler is different from what constituted rigor for Euclid.

2. Most mathematics isn't done as symbol manipulation. Mathematicians rely on their human intuitions. We share a lot of the same cognitive structures but we each have our own preferences.

"It must be admitted that the use of geometric intuition has no logical necessity in mathematics, and is often left out of the formal presentation of results. If one had to construct a mathematical brain, one would probably use resources more efficiently than creating a visual system. But the system is there already, it is used to great advantage by human mathematicians, and it gives a special flavor to human mathematics." - Ruelle (1999)

Interesting idea: if there are differences between how men and women think, there could be a male and female mathematics. I doubt there is any significant difference though. Likewise, autonomous AI will almost definitely do mathematics with a distinctly different flavor from human mathematics even though they should be mutually intelligible.

3. What we think is important to study is what we think our peers and superiors value. A grad student does mathematics their adviser thinks is interesting. A grad student chooses their adviser based on their interests. Which fields get grant money? Which are "hot"? Which fields are all but abandoned even if they have legitimate open questions?

4. Mochizuki has published a proposed proof of the ABC conjecture. That's a huge result. It has not yet been widely accepted because he worked alone for several years and the concepts he has come up with are very foreign to every other mathematician. So, a lot of the work of "proving" the ABC conjecture is teaching his ideas to other people even though he has produced a detailed proof. You can't just read the proof and understand it.

5. This isn't math, but physics. It's in the news recently that a time crystal may have been constructed. It's not entirely clear if a time crystal can even exist. How can two physicists look at the same experimental data and hold two different positions on this question?

6. Likewise, https://www.quantamagazine.org/20140827-quark-quartet-fuels-...

Physicists, hardest scientists of them all, getting really emotional about QCD? But I thought science was about objective facts! "Objectivity" is what remains when the science has settled, it is not the science itself, and it certainly is not a permanent state.

P.S. http://plato.stanford.edu/entries/process-philosophy/