From wikipedia:
“Solipsism is the philosophical idea that only one’s own mind is sure to exist.”
But I saw the Pythagorean theorem, for instance, before I even knew what the notation meant. Now I can prove it and the proof makes sense. Hence, another mind proved it before I did. The same is true for any mathematical theorem I am not the first to prove. To retain solipsism I would really have to be a mathematical super genius, but not be able to access that genius when sitting in front of a math book. Descarte said: I think therefore I am. The next step should have been the above argument: therefore others exist.
There’s a school of solipsism that posits “your” mind is simply one part of a greater self. If that’s the case, there’s not necessarily a contradiction with the idea that there’s another aspect to “self” that is a mathematical genius unknown to other parts.
Solipsism by definition assumes that your mind is creating the entirely of your perception of the world itself - everything is a figment of your imagination, including other people. The fact that some of those other people do math doesn’t change matters; it’s presumed that actually your subconscious did that math and is now pretending that the imagined other person did it.
Solipsists are kind of self-aggrandizing, aren’t they? They assume their minds are really, really smart and creative - genius level a hundred times over. Probably quite the ego boost, give or take the existential despair.
What’s the difference between a mind that exists in a universe with other minds, and a mind that exists alone in the universe but has other parts of itself that it can’t access?
If I have other parts of my mind that think different thoughts than I do, then in what way are those other parts of my mind part of my mind?
If I just refuse to say that these mysterious other parts of the Overmind that generate all that content aren’t me, then solipsism is refuted. And I do refuse to call those other mysterious things that aren’t part of my mind “me”, because they aren’t.
If there was a discernible difference between the theorized ‘greater mind’ and the real universe, then we could leverage that difference to disprove (or prove) solipsism.
But the point of solipsism isn’t to say that other things are literally controlled by your conscious minds like puppets; it’s to devalue all of the rest of reality based on an undefined ‘realness’ that you claim nothing but you has. Doing this isn’t entirely insane, because there really are things in reality that do indeed falter under closer examination, like mirages, illusions, reflections, and payday loans. Solipsism is just taking the fact that it’s possible for things to be unreal, and applying it to everything without rhyme or reason. Well, everything but onesself, because if you disclaim yourself Descartes starts slapping you about the face.
I think it comes with the territory for them - it’s not like they can form a club and by doing so, have reasonable and balanced debates with one another.
Reported
To be clear, solipsism is not the claim that nothing outside of the mind of ‘you’ whomever ‘you’ is doesn’t exist, merely that we have no way of being certain that those things external to ‘you’ exist. It’s the difference between agnosticism and atheism.
Math doesn’t disprove it because firstly math is a mental construct in and of itself. Math is probably the least likely thing to disprove it. Your example actually helps their case. You’re saying that ‘you’ knew the Pythagorean theorem before ‘you’ had a name for it. That would be something to be expected if ‘you’ were just inventing the ‘world’ out of whole cloth. It would be like saying I ‘knew’ what a bird was before I was given its name. Of course you did, if you were just a brain in a jar, ‘you’ created the bird and then ‘you’ created the name. Why would that be unexpected let alone proof that the external world exists?
I identify strongly with Academic Skeptics that deny the possibility of knowledge; thus the true nature of the world is unknowable. I’m not sure that I even agree that there are degrees of probability since that implies a knowledge of the probability of the truth of a statement and I don’t think that’s possible to even guess at. I can only act via leaps of faith that things are what I generally believe them to be. I have no other option short of staring at a wall until my existence presumably ends if it ends at all. So it strikes me as best to just learn to deal with uncertainty as best I am able.
Not defending solipsism; but it is certainly true that there are parts of your mind that you can’t access. For example, you have no access to the actual algorithms your brain uses to judge the distance and speed of a moving object with enough precision to allow you to reach out and catch it with your hand!
However, if “your” algorithms happened to be better than anyone else’s it would feel a little awkward to receive praise for something your conscious mind is unaware of, in addition to more purely physical talents. In addition we don’t tend to blame people as much for their subconscious thoughts. All this tells me that we consider our conscious mind to be “us”. Therefore, solipsism is incorrect because even if you are a subset of another entity who is actually controlling everything, that higher entity is not you.
I would like to make it very clear that while “you” are all aspects of my own consciousness, I deeply appreciate “you” all for doing some important philosophical heavy lifting for me.
Actually I am saying I beheld the Pythagorean Theorem before I even knew what the notation meant. Now I know what the notation means and I can prove it, and the proof makes sense. If I am the only mind, how could I by chance “dream” a precise, correct mathematical theorem before I had the mathematical maturity to prove it? And it isn’t just a one off. I can open up lots of math books and behold theorems I would have to do a lot of study to be in a position to prove (before looking at the proof in the book).
Nothing refutes the concept of solipsism except that it is an idiotic and juvenile idea that even most philosophy majors move beyond by their junior year. It’s right up there with, “What if there is, like, a hole universe in my fingernail? Whoa!”
Stranger
A potential response might be because mathematical theorems aren’t real except in your mind. You’re inventing the concept and then later inventing the proof of the concept. Math is an invented construct that you created, you just haven’t necessarily created the proof of this construct. It’s even possible that you already have created the proof subconsciously, but not yet articulated it into your conscious mind.
So, in your head, you invent this representation of a thing you call a right triangle. It’s not real and may not represent anything that is possible in the ‘real’ external world whatever that may be. You give it attributes that you invent ways to measure. You then notice that one side is a little longer than either of the other two sides in your imaginary world. Eventually you end up deciding exactly how long this thing is and invent a way to represent it with other made up things that you call letters. You then decide that’s not enough and go about inventing a ‘proof’ of why this works.
A guy making up a D&D world is basically doing the same thing only consciously. Terry Pratchett probably ‘knew’ about octarine before he named it and the presence of ‘octagon cells’ in wizard’s eyes is not proof that octarine is real simply because he also made up those.
I think it’s possible. I mean, have you ever really looked at your fingernail? :eek:
To be fair, Bertrand Russell noted that we are most certain about subjective things, more so than objective things. We can’t say for certain that our perceptions are correct, but we can say that perceptions exist.
Or maybe I’m just talking to myself. 
I had not heard the OP’s argument before. I find it persuasive: while I can imagine some folks figuring out the Pythagorean Theorem, I don’t think I could. Never mind calculus. So I’m pretty sure not-MfM exists.