OK, Just in case you are honestly not able to see the contradiction and not just trying to do a 'gotcha' on me:
Let's say That at this point in your life you are not convinced that we have free will. Furthermore, let's say you think there is a chance that 'determinism' is the reality. If determinism is the reality, how the **** would you know? All your clever tools for thinking, logic, reason, philosophical truisms, etc., would just be the false pre determined patterns in your brain that you have no way of determining whether they are True or false. They are just the way you are predetermined to see things. Go all the way back to Aristotle. A is A? How do you know that? There may be some predetermined rule that says on the 100,000th time you look, A may actually be B.
That is probably the appeal that mathematicians find in their 'pure' field see/feel in it. They see their axioms as consistent and repeatable and so they cling to them as something outside and bigger than themselves with which to anchor their reality and so they cling to it at all costs, no matter how cold and sterile it leaves them. Here there is at least 'proof'.
No, I'm not questioning the laws of math. A really is A. Nor am I questioning the even more obvious existence of free will. Even thought the consequences of free will are harder to deal with.
But If determinism is the reality, I can save myself the trouble of thinking about 'it' and just say 'whatever ...'. Because nothing I 'thought' would matter anyway, it's all predetermined. And therefore, it's not debatable. Assuming 'free choice' is the only way that 'A is A' or 2+2 = 4 means anything.