Hi, I am a mathematician and I guess most mathematicians would not agree with this. I am quite new here and I am looking forward to reactions of rationalists :-)
I, personally, distinguish “real world” and “mathematical world”. In real world, I could be persuaded that 2+2=3 by experience. There is no way to persuade me that 2+2=3 in mathematical world unless somebody shows me a proof of it. But I already have a proof of 2+2=4, so it would lead into great reform of mathematics, similar to the reform after Russel paradox. Just empirical experience would definitely not suffice. The example of 2+2=4 looks weird because the statement holds in both “worlds” but there are other paradoxes which demonstrate the difference better.
For example, there is so called Banach-Tarski paradox, (see Wikipedia). It is proven (by set theory) that a solid ball can be divided into finitely many parts and then two another balls of the same size as the original one can be composed from the pieces. It is a physical nonsense, mass is not preserved. Yet, there is a proof… What can we do with that? Do we say that physics is right and mathematics is wrong?
Reasonable explanation: The physical interpretation of the mathematical theorem is just oversimplified. This part of mathematics does not fit to this part of physics. The false statement about physics is just different from the true mathematical statement.
But the Banach-Tarski paradox has no physical equivalent. We can not test it empirically, we can just believe the proof. This is probably what I would think if my experiences showed me that 2+2=3. It would appear that in our real mysterious world just 2+2=3 but in mathematical world, which was designed to be simple and reasonable, still 2+2=4.
Similarly, we can guess whether and how the physical universe is curved, yet the Euclidean space will be straight and infinite by definition, no matter what we will experience.
Sure, it can be argued that if mathematics does not reflect the real world then it is useless. Well, set theory is a base for almost all math fields. Even though the particular result called Banach-Tarski paradox have no practical use, more complicated objects in the mathematical universe are used in physics well. Restriction to just “empirically testable” objects in mathematics is a counter-intuitive useless obstacle. In such view, there is no sixth Ackermann number or the twin prime conjecture has no meaning. I can barely imagine such mathematics.
I understand that you may want a simple way to handle theists but abandoning abstract mathematics (or calling it “false”) is definitely not a wise one.
I came across this site and it seems quite interesting to me. I believe that the discussion format can influence the discussion itself a lot. Not sure whether exactly the Kialo format is optimal but I consider Kialo as at least a promising attempt.