I know it's an off beat question but I thought a philosophical answer would be better. I've been trying to study some different sciences in my life, ranging from biology to mathematics, and if I try to explain to people why I like mathematics above the others, I think the most important reason for me is that mathematicians, in the end, almost always seem agree about something.
I mean, sure, sometimes, I disagree about something with some other student, but I'm sure that either he can convince me that I am wrong, or I can convince him that he is wrong. Or if we are really stubborn, I'm sure that we can go to a teacher, and however stubborn we may be, in the end, one will be convinced that he is actually wrong.
Well, in all other sciences, the opposite seems to be true. If for example you look at health sciences, then you hear a scientist, that studied this matter for years say almost the exact opposite of some other scientist. And those scientists debate with each other, and in the end they still disagree.
Even in physics, you have great minds like Albert Einstein, who was convinced that "God doesn't play dice," disagreeing about this subject with other scientists until the end of his life.
So in my experience, this doesn't apply to mathematics so much. The only mathematician nowadays that I've ever heard of that strongly disagrees with other mathematicians is N J Wildberger. I was was watching this video,
where he is trying to convince the audience why they should change their mathematical point of view. What interested me most is that he claims that historically mathematicians disagreed much more than we do now, which I wasn't really aware of.
So here is my question:
Am I right, that almost all mathematicians, in the end, agree about things in mathematics? Or are there many more mathematicians like NJ Wildberger that I'm not aware of?
If I'm right in (1), I'm curious, what makes mathematics so that mathematicians agree? I've got my own ideas about this, but I would like to hear others about this. What is the big difference between mathematics and the other sciences that makes mathematicians agree much more. And if I'm wrong in (1), can you give me some nowadays mathematical debates, where those disagreements are discussed.
Is NJ Wildberger right that in the past mathematicians disagreed much more?