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 to agree about something.
I mean, sure, sometimes, I disagree about something, with some other student, but I'm sure that either he can convinces 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 how 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 you for example 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 if in physics, you have great minds like Albert Einstein, who was convinced that "God doesn't play dice." and disagreeing about this subject with other scientist until the end of his life.
So to my experience, this doesn't apply to mathematics so much. The only nowadays mathematician that I've ever heard of that strongly disagrees with other mathematician is N J Wildberger. I was was watching this video,
https://www.youtube.com/watch?v=5CiiGdaYEPU
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 are my question:
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Am I right, that almost all mathematician, in the end, agree about things in mathematics ? Or are there much more mathematicians like NJ Wildberger that I'm not aware of ?
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If I'm right in (1), I'm curious, what makes mathematics so that mathematicians agree? I've my own ideas about this, but I would like to hear others about this. What is the big difference between mathematics and 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.
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Is NJ Wildberger right that in the past mathematicians disagreed much more ?
Best Answer
As an example of a mathematician who disagrees with lots of things in standard mathematics, you might consider Doron Zeilberger. He has lots of controversial opinions, the main one being that demanding rigorous proof is counterproductive (we'd be better off having a more 'experimental' view of truth). He sometimes comes close to saying that mathematics using infinities is wrong (or more accurately, meaningless).