Mathematics

Are emotions involved in conclusions/reaching conclusions in mathematics?

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Emotions are not involved in any direct way in our mathematical conclusions (for the conclusions are about numbers, or groups, or vector spaces, or sets, or whatever, not about human things like emotions.) And whether a purported conclusion is indeed a mathematical truth is an objective matter: again, emotions don't come into it.

They are not involved in the proofs of the conclusions either (for proofs are deductions from more or less explicit premisses about numbers, or groups, or vector spaces, or sets, or whatever, to conclusions about such things, and still don't mention emotions). And whether a purported proof is indeed a mathematical proof is again objective matter.

Does that mean emotions have no place in mathematics? Well, we do think of some proofs as beautiful or elegant or cute. And this, you might well think, is a matter of how we respond -- respond emotionally, in a broad sense -- to the proofs. And what makes a mathematician seek to prove a result in the first place (elegantly or otherwise)? It could a utilitarian desire to tick enough research boxes to get tenure. But it could be a genuine love of her topic, a passion to find out more about it. And those are emotional motivations, we might say.

In short: emotions might get the mathematician going, and might be reflected in her aesthetic responses to what she finds: but the body of mathematical knowledge she produces doesn't itself "involve" emotions.

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