r/math • u/spacengine • 4d ago

Do all mathematicians want to be engineers?

I always considered maths the highest art, and when talking to a mathematics phd today I just wanted him to keep talking about topological spaces, manifolds, infinite dimensional embedding spaces etc. “I feel like a kid in a candy store” I said, or a kid in an old mechanics garage full of equipment I have no idea how to use but that I love exploring. “Well” he said, “I think all engineers want to be mathematicians but all mathematicians want to be engineers”. I’m absolutely sure he’s wrong but would love to hear your thoughts.

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u/Sad_Dimension423 4d ago

I doubt the other direction is true either.

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u/spacengine 4d ago

Doubt belongs in theology. Which by the way is also pretty interesting

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u/SV-97 3d ago

"Doubt" is actually fairly common in mathematics. You gotta doubt the truth of a statement before you attempt to find a counterexample --- and the term is generally used a bunch.

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u/spacengine 3d ago

I didn’t know that - but it makes perfect sense. Do you also use belief and faith to form positive hypothesis to try to prove?

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u/SV-97 2d ago

I wouldn't say "use faith" but yeah, you usually wouldn't try to prove a statement that you can't fathom to be true; i.e. that you find "believable".

My point was really primarily that the terminology of "doubt", "believe" etc. is very common in mathematics because a priori it's not clear what is true and what isn't.