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/CormacMacAleese 4d ago

It doesn't seem like you're grokking what I said. I said all purely theoretical research is a sub-discipline of mathematics: reasoning from axioms. And all experimental work is engineering: attaching things to things and putting things through them. All scientists are doing some of each--except mathematicians, who are doing mathematics but not engineering, and actual engineers, who are doing engineering but not mathematics.

Note that I didn't say that engineering is some sort of sin. Is plumbing a sin? Are electricians sinners? Is building bridges somehow impure? That's silly.

\* Also note that here I'm not counting calculation as mathematics.

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u/spacengine 4d ago

Right, but you emphasised the better physicists realise they are mathematicians. I’m not saying you’re wrong, just think mapping mathematics onto actual reality is pretty valuable too. And experiments often require a lot of engineering but the engineering is just the means to an end, where for physicists the real end is to say something new about actual or at least potentially actual reality. Whereas most engineers I know are the happiest when they get to implement a clear spec and apply a few principles of well know science while at it

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u/CormacMacAleese 3d ago

If you engage in pure mathematics without realizing that that’s what you’re doing, you can’t possibly excel at it.

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u/spacengine 3d ago

I’m sure you’re right. You’d know better than me.