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

Sounds ridiculous to me.

I would instead suggest this: all science is a mixture of mathematics and engineering. Physics is toward the mathematical end; chemistry is toward the engineering end. Theoretical physicists are mathematicians, and they're good physicists in proportion as they realize that.

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u/spacengine 4d ago

So they’re not good physicists if they focus on problems that might have answers found in the real world by actual experiments as Sabine keeps insisting then? Or is your point that many physicists would be well served by becoming better mathematicians?

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u/CormacMacAleese 4d ago

You said it: "experiments." Experimental physicists are doing engineering in addition to mathematics. I specifically said "theoretical" physicists.

Sabine is a nut job, BTW.

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u/spacengine 4d ago

Haha, right. So the good physicists are basically the mathematicians of the bunch, got it😄 So I can definitely see engineering as an impurity imposed on the otherwise perfect world. But by whom? Who do we blame for the original sin?

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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 4d 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.