Timeline for What can I tell a student I am mentoring who claims: "I want to do pure mathematics because it is superior to any other subject in the world"?
Current License: CC BY-SA 4.0
9 events
| when toggle format | what | by | license | comment | |
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| Apr 9 at 23:32 | comment | added | bubba | Regarding “what can be more beautiful than pure mathematics”. Beauty is somewhat subjective, but here’s a few things on my list: ocean waves breaking, clouds billowing in the sky, sunsets, tigers, hawks hovering in the wind, my child, my wife. Pure math isn’t even in the top ten, for me, though $e^{i\pi} + 1 = 0$ might come close. | |
| Apr 8 at 14:19 | comment | added | Jochen Glueck | (Just for the record, it did not downvote.) | |
| Apr 7 at 20:50 | comment | added | nick012000 | "Regarding for instance Newton's second law F=ma: What is the "gift of pure mathematics" here?" I'm pretty sure it's the existence of mathematical equations at all. Have you ever read the really old mathematical texts from before equations were invented? They tended to be quite wordy. | |
| Apr 7 at 9:32 | comment | added | Jochen Glueck | @learner: The derivative dv/dt in Newton's second law is neither an equation nor a relation, though. Calling derivatives and calculus "pure mathematics" is also quite a stretch. And, most importantly, the derivative in Newton's second law is certainly not a gift of pure mathematics. It was invented by Newton himself in order to do physics. That said, yes, there is obviously a lot of mathematics in the sciences and in engineering and it is very useful there. But this doesn't explain the meaning of your sentence that I cited, nor does it explain how this sentence helps to answer OP's question. | |
| Apr 7 at 7:15 | comment | added | Jochen Glueck | @nick012000: I do of course know how mathematical equations in physics look like. I just don't understand the meaning of the sentence I cited. Regarding for instance Newton's second law F=ma: What is the "gift of pure mathematics" here? You can, of course, also consider more complicated stuff, say Schrödinger's equation. But again what is meant by "gift of pure mathematics"? The fact that one can write down a PDE? The insight that the equation is well-posed since the Hamiltonian is self-adjoint? But the latter insight (called Stone's theorem) is not an equation. | |
| Apr 6 at 21:18 | comment | added | nick012000 | @JochenGlueck I think he's talking about things like "F=MA", "V=IR", or "E=Mc^2". | |
| Apr 6 at 17:04 | comment | added | learner | @JochenGlueck, As a PhD scholar in number theory, it is my understanding. I am completely convinced what I said. "Mathematical equations/relations" governs the universe, no one can deny it. | |
| Apr 6 at 14:09 | comment | added | Jochen Glueck | "'Mathematical relations/equations' are the biggest gift of pure mathematics." No offence intended - but as a mathematician I have no idea what this sentence is supposed to mean. | |
| Apr 6 at 10:35 | history | answered | learner | CC BY-SA 4.0 |