is it true that physics and maths majors are more successful physicians than bio majors?

[Lawpy]

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The early pioneers of math were physicists because it really required practical problems that required an extensive mathematical language. But the field of mathematics has been pioneered by mathematicians, and many problems in physics are being answered totally or partially by mathematicians (paging Professor Tao). Call it returning the favor. 😉

But yes, mathematics is a language, and it's great at describing the physical world. That doesn't discount the amazing things being done in pure math. It just makes math that much more awesome. 😀

At that point, pure math is really just logic and philosophy. You're just using definitions and axioms to prove theorems, and then utilizing those theorems to prove other (often larger and more fundamental) theorems and lemmas.

Proofs can be derivations as well.

 

[Matthew9Thirtyfive]

At that point, pure math is really just logic and philosophy. You're just using definitions and axioms to prove theorems, and then utilizing those theorems to prove other (often larger and more fundamental) theorems and lemmas.

Proofs can be derivations as well.

It's true that pure math is logic in the sense that logic is general principles of valid reasoning. But it's not just using axioms and definitions to prove theorems. Yes, pure mathematics requires proofs, which is essentially a form of logical reasoning. In fact, in areas of set theory, you might argue that it is more philosophical than mathematical.

However, mathematics has a larger toolbox than philosophy. In fact, it was a logical paradox that led to the discovery of calculus (coming full circle--no pun intended).

 

[Lawpy]

It's true that pure math is logic in the sense that logic is general principles of valid reasoning. But it's not just using axioms and definitions to prove theorems. Yes, pure mathematics requires proofs, which is essentially a form of logical reasoning. In fact, in areas of set theory, you might argue that it is more philosophical than mathematical.

However, mathematics has a larger toolbox than philosophy. In fact, it was a logical paradox that led to the discovery of calculus (coming full circle--no pun intended).

Interesting perspectives. Honestly, i think much of the pure math was established after mid-19th century, when fundamental concepts were overhauled and subjected to very rigorous proofs in a strictly defined philosophy. This led to calculus being redefined and rederived under principles/theorems of real analysis (that's where Riemann integrals come into play).

I personally don't put much weight into the original discovery of calculus and the logical paradoxes involved when there was a fundamental shift few centuries later. It's from this modern format and definitions that I think math behaves largely as a philosophy rather than a unique subject.

Then again, i'm biased, since I lazily attribute empirical/observational discoveries to science and theoretical/deductive reasoning and proofs to philosophy.

 

[Matthew9Thirtyfive]

Interesting perspectives. Honestly, i think much of the pure math was established after mid-19th century, when fundamental concepts were overhauled and subjected to very rigorous proofs in a strictly defined philosophy. This led to calculus being redefined and rederived under principles/theorems of real analysis (that's where Riemann integrals come into play).

I personally don't put much weight into the original discovery of calculus and the logical paradoxes involved when there was a fundamental shift few centuries later. It's from this modern format and definitions that I think math behaves largely as a philosophy rather than a unique subject.

Then again, i'm biased, since I lazily attribute empirical/observational discoveries to science and theoretical/deductive reasoning and proofs to philosophy.

Calculus has been refined many times since its discovery. Not sure how that colors its history. The theory of evolution has been refined a number of times, but that doesn't change its past.

Like science, mathematicians build on what exists. Fermat discovered ways to find extrema and to perform integration using summation. Cavalieri came up with his method of indivisibles. And of course, Descartes. There are of course, others. The point is that Newton and Leibniz had to take what was there and extend it--use it in a novel way.

A more recent example is Andrew Wiles and his proof of FLT.

Riemann just completely revolutionized mathematics (geometry/number theory) and mathematical physics (uh, general relativity?). Started out as a philosopher. 😉

ETA: I agree that pure math is and can be quite philosophical. But there is more to it.

 

[Lawpy]

Calculus has been refined many times since its discovery. Not sure how that colors its history. The theory of evolution has been refined a number of times, but that doesn't change its past.

Like science, mathematicians build on what exists. Fermat discovered ways to find extrema and to perform integration using summation. Cavalieri came up with his method of indivisibles. And of course, Descartes. There are of course, others. The point is that Newton and Leibniz had to take what was there and extend it--use it in a novel way.

A more recent example is Andrew Wiles and his proof of FLT.

Riemann just completely revolutionized mathematics (geometry/number theory) and mathematical physics (uh, general relativity?). Started out as a philosopher. 😉

ETA: I agree that pure math is and can be quite philosophical. But there is more to it.

Guess i need more exposure to pure math then. And always enjoy a good history of mathematics

 

[Matthew9Thirtyfive]

Guess i need more exposure to pure math then. And always enjoy a good history of mathematics

Yeah, it's super cool. Pure mathematicians are like the ultimate theorists to me. I find it really cool, but alas, my research interests always tend towards the applied.