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What's a mathematician to do? (2010)

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Re: What's a mathematician to do? (2010)

#81

Post by aleph_minus_one »

transitorykris wrote: post #33
nimonian wrote: post #21

Earlier quoted context omitted.

It's a delightful counterintuition that your gut feeling is mostly wrong: https://webhomes.maths.ed.ac.uk/~v1ranick/papers/wigner.pdf Far from being motivated by some applications, the most useful discoveries in mathematics are usually discovered "for their own sake" and their application is only discovered later. Sometimes centuries later!

Parents reads as a comment on the usefulness of applying mathematics to problems in the world (applied mathematics) and discovering mathematical problems that push mathematics forward (pure mathematics) in the process. Pure mathematics is incredibly important, but I’d hardly count it as useful if we need to wait centuries.

> but I’d hardly count it as useful if we need to wait centuries.

This is not the fault of the mathematicians.

Re: What's a mathematician to do? (2010)

#82

Post by kcexn »

skybrian wrote: post #32
nimonian wrote: post #21

Earlier quoted context omitted.

It's a delightful counterintuition that your gut feeling is mostly wrong: https://webhomes.maths.ed.ac.uk/~v1ranick/papers/wigner.pdf Far from being motivated by some applications, the most useful discoveries in mathematics are usually discovered "for their own sake" and their application is only discovered later. Sometimes centuries later!

If so that seems like an opportunity for people who want to work on applied math? There’s a big backlog of techniques that so far have not been useful.

Absolutely! The backlog is enormous though, and much of mathematics requires a great deal of work to understand it to the depth required before a novel application becomes apparent.

Re: What's a mathematician to do? (2010)

#83

Post by beyonddream »

fasterik wrote: post #80
beyonddream wrote: post #78

I am glad to see this today - after reading Tim gower's recent post on chatgpt 5.5 pro's phd level research ability I was feeling slightly sad about the future of math research. Interestingly enough, the moment I saw the title I thought of Bill Thurston's famous article "On proof and progress in mathematics" and the top comment on the OP's thread is from him! Reading his reply sort of gave me the antidote to the temp…

Why did it make you sad? I can see why it would make training researchers harder, but once someone attains a postdoc-level skill in mathematics research, wouldn't having a PhD-level AI assistant just boost one's ability to do more ambitious research?

You should read that essay! The model is capable of producing phd level research on it's own with minimal set of prompt's. I was sad because of this paragraph:

"That view is that there is still a great deal of value in struggling with a mathematics problem, but that the era where you could enjoy the thrill of having your name forever associated with a particular theorem or definition may well be close to its end. So if your aim in doing mathematics is to achieve some kind of immortality, so to speak, then you should understand that that won’t necessarily be possible for much longer — not just for you, but for anybody."

He may seem to imply the end is only for some subset of reasons but if you read the entire essay he is just trying to give hope where the rest of the essay is really damning!

Re: What's a mathematician to do? (2010)

#86

Post by lmm »

jvans wrote: post #26
bloaf wrote: post #16

So I've got a gut feeling that math (like human languages (like programming languages)) is best learned in service of some greater end. I look at some truly impressive projects like CLASP which sprang into existence not because of someone noodling around, but because they had a bigger goal which required the team build it. So my advice to any mathematician who feels lost, like they don't know what to work on, would b…

Lots of fun counter examples to this. Complex numbers were introduced in the 1600s with no practical application for almost 300 years until they were used in electromagnetism and quantum mechanics.

> Complex numbers were introduced in the 1600s with no practical application for almost 300 years.

On the contrary, complex numbers were introduced to make the cubic formula work.

Re: What's a mathematician to do? (2010)

#87

Post by fatih-erikli-cg »

Nothing. Your personal computer comes with written code. They are written by people who they live in malls. So they deny that they were using your computer and they claim that the written code is math. You pay their fastfood money when you buy a computer. Ask how a square root is calculated if you see mathematican. It is loop that starts from 0 to the answer. Computer does that.

Re: What's a mathematician to do? (2010)

#88

Post by [deleted] »

fatih-erikli-cg wrote: post #87

Nothing. Your personal computer comes with written code. They are written by people who they live in malls. So they deny that they were using your computer and they claim that the written code is math. You pay their fastfood money when you buy a computer. Ask how a square root is calculated if you see mathematican. It is loop that starts from 0 to the answer. Computer does that.

[deleted]

Re: What's a mathematician to do? (2010)

#89

Post by srean »

thaumasiotes wrote: post #60
ajs1998 wrote: post #48

Earlier quoted context omitted.

This is why I think Brady Haran is one of the coolest living mathematicians. Numberphile is educating a new generation of young mathematicians for anyone with access to youtube. Accessible math communication is so important. So many cool things are buried in textbooks and papers the average person would never read.

Numberphile doesn't do any education. That's like saying the Discovery Channel is educating a new generation of zoologists.

"If you want to build a ship, don’t drum up the men to gather wood, divide the work, and give orders. Instead, teach them to yearn for the vast and endless sea" -- Saint-Exupery

This is exactly what Numberphile does. Those who are hooked will find the resources on their own. They need a reason to look for them and Numberphile gives them one.

Re: What's a mathematician to do? (2010)

#90

Post by ivansavz »

vladislavp wrote: post #43

a) Individualized teaching methodology. We come with different backgrounds, therefore different types of analogies/examples, different levels of background material, different (but systematized) levels of presentation should be used. The same ask should be applied to kids learning through starting at preschool. b) Readable mathematics papers where the compact notations are abandoned, and narrative, visualizations are…

I've been thinking a lot about your point b) over the years.

I'm conceptualizing a piece of knowledge as an interface that can be `implemented` but with different classes (explanations renderings for different audiences).

For example, the "derivative interface" represents knowledge of the concept of derivative operations and basic skills to compute derivatives of various functions. The interface doesn't specify HOW to teach this topic or HOW DEEP, so there are multiple implementations:

  - basic visual explanations (for kids)
  - basic algebra steps (for high school)
  - standard explanation (for undergraduate students)
  - compact explanation (a reviee for grad students)
The above implementation are polymorphism due to the "reader level of knowledge," but there could be other, e.g. derivatives explained using code like in Sec 4.1 in this calculus tutorial[1].

It would be A LOT of work to produce all these explanations but it would make for a kick ass math textbook that you can pick up and learn, no matter what your level is (instead of getting lost or bored and looking for another resource).

[1] https://minireference.com/static/tutorials/calculus_tutorial...

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