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What's a mathematician to do? (2010)

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

#91

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?

> once someone attains a postdoc-level...

... they will discover that level is already crowded by LLMs

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

#92
post #89

Earlier quoted context omitted.

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.

I agree with that, but inspiration is not education. If you watch everything Numberphile has produced, you'll come out of that with no new skills and trivial new knowledge.

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

#93

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 t…

@ivansavz, thank you for the followup and sharing your thoughts on b).

Some time ago, when my Dad asked me to teach him a bit of programming, I made a huge mistake. I was arrogant, and thinking to teach him in a way I learned. And it was totally wrong, totally wrong on many levels on the approach, on the emotional aspect of it.. just totally wrong.

He is no longe with me, and I keep coming back to this, as I cannot fix it.

So from that time, gradually I started unpacking, if he were alive today -- how would I do that differently.

It is at that time (now 20+ years ago) that I started coming up with these

personalized learning, audience specific rendering of the material. And think these two need to be combined together.

My Dad had different analogies and reference points than me, and also he was brighter, faster in many ways, while I tend to be slower and less visual and I have easier time with hypotheticals/and abstractions.

So the personalized part has to reflect the differences. Another example, every time I open a book on statistics I see pocker, cards and various other things -- I have no idea about. These are not great analogies/examples for me as I struggle to grasp the context.

Yet, I also appreciate (now, when it is late) that others are different than me.

So my thought here in a way, similar to yours but merging together student's-level plus students personal experience/background.

So in that context I would say

1). Each student has to built out (may be even gradually) a profile of preferences (background, subject level, visualization proficiency, many other nuanced cognitive differences). May be bulding it answering some sort of logntitudional survey (over time) is a right approach here.

2) The presentation material would be separate into core , presentation, assessment

3) core stays the same and developed by the core instructor/teacher author

4) presentation is developed my multiple means and authors 4i) by the author(s) themselves adopting some 'default student profiles) 4ii) by author(s) authorised contributors that develop materias for other student profiles

5) assessments done in same way as (4).

Then when I as student order (buy) or download or subscribe to the given textbook or a class I specify my profile (that's built in (1)), may be some other learning preference, click 'generate' (or subscribe if that's an online class) and I get the 'rendered' material that I then use.

(of course if the whole system also has online presense, then there is a benefit of a 'forum-like' community around similary-rendered materials -- as it will have folks with, presumably, similar profiles, and the same about assessments).

--

I agree with you that the students agent may dictate the type of rendering so to speak for the materials. In way, i am thinking to capture that with the longtitudional survey updating student profile, through their lifelong learning journey.

WRT a lot of work, agreed I am hoping that 4ii) is an attempt to partially address it.

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

#94

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.

I've seen this floated as a response to the current anxieties over LLMs in math. Namely in applied math, LLMs being good at pure math may actually allow the import of pure math techniques. Unclear if that will pan out, but it's interesting to consider.

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

#95
post #89

Earlier quoted context omitted.

"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.

I agree with that, but inspiration is not education. If you watch everything Numberphile has produced, you'll come out of that with no new skills and trivial new knowledge.

Pedantically speaking you may be correct about Numberphile, but many times Numberphile provided the exposure and critical nudge to follow up on a piqued curiosity. That did end up imparting new skill.

However I will push back on the claim that inspiration is not education. It may not be sufficient on its own when resources are not readily available. But now that they are it's the inspiration and persistence that are the missing magic sauces.

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

#96

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.

Can confirm: am mole person, live at mall.

Write software for fastfood which decides the fate of millions.

Don't know who I work for or what qualities made me get the job.

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