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What's a mathematician to do? (2010)

mathoverflow.net

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

#61

Post by susam »

getnormality wrote: post #5

From one of the answers: > mathematics only exists in a living community of mathematicians that spreads understanding and breaths life into ideas both old and new. The real satisfaction from mathematics is in learning from others and sharing with others. All of us have clear understanding of a few things and murky concepts of many more. There is no way to run out of ideas in need of clarification. Yes! And this appli…

> From one of the answers [...]

Thank you for highlighting that answer. It is one of my favourite pieces of writing about the culture of mathematics. I just want to add that that particular answer is now affectionately known as Thurston's Paean.

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

#62

Post by dang »

Related. Others?

Bill Thurston's answer to “What's a mathematician to do?” (2010) - https://news.ycombinator.com/item?id=23461983 - June 2020 (21 comments)

Bill Thurston answers: What's a mathematician to do? - https://news.ycombinator.com/item?id=15578866 - Oct 2017 (25 comments)

What's a Mathematician to do? - https://news.ycombinator.com/item?id=8265509 - Sept 2014 (44 comments)

Bill Thurston's answer to "What's a mathematician to do?" - https://news.ycombinator.com/item?id=4419859 - Aug 2012 (1 comment)

Edit: bonus relateds:

https://news.ycombinator.com/item?id=43345503 (March 2025)

It's not mathematics that you need to contribute to (2010) - https://news.ycombinator.com/item?id=36744690 - July 2023 (65 comments)

Knots to Narnia – Bill Thurston (1992) [video] - https://news.ycombinator.com/item?id=34426275 - Jan 2023 (8 comments)

On Proof and Progress in Mathematics (1994) - https://news.ycombinator.com/item?id=31960487 - July 2022 (1 comment)

On Proof and Progress in Mathematics (1994) [pdf] - https://news.ycombinator.com/item?id=12280139 - Aug 2016 (8 comments)

Bill Thurston has died - https://news.ycombinator.com/item?id=4419566 - Aug 2012 (18 comments)

On Proof And Progress In Mathematics (1994) [pdf] - https://news.ycombinator.com/item?id=2582730 - May 2011 (1 comment)

On proof and progress in mathematics (1994) - https://news.ycombinator.com/item?id=982335 - Dec 2009 (5 comments)

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

#63

Post by rustymather »

lisper wrote: post #45

> One can rewrite their books in modern language and notation or guide others to learn it too but I never believed this was the significant part of a mathematician work There's yer problem right there. Good pedagogy is hard and highly undervalued. IMHO Grant Sanderson (a.k.a. 3blue1brown) is making some of the most significant contributions to math in all of human history by making very complex topics accessible to o…

Seconded. Good pedagogy is like fertilizing the soil- it creates conditions conducive to learning in order to do good research.

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

#64

Post by susam »

dang wrote: post #62

Related. Others? Bill Thurston's answer to “What's a mathematician to do?” (2010) - https://news.ycombinator.com/item?id=23461983 - June 2020 (21 comments) Bill Thurston answers: What's a mathematician to do? - https://news.ycombinator.com/item?id=15578866 - Oct 2017 (25 comments) What's a Mathematician to do? - https://news.ycombinator.com/item?id=8265509 - Sept 2014 (44 comments) Bill Thurston's answer to "What's a…

It's not mathematics that you need to contribute to (2010) - https://news.ycombinator.com/item?id=36744690 - July 2023 (65 comments)

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

#65

Post by zozbot234 »

susam wrote: post #56
lisper wrote: post #45

> One can rewrite their books in modern language and notation or guide others to learn it too but I never believed this was the significant part of a mathematician work There's yer problem right there. Good pedagogy is hard and highly undervalued. IMHO Grant Sanderson (a.k.a. 3blue1brown) is making some of the most significant contributions to math in all of human history by making very complex topics accessible to o…

Good pedagogy is a problem even for graduate-level mathematics students and professional mathematicians. The proofs in many graduate-level mathematics textbooks are, in my humble opinion, not really proofs at all. They are closer to high-level outlines of proofs. The authors simply do not show their work. The student then has to put in an extraordinary amount of effort to understand and justify each line. Sometimes a…

These days it's easy to just look for the details to any proof on mathlib. Of course a computer checked proof is not always super intuitive for a human, but most of the time it does work quite well.

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

#66

Post by ajs1998 »

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.

I simply don't care to gatekeep what counts as education. It has taught me things from videos I can still recall a decade later and pushed me to explore different areas of math I wouldn't have done otherwise.

It's education for whoever finds it educational

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

#67

Post by dang »

susam wrote: post #64
dang wrote: post #62

Related. Others? Bill Thurston's answer to “What's a mathematician to do?” (2010) - https://news.ycombinator.com/item?id=23461983 - June 2020 (21 comments) Bill Thurston answers: What's a mathematician to do? - https://news.ycombinator.com/item?id=15578866 - Oct 2017 (25 comments) What's a Mathematician to do? - https://news.ycombinator.com/item?id=8265509 - Sept 2014 (44 comments) Bill Thurston's answer to "What's a…

It's not mathematics that you need to contribute to (2010) - https://news.ycombinator.com/item?id=36744690 - July 2023 (65 comments)

Inserted. Thanks!

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

#68

Post by gosub100 »

rdevilla wrote: post #8
getnormality wrote: post #5

From one of the answers: > mathematics only exists in a living community of mathematicians that spreads understanding and breaths life into ideas both old and new. The real satisfaction from mathematics is in learning from others and sharing with others. All of us have clear understanding of a few things and murky concepts of many more. There is no way to run out of ideas in need of clarification. Yes! And this appli…

> Everything people have figured out needs to be in living form to carried on. It would appear that LLMs are invalidating this claim. Things can live in synthetic form and carry on just fine. Instead of cultivating a population of learned minds we are just feeding a few dozen egregores of models and training corpuses.

All LLMs do is launder other people's IP. So I don't think you invalidated any other claim.

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

#69

Post by xiaoyu2006 »

bobajeff wrote: post #58
lisper wrote: post #45

> One can rewrite their books in modern language and notation or guide others to learn it too but I never believed this was the significant part of a mathematician work There's yer problem right there. Good pedagogy is hard and highly undervalued. IMHO Grant Sanderson (a.k.a. 3blue1brown) is making some of the most significant contributions to math in all of human history by making very complex topics accessible to o…

I like to watch 3blue1brown too but I think it's a bit of an exaggeration to say his topics are accessible to normal folks. From my perspective I think it's more realistic to say he makes videos that shows you the beauty in math without having to understand it really. Which is valuable since most people get turned off on math because tiresome drills and tests hammered into them at school by people with zero interest…

Quite true. Real math needs practice and calculation to build the intuition and motivation towards the abstraction we want to construct. The video is more of a complementary material to the boring lectures (my prof uses 3b1b videos sometimes).

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

#70

Post by stevenhuang »

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 topics are presented engagingly these efforts will no doubt inspire the next generation.

Young people are curious, sometimes all they need is a spark and to be introduced to a new topic in an engaging way. These forms of content deliver that spark.

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