So a substantial number of students this semester have come to me asking “what even is math research?”. Some interested in getting involved, some just curious. It’s like I have no response to this, but I was wondering if anyone had a resource that could explain this to a college freshman. - ThreadSky

tienchihmath.bsky.social • 8 days ago

So a substantial number of students this semester have come to me asking “what even is math research?”. Some interested in getting involved, some just curious.

It’s like I have no response to this, but I was wondering if anyone had a resource that could explain this to a college freshman.

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visualalgebra.bsky.social•8 days ago

Hold up your phone and say "this is a new invention." Until last year, it had never been made before by ANYONE in human history. But that doesn't mean that the engineers who made it discovered things that Thomas Edison and Alexander Graham Bell simply missed. 1/5

visualalgebra.bsky.social•8 days ago

That's because it couldn't have been invented in 1885. Or in 1995, 2005, or even 2015. Its creators just built off of what had been done before, added features, and made it better. It's still a new invention, though, done by smart well-trained people. 2/5

visualalgebra.bsky.social•8 days ago

Math research is like the theoretical version of that. Many problems that people work on today wouldn't have existed in 1995. Or in 2005, or 2015.

I've found that people can relate to that analogy. 3/5

visualalgebra.bsky.social•8 days ago

Then, give examples. How do QR codes work? How does your bank account validate your encrypted password without storing it on their servers? How does Netflix know what movies to suggest to you? How does Google maps find the shortest route between cities? 4/5

visualalgebra.bsky.social•8 days ago

How does an airline schedule thousands of flights a day, with minimal wait time and without their planes being half-empty? Math problems are all over our everyday lives, but we don't even realize it. And many of these problems wouldn't have made sense 100, 50, or even 20 years ago. 5/5

tienchihmath.bsky.social•8 days ago

This is awesome, thanks!

visualalgebra.bsky.social•8 days ago

Oh, I also talk about patents. There were approx 150,000 in the US last year. And *every one of them* was a new invention to mankind. But very rarely are any comparable to the lightbulb, automobile, steam engine, etc.

Published theorems are the math research analogue. People “get that.”

mathforge.org•8 days ago

In case it's of any use, here was my attempt to trace the story of a proof to show the scaffolding of how it came to be.

https://loopspace.mathforge.org/IMathematician/StoryOfAProof/

afreeparticle.com•8 days ago

#iTeachMath #MathSky

malmeida.bsky.social•8 days ago

A former student is doing a math REU (I only ever did physics ones) and I'm looking forward to asking him about his experience!

hannabennett.bsky.social•8 days ago

I still have the notebooks I used during grad school while figuring out my thesis, and I show them to students who ask this. They’re kind of a chaotic mess of me working through examples, doing the same things over and over, the occasional doodle or me complaining that something didn’t work, etc.

tienchihmath.bsky.social•8 days ago

I was going to show them some of my latex notes to myself and iPad drawings. There are occasional swears when working out the details of a line which didn’t make sense yielded a counterexample.

clontz.org•8 days ago

Something to add to https://openmathbooks.org/what-do-mathematicians-do 😅

mathforge.org•8 days ago

📌

tienchihmath.bsky.social•8 days ago

I’m really glad this project exists, and I’m happy to contribute something if there is a need/desire!

clontz.org•8 days ago

The goal is for this to be a community project! Would love your input.

maria-naturalmath.bsky.social•8 days ago

We start every math circle asking children and their parents (5yo and up), "What do mathematicians do?" Maybe they can have a page in your project?

clontz.org•8 days ago

Sounds like a neat contribution!

chrisstaecker.bsky.social•8 days ago

I made a short video about what it’s like to do it-
https://youtu.be/yckPYJgjXeY

tienchihmath.bsky.social•8 days ago

"It took about two hours of work in a long and boring faculty meeting. They had food, so I went, but they can't make me pay attention" no they can't!! 💪💪💪

tienchihmath.bsky.social•8 days ago

This is amazing, will definitely share this. Have you thought about a Journal for Humanistic Mathematics paper about this?

chrisstaecker.bsky.social•7 days ago

Thanks!
never thought about writing it up- worth considering...

cubesart.bsky.social•7 days ago

Could you please document that process too? Thx

tienchihmath.bsky.social•8 days ago

lol, It's *not* like I have no response to this. Man, negating a statement sure changes it's meaning doesn't it 😆?

mathartforall.bsky.social•8 days ago

Are they asking about independent research projects or assisting existing research? Both?

tienchihmath.bsky.social•8 days ago

Both and also unclear what math research even is. I think most people think new math hasn’t been done since the 1500’s.

mathartforall.bsky.social•8 days ago

Independent wise I have advised HS seniors.

1. You can study anything you are interested in.
2. You don't have to discover anything new.
3. You don't even have to succeed in proving a modest conjecture

We need YOUR perspective on mathematics to keep this adventure moving.

Something like that?

tienchihmath.bsky.social•8 days ago

I think that’s all great advice, thanks! But they don’t, I think, get at heart of “what is it exactly you all do?”

mathartforall.bsky.social•8 days ago

"what is it exactly you all do?" - such a wide range of mathematics and mathematicians, hard to know where one might start. There is the day to day practice and there is the passion that underlies that.

It is work of pure imagination - a lot of "yeah, but what if?!?!?"

imho

pauldrowe.bsky.social•8 days ago

I’m in industry(-ish) but i feel like I should have better advice. Sadly I don’t. The best I’ve got is to encourage natural questions until they reach one that doesn’t have an answer. I think most students will be surprised how quickly that happens. What to do next is a challenge though.

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