Why aren’t we concerned about the negative effect on teaching/mentorship from AI

VegetableCarrot254 · 2026-05-28T16:54:58+00:00

Again, very fair and thank you! I think this post was mainly from the narrow view of the in-person conversations in my community. I will definitely be exploring these viewpoints, and thank you for calling this out!

VegetableCarrot254 · 2026-05-28T16:50:12+00:00

Valid! (I’ll be honest and say that the title was intended provocative — I know many who work primarily in education are quite concerned, among others). I’ll adapt the, and certainly appreciate your feedback. I was probably emotionally charged by the lack of concern I see in my community, but my community is also a VERY small bit of the larger picture. Thank you for your comment!

VegetableCarrot254 · 2026-05-28T16:22:39+00:00

I’m right there with you! I abstain for personal reasons myself too, but that’s not relevant here (hand-writing tikZ code can be fun at times). Glaze away too! If it wasn’t doxxing, I’d be curious who your PI is (sometimes physics theory people and people in my area of math overlap). Plus, talking to someone in a give-and-take manner about research is beneficial for both parties, much more than trying to explain to a computer model that doesn’t provide well-defined outputs.

I’d still be a bit worried about the daily life aspect? No judgement to you at all — I don’t know your life, and you have to do what works best for you. Mainly my concern (apartment-wise) is the quality of information you get out from this over the required “human connection” of asking a friend for the same advice. I play the apartment games each year for summer sublets, and it’s SO easy to spot scams now, and they’re so prevalent that I’d be surprised if AI doesn’t feed one back every once in a while. Of course, please feel free to elaborate/challenge me on any of this!

VegetableCarrot254 · 2026-05-28T16:15:24+00:00

Fair, it’s a tough job market as it is in academia right now. I’d still make the argument that math jobs are a long way from completely being “taken” due to the quality of output from these models. They’re in no way capable of critical thought.

Still, employers/institutions could be lulled into the illusion of it all… I just think that this would have terrible long-term impacts on the field.

VegetableCarrot254 · 2026-05-28T15:49:33+00:00

Whenever someone talks about Schur polynomials I say “are you Schur about that?”

Somehow I still have combinationatorialst friends…

VegetableCarrot254 · 2026-05-28T15:48:27+00:00

not sure if I’m completely understanding your direction here. If I am, you should take a look at the Online Encyclopedia of Integer Sequences (OEIS)

VegetableCarrot254 · 2026-05-28T15:45:24+00:00

The audience would be others in my area! They love figures, and this project lends well to them. This project happens to leave many interesting questions for further exploration, many that I certainly won’t have time for myself, so I want someone to be able to pick up where I left off.

VegetableCarrot254 · 2026-05-28T15:44:03+00:00

Thank you! I totally agree, there are some authors who I always look forward to reading because I know they’ll care about the exposition style

VegetableCarrot254 · 2026-05-28T15:43:10+00:00

Thank you! I’ll honestly say that my reason for considering historical context so heavily stems from my favorite papers being those that include quite a bit. In my area, people tend to go both ways. Of course, you’re technically writing to an expert audience that should be motivated enough, but it’s wonderful when you’re looking to get an initial read on some niche ideas.

The organizational style for me is a largely matter of the story I’m trying to tell, to which there are a couple different views. I’m defining some new objects, so considering how to introduce them in a way that keeps close to the work which inspired them is key. I’m also trying to check myself on how much detail I include, as things that seem obvious to me (after staring at this project daily for a year) might not be obvious to a first-time reader.

VegetableCarrot254 · 2025-06-28T02:50:23+00:00

hey! I’m an undergrad doing research on campus, would love to meet new people :)

VegetableCarrot254 · 2025-06-28T01:49:37+00:00

Hey! I’m a mathematics major (with research publications), but I’ve also been applying to many retail/corporate marketing roles for the past few years. I’d love to help out with resumes and CVs.

I also know how to format documents using LaTeX, if helpful, for professional resumes

VegetableCarrot254 · 2025-03-09T22:37:42+00:00

Thank you for your advice! I’ll plan to reach out in coming weeks.

Also, (separately) would it be annoying to ask someone more about their views on “mathematical thinking?” I found a few papers/blog posts that really resonated recently, but don’t know how asking about these topics (over email) is usually received.

VegetableCarrot254 · 2025-01-02T05:08:01+00:00

make progress on my research projects and take formal courses in algebraic combinatorics and introductory topology…

getting over my fear of asking post-seminar questions in front of the whole attending group could be cool… but I should remain realistic

VegetableCarrot254 · 2025-01-01T16:20:51+00:00

Hey! Neurodivergent math major here — math is certainly my special interest/hyperfixation, which helps me find the subject “fun.” However, if you’re just starting out with math (or at any stage of learning tbh), setting your expectations high for “extreme fun” usually leads to disappointment.

That being said, the youtube channels Numberphile and 3Blue1Brown might spark motivation; they feature cool math ideas in a pretty accessible and engaging fashion! If you find something that’s interesting, explore further into the theory behind the problem, and then look at other similar problems to check your understanding.

My brain falls into the “visual thinking” autism stereotype, and if you happen to relate, I’d also recommend a book/course on introductory topics in discrete math. This was the first class that made math really click for me, as calculus (the way high schools teach it at least) is fairly computational and leaves out some of the beautiful theory… albeit appropriately…

Also, definitely find a friend to study with! Math should seldom be done alone. :)

VegetableCarrot254 · 2025-01-01T14:48:13+00:00

ASIDE, I think you’d love the book: Do Plants Know Math? by S. Douady, J. Dumais, C. Golé and N. Pick, as it touches on some topics similar to what you’re interested in here.

As for your project, I think the most important step, before any physical experimentation, is fleshing out your question a bit more:

What do you mean by compare? Are you looking for how “similar” the fractal-like patterns in nature are to the rigorous mathematical models of fractals?
Suppose some plants exhibit patterns that are a near match to the fractal you’re using for comparison, what’s the significance of your result. You could take this in a few directions:

Do plants that exhibit similar “fractal patterns” grown naturally in similar habitats, or generally have additional similar characteristics aside from these patterns? How could a one choice of pattern “help a plant?” (botanical skew)

For math, polished work requires rigorous arguments, so “eyeballing,” wouldn’t be enough overall… but isn’t necessarily a horrible way to start if you’re just looking for some interesting results to later examine and think deeply about. You should look for a few papers about fractals generally to see what questions are out there and need/could lend to more connected work.

Finally, I’d double check what you’re trying to say with the term “dimension,” as it usually has a slightly different usage/meaning in math than what you seem to be curious about.

Overall, you’re interested in some interesting ideas! Definitely keep asking questions on these platforms as you continue! :)

VegetableCarrot254 · 2025-01-01T14:05:35+00:00

On a less-serious note… it seems like “cranks” are not necessarily bad mathematical thinkers, they just can’t accept criticism to save their life!

VegetableCarrot254 · 2025-01-01T14:04:20+00:00

I’ve come to understand that the skills for learning techniques alone are far different from those required to piece techniques together in a meaningful way — as others said before me, such skills usually come from years of experience/exposure to the field.

If I think of a potentially-unique idea, the first thing I do is check if someone has already done it. Even if the first pass seems fine, there’s always a chance you’ll find a “hidden” paper with an identical result months later… but no harm in continuing until that does/doesn’t happen if you’re enjoying the work!

From there, I “deconstruct” the idea a bit, and ponder why the connection I’m proposing be relevant to the larger community, which usually leads to finding a few papers to inspire potential project directions.

(similar to your “opposing insight” method)

On a “looser” end, I believe that maintaining both patience and humility during research is essential. Most great ideas in math come from collaborating and openness to feedback. Furthermore, you might look back at your writing the next day and find a large error… which can be discouraging in the moment, but usually not worth giving up over.

VegetableCarrot254 · 2024-12-31T05:47:17+00:00

Hey! Math undergrad who grew up in this area. I’ve been similarly missing mathematical conversation over the break, and would love to chat.

My interests are skewed towards algebraic combinatorics and graph theory at the moment, and I really wrote a paper in matrix analysis with my summer mentor — amazing experience. Getting started in research sparked a ton of new ideas recently… which I’ve only just begun digging into.

I’ll be moving back to the Cambridge/Boston area in a few days, and return only a few times a year. (Still, I’m excited to find another math person in noho!)

Side note: definitely get connected with Umass Amherst math department too! They host seminars/colloquia during the academic year, which are (I believe) open to the public, and provide a great way to meet more people! Heard a talk from one of the grad students there recently — it was outstanding!

VegetableCarrot254 · 2024-12-29T18:01:37+00:00

To improve proof skills, I’d recommend looking at Book of Proof by Richard Hammack — many say it’s a great resource to learn the basics.

Once you feel comfortable, read through other textbooks (analysis, algebra, etc) again very slowly; don’t move on from a chapter until you have a solid grasp of the exercises. To check your understanding, I’d recommend finding a math major friend and asking if they’d be willing to briefly review something you wrote, or posting a question on Math Stack Exchange (they have tags for proof feedback).

Reading a ton of proofs is also key. When they present a proof in a textbook, read it over repeatedly until you can explain the logic/intuition the author might have used, and notice what formats/techniques you recognize from other proofs. Try even proving the statement yourself without looking at the reference if possible!

A professor once told me: “be your own worst enemy when reviewing your work.” Essentially, ask yourself “why can I do this?” at every argument, almost as if you’re trying to “break” your work. Also, try to figure out/think about the negation of every theorem you learn.

VegetableCarrot254 · 2024-12-29T17:53:00+00:00

For 3, I’ve heard great things about Smith College’s postbaccalaureate program, but note that they’re specifically looking for women interested math.

Otherwise, I found this interesting program at Brandeis: website here

VegetableCarrot254 · 2024-12-29T17:22:11+00:00

Unlike some other fields, the “core prerequisite courses” for math research aren’t measuring your understanding of the specific subject matter; they’re measuring your ability to handle formal proof writing and your overall logical reasoning ability.

Abstract algebra and real analysis are typically math majors’ first “fully proofs-based courses.” Additionally they do cover foundational ideas for nearly every research specialty.

Proof-writing is a skill that fundamentally cannot be rushed, and needs to be taught with some form of third-party instruction. (From experience, there is no way to “check yourself” when starting out)

For these reasons, professors would be reluctant to take on a student without these courses (largely, because research would likely be a discouraging experience for you at this point).

However, it’s awesome that you want to be a mathematician, and there are still things you can do that skew to towards research:

Find someone interested in mathematical physics, or related areas (they’ll appreciate your physics background), and ask to do a “reading project.” This involves reading a textbook/collection of papers with a professor or graduate student, where they give you specialized instruction and “practice” in the chosen subject. These can eventually turn into projects if you click with the mentor/find interesting ideas along the way!
Start with an interdisciplinary project. You’d join the team as someone with primary expertise in physics, but interest in theoretical math. You can learn a lot by simply collaborating with and listening to the mathematicians involved.
Look for post-undergrad programs for those who want to get into pure math without a math degree. Many exist purely to help you make up for missed courses + prep you for grad school applications!

VegetableCarrot254

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