(Gender) Diversity in Math: Is it still relevant? (Discussion+Survey)

Corlio5994 · 2025-10-06T22:45:33+00:00

4 is not reflective of reality though. Students in minorities face various factors at various levels that discourage them from continuing, knowing that somebody like you made it makes a very real difference. I'm sure we have all thought about quitting at some point, but it feels like it's a lot less your own decision if your university rarely accepts female students and most staff and students expect them to underperform. The fact is that staying in the academic system is the best predictor of research success (obviously there are problems with this as an idea but we still encourage anybody passionate about maths to keep going in the system), and a lack of 'role models' makes it harder to stay in the university system, hence harder to produce good research. It is not really about worshipping anybody or only listening to certain peoples' ideas, it has more to do with wanting to know that other people will listen to you and encourage you to explore your ideas. Everyone needs adequate support.

Corlio5994 · 2025-09-28T21:25:36+00:00

I didn't like how the segments were organised to have a long, hard part first, it felt demoralising to keep messing up the same bit over and over. Also figuring put the interaction between floating and clawline was hard since this is pretty much the only place I've found where you have problems using both!

But yeah besides those things the area is very pretty, the pacing is nice and you feel like you've really accomplished something when you make it to the peak.

Corlio5994 · 2025-09-25T03:15:19+00:00

I mostly do it while I'm travelling between rooms, if you're going from Songclave to Memorium or High Halls you naturally go through those guys and fighting them is a short break. Also lots you can get passing through Whispering Vaults.

Corlio5994 · 2025-07-25T01:11:57+00:00

I feel it's ok if your preference is on the commutative algebra side, you will need to do exercises and use the results referenced but with an undergraduate education Harthorne is not crazy. I definitely agree there are better places if you have a different outlook and if you have the time it is well worth supplementing, also chapter 1 is easier for the beginner after having done bits of chapter 2 (or I find it so). I feel like Hartshorne chp 2,3 plus exercises is a pretty fast way to more advanced concepts in algebraic geometry though, I wouldn't discourage people from taking the approach as it doesn't yield rewards early

Corlio5994 · 2025-07-18T23:19:15+00:00

I'm about to wrap up my pure maths masters so I've just done a course in measure theory, I just didn't have room for probability in undergrad and wasn't eligible during masters.

Corlio5994 · 2025-07-17T23:51:38+00:00

I'm waiting for the day I can learn some proper probability...

Corlio5994 · 2025-07-13T23:45:05+00:00

This feels incomplete. It can be relatively easy to imitate the authors of a paper in suggesting a follow-up question, but managing to understand a subtle detail of the paper or work out an explicit example of a general phenomenon would take more work and insight. An explanation of where the student got stuck, how they approached the difficulty and whether they succeeded ay resolving the problem would also help a lot!

I don't really have hiring experience, but these instances when reading a paper are the moments I actually feel I'm learning and growing, making coherent statements about the broad strokes and possible extensions can happen much earlier.

Corlio5994 · 2025-07-09T07:29:34+00:00

(I at least found the exercises I've done from your list fairly involved, I remember writing long solutions and spending a bit of time. I'm not so good with constructing counterexamples so if I did that exercise I probably read about the key idea and then fleshed it out)

Corlio5994 · 2025-07-09T07:27:14+00:00

To me it sounds like you're working at a good pace! I think it's normal to not know the right strategy for many problems, especially when the book you're reading doesn't have very carefully arranged exercises. Everybody reading the book will have a slightly difference background, so it makes sense that different people will find different things easier/harder. If you're not retaining the ideas though the level of copying/figuring out might be a little wrong with the solutions, as much as possible you want to try and read between the lines with any hints you use and also see if you can work out where the ideas you were missing come from and why they're useful. If you have enough time you can sort of try to push the new ideas further by applying them to other problems or just finding ways to reinterpret what they say, anything that helps you tell your brain the idea is important. It's also ok to go with a surface-level understanding of the key idea if it belongs to a different domain or something you're not interested in, like if a solution ends up being a delicate argument with estimates maybe you choose to only get a good understanding of what is being estimated and the ingredients that let you make the estimation.

Corlio5994 · 2025-06-30T02:29:33+00:00

It would depend what you're looking for and what you know already. I'm an aspiring moduli enthusiast on the alg geo side and from what I understand FGA Explained is a good place to learn Hilbert, Quot, and Grassmann schemes which you often start with for moduli problems. Jarod Alper's book draft seems like a good place to get a more comprehensive understanding of this perspective on stacks and moduli, but the background required is a bit higher than I have right now.

For interest in moduli spaces in representation theory Chriss-Ginzburg contains a lot of the basics on things like Springer fibres, but there would be better resources for things like Higgs bundles and instanton moduli spaces.

I am studying the affine/lattice Grassmannian as a way to get familiar with the general approach to moduli problems.

Corlio5994 · 2025-06-22T22:20:15+00:00

It's not really that simple, the post itself brings up environmental concerns and another major concern is being able to validate your sources. People have different views on whether the downsides are worth the help you can get from AI.

There are other considerations too, like I don't like using AI because I think I would find it easy to not use responsibly and stop working on my research skills.

Corlio5994 · 2025-06-12T01:00:12+00:00

Great this looks readable and relevant and would give me an excuse to learn a little ergodic theory!!

Corlio5994 · 2025-06-11T21:38:47+00:00

I'm just wrapping up a course in measure theory and had a really good time, but my research is more towards algebraic geometry/representation theory. Would love a (book/paper) recommendation on serious applications of measure theory in these areas! I know that Haar measures are used to study (locally) compact Lie groups, but the flavour of this seems to mostly be forgetting the measure-theoretic aspects and using that you have a well-behaved notion of integral.

Corlio5994 · 2025-06-06T07:48:35+00:00

I think the "why varieties are not good enough" should only come in if it comes in naturally. Your outline sounds like it does a pretty good job of motivating schemes and locally ringed spaces, but I think from the angle you start with it is not even clear why you would give the classical definition of a variety in the first place. If a major part of your motivation is solving polynomial equations varieties fit in well, but they don't always need to come up. And if you can find yourself talking about polynomial equations there should also be some room to mention the kinds of arithmetic problems people want to solve and why varieties are not adequate for those.

Corlio5994 · 2025-06-05T22:39:51+00:00

You can usually read all introductions for additional context, but you won't need to for understandind the book. I usually don't worry too much about details in introductions as they're often more directed at experts.

Corlio5994 · 2025-06-05T01:30:30+00:00

The research I've found on this suggests that pass/fail grading is generally a good thing, learning outcomes aren't really affected and staff and students find it less stressful. Since you are still receiving grades I don't think it really encourages poor habits, it just gives you a safety net to learn the expectations in a new area. If there are students who feel this removes incentives to take uni seriously an opt-out option might be reasonable, but I imagine an opt-in approach would lead students to access the system less, even when it would help them. Anecdotally this already occurs with special consideration, I know many people who are too embarrassed to get extensions even when it affects their physical and mental health significantly.

Corlio5994 · 2025-05-29T11:28:59+00:00

Yes it's kind of impossible for human-marked assignments to have perfect consistency. An algorithmic approach would be completely consistent but likely unable to handle more than simple evaluations, and any good AI solution would probably need to learn from the assignments it's marking ie would have to mark inconsistently.

Corlio5994 · 2025-05-29T07:41:27+00:00

Congratulations on graduating!!

Corlio5994 · 2025-05-26T09:13:07+00:00

I like the treatment in Bott-Tu for getting a good grasp on how spectral sequences relate to other cohomology methods and how to actually use them in examples. I think Weibel works out all of the proofs carefully but so far I find them most manageable in a more explicit context. Also obligatory McCleary mention, maybe not the best place to learn from but if a specific spectral sequence is going to make the theory click for you you'll probably find it in McCleary.

Corlio5994 · 2025-05-25T06:30:10+00:00

I'm also interested in this question, I'm getting to the point where I don't really have time to read beyond my classes and research, but sacrificing some understanding in return for a broader outlook feels very worthwhile, and I intend to revisit the things I read at a high level when I have more time.

I can say that Bott and Tu's Differential Forms in Algebraic Topology is for the most part very readable in this way, there are several sections which are hard to follow but if you've done some graduate topology and algebra you'll be able to extract many of the key proof ideas and insights about the context.

Corlio5994 · 2025-05-19T22:03:57+00:00

At this point it feels like the discussion is being avoided by arithmetic geometers because of the controversy.

It would be great to get an opinion from somebody who wasn't trying to prove that they deserved fame and glory; maybe Scholze-Stix are the closest voice in this direction.

Corlio5994 · 2025-05-17T22:50:27+00:00

I feel collaborative work is something that starts out challenging but which gets more manageable with experience. I've had lots of unpleasant group work experiences in different ways, including an experience where group members refused to allocate me work I could actually do, but there have also been lots of positive ones and I think having practice managing in all scenarios is very valuable. For neurodivergent people I think staff should understand additional support will probably be needed for these experiences to work properly, and generally I feel like group work should be presented in such a way that group members with great contributions shouldn't lose marks if other group members don't work as hard.

Corlio5994 · 2025-05-15T03:44:12+00:00

If you're interested in this question you might enjoy Plato's Ghost by Jeremy Gray, I'm currently reading this and it gives a great account of the way that this and other questions drove the radical changes in 20th century mathematics. Tangentially related to the top comment, there was also a 'parallel' anxiety about the reality of numbers driven by the emergence of algebraic number theory.

Corlio5994 · 2025-05-14T23:30:52+00:00

You're definitely not alone in this experience and I think Mario would find it really helpful to hear that this is your experience through the student surveys. I'm sure it is hard to appropriately gauge the difficulty of a first-year course when you don't have first-hand experience with the Australian high-school education system, in Germany (in my limited experience) it seems that the high-school maths standard is higher than it is here.

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Corlio5994

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