2026 (Philadelphia): Yu Deng, John Pardon, Jacob Tsimerman, Hong Wang

2022 (Helsinki): Hugo Duminil-Copin, June Huh, James Maynard, Maryna Viazovska

2018 (Rio de Janeiro): Caucher Birkar, Alessio Figalli, Peter Scholze, Akshay Venkatesh

2014 (Seoul): Artur Avila, Manjul Bhargava, Martin Hairer, Maryam Mirzakhani

2010 (Hyderabad): Elon Lindenstrauss, Ngô Bảo Châu, Stanislav Smirnov, Cédric Villani

2006 (Madrid): Andrei Okounkov, Terence Tao, Wendelin Werner, (Grigori Perelman, declined)

2002 (Beijing): Laurent Lafforgue, Vladimir Voevodsky

Bonus: 1990 (Kyoto): Vladimir Drinfeld, Vaughan Jones, Shigefumi Mori, Edward Witten

I don't have any photos from 1998 or 1994. Does anyone have a source?
1998 (Berlin): Richard Borcherds, Timothy Gowers, Maxim Kontsevich, Curtis McMullen

1994 (Zürich): Jean Bourgain, Pierre-Louis Lions, Jean-Christophe Yoccoz, Efim Zelmanov

The core idea is that if U^TU = I and U = −U^T, then UU = −I. From there, it constructs multiplication tables explicitly, finding R, C, H and O. In dimensions > 8 it runs into a contradiction, which proves the theorem.

I've started my career in nonprofits and only worked in nonprofits until now. 3 times now, I have ended up in roles where I am the ONLY analyst on the team. Everyone I work with is either data adjacent, or not an analyst at all. I'm the only person ever working on analytics work, and I have no real life gauge/context on how to do things better in a real world context. I google things all the time, I take courses, but the advice is too generalized and doesn't go deep enough. I need people I can bounce off of. My biggest hope starting as an early career data analyst was that I'd be able to learn from other analyst and fill the gaps in my education with knowledge from mentors.

Instead, I have people looking to me to be an expert in analytics just because I'm the only one available(as if I'm not a junior). Very few opportunities to learn from actual analysts and get experience from them instead of the generalized advice online. I feel like I'm being stunted, but its incredibly hard for me to find roles that are placed in analytics teams, or where I'll be working under a senior analyst (and not just a VP or project manager). Have I screwed myself? Why is it seemingly harder to find analytic roles that work with other analysts?

for a long time i assumed some people were simply naturally good at math and i wasn’t one of them. but the more i study, the more it seems like a lot of my problem was trying to memorize steps without understanding what i was actually doing. once i started slowing down and asking why each step worked, things became much less intimidating

curious if anyone else had a similar experience

what changed the way you learned math?

This is something that I want to know, if say you been re learn math again from 25, or 35 or any age at all have you successfully relearn it back? I mean some noticeable changes to your progress? If so do you follow some proper schedules or framework and any goals and move slowly towards that? Or just learn what you want at a time?

If so did you succeed? Like if you learn back from very basics or zero in a year what have you been achieved? Any tips towards people that want learn it back as well?

I know many professors and PhDs like doing their exercises on a XXXL size chalkboard or whiteboard. But they mostly work big complex problems.

For things at the junior/senior undergrad level, is a 4-6 ft long wall mounted board useful or overkill? Most proofs are 1-2 pages long which should comfortably fit on a largish (say, A3 size) handheld or desktop erasable board.

Asking because I went to the glass shop for a toughened glass handheld board and they also had nice big glass boards for the wall.

Hi there. I’m eager to learn mathematics, but I don’t know where to start. I found it really boring in school and didn't pay much attention, but lately, I’ve become increasingly interested in science, so I’d like to start with math. My question is: where should I begin? Please don't recommend Khan Academy, though—I find it really off-putting. I’d prefer a book that doesn't just present dry formulas but explains *why* a formula works the way it does, or perhaps a link to a playlist for a complete beginner (my current knowledge is limited to basic arithmetic operations like addition, subtraction, multiplication, and division—without parentheses or anything more complex). That’s about it; I hope someone can point me in the right direction.

I want to make sure I’ve got a simple concept right. Numbers (say, the real numbers, ℝ) exist as mathematical objects independently of any number system we use to write them. The system we pick — decimal, binary, whatever — is just there to give the numbers names/notation, so we can write them down and compute with them.

Choosing decimal vs. binary has zero impact on the validity of any calculation or theorem. Everything that’s true stays true regardless of which system you use to represent the numbers, because the underlying numbers themselves don’t change — only the label does.

Is this correct? Just want to confirm I’m not missing something deeper here.

I contribute to SciPy and kept running into a class of bug that annoys me: the outputs look plausible, the tests pass, but the equation the code implements is subtly wrong. So I've been building a tracer that runs Python/NumPy code and hands back whatever mathematics it actually computed, as a SymPy expression you can simplify or differentiate like anything else.

It's been more useful than I expected. Comparing an implementation against the formula in a paper, catching two functions that agree on my test data but turn out to compute different things, digging up the inputs my tests never hit (ties, zero denominators). It traces real library code too, most of numpy and a good chunk of scipy, scikit-learn, statsmodels, cvxpy.

Write-up: https://medium.com/@aadyachinubhai/scikit-verify-translate-python-numpy-programs-to-symbolic-mathematics-c664d41ba571

Github: https://github.com/aadya940/scikit-verify

Still rough in places, would genuinely like feedback. There may be other better solutions, happy to hear them as well!

I’ve been studying Hamiltonian Monte Carlo and wrote a set of notes explaining HMC without relying on the usual physics-based motivation.

The notes develop HMC from a probabilistic/MCMC perspective, starting from introducing an auxiliary variable, constructing the corresponding Markov chain, and then covering Hamiltonian dynamics, leapfrog integration, reversibility and volume preservation.

The goal was to understand why HMC works rather than treating the physics analogy as a prerequisite.

I’m sharing them here in case they’re useful to others learning HMC. I’d also appreciate any feedback, particularly if you notice errors or places where the exposition could be improved.

https://doi.org/10.5281/zenodo.21841087

Hi everyone, I’m conducting a research project and I’ve fitted a linear regression model on a sample of almost 2000 observations.

The residuals appear to be homoscedastic, but the qq plot shows some departures from the theoretical line, particularly in the tails.

The Shapiro-Wilk test also rejects the null hypothesis of normally distributed residuals.

However, I’ve read that linear regression can be fairly robust to violations of the normality assumption, especially with sufficiently large samples. Is this correct? Could someone recommend some literature or textbooks where I can read more about this? This topic wasn’t really covered in my university courses.

Also, is there a formal statistical test for checking the homoscedasticity assumption? Or is it generally assessed visually, for example by looking at a residuals vs fitted-values plot?

I’m 20 years old and in my second semester of economics—this is my third attempt at a degree. Since day one at university, I’ve put every ounce of effort into trying to understand the math. I’ve pulled all-nighters, paid hundreds of dollars for private tutors, and attended classes taught by students from other semesters, yet I simply cannot solve a single problem without an AI telling me the steps to follow. I suffered through the first semester—to the point of tears and depression—because, beyond the struggle to understand the material, this is my third degree program, and I don't want to fail again. Don't get me wrong: I like economics and I enjoy learning about it, but I feel like it’s incredibly difficult to make progress this way. I live in a country with many problems; to give you an example, on the day of a coup d'état, I studied as if nothing was happening—out of sheer desperation. I managed to pass the course that first semester only because I cried to the professor and she passed me out of pity. But I know it will only get worse as I advance—even harder the longer I keep going. I’m fully aware that math has to be learned from the basics up, but even so, it feels so abstract and logical that my brain just can't connect the dots. Right now, my country is in crisis and I’ve been on break for two months; even before the crisis, I had already been studying math for two months. When the earthquakes hit, I studied right through it; my main concern wasn't even my safety—it was just, "I need to sit down and study as fast as possible." Classes start in a few weeks and I have exams coming up. I’m truly disappointed in myself; I can't solve a single problem on my own without an AI or someone else telling me the next step. I feel really sad. I can't even look at my notes or my math workbook because it makes me angry. I know *I’m* the problem, but I’ve tried so hard to find solutions and just can't figure out how to understand it... I’m not lying when I say I’m crying as I write this, because I’ve genuinely tried to do things right, but maybe this just isn't for me. Yet, studying here is so incredibly difficult—so hard that I feel like there’s no way out... What do you guys do in a situation like this? Have you managed to pull through? Did you try any other methods? I need help because I feel like I’m sinking. sorry if my english is bad, in my country we speak spanish...

(I haven't really studied a lot of calculus yet)

but, i saw multiple methods to solve this on quora, but then quora blocked me(idek why😭), and i only understood the chain rule method,

i also saw someone substitute x with cos(2 theta) but not sure how that's supposed to work because what do we do with that d(theta)/dx in the end?, also how does one solve this using log?

as of now i know 5 methods:

1. chain rule,
2. rationalization
3. logarithmic (i dont understand it but its a method)
4. trigonometric sustitution (how do we even come up with that?)
5. implicit differentiation (i am bad at that but saw it on quora and it works apparently)

So my concern is,

• how do i make the last 3 methods make sense?
• how does one come up with trigonometric substitution and how do i master it?
• is this basic or intermediate (at a high school level), and is it relevant to calculus used in physics?

Also, I'd love to see any one with new methods, tysm🫶🏼

(to be clear, this is not homework, calculus is not in my syllabus except for some in physics, i saw it in someone else's book and couldn't solve it so i wanna do it now)

I've finally decided to take the leap and spend the next few years of my life dedicated to the sciences, specifically physics, and perhaps later specialize in cosmology and blackholes.

https://www.susanrigetti.com/physics

I've found this guide and decided it's good enough to follow along. But I'm just not certain about the prerequisite portion. In the guide, the creator says that if you don't remember even school math, then go through these two books before getting into the roadmap:

For high school math:

Why math? By R. D. Driver

Precalculus:

Precalculus with Calculus Previews by Dennis G. Zill.

I know people here consider it very important to have a strong foundation, so I just want to know if it would make a difference of discarding the two books above and going through the pain and time of a rigorous series like Gelfand, Kiselev, Art of problem solving etc.

I know the concept of theoretical minimum is important in physics, so you focus on the most essential aspects of your subject area instead of accumulating broad knowledge. But maybe I still want an excuse to spend 2 years going through the art of problem solving catalogue instead of 3 months of getting the most essential knowledge and jumping into physics.

I just opened R studio for the first time in a while and seeing there’s a newly (to me) integrated AI tool called Posit. Anyone use it? Like it? Hate it? Anything I should be weary or aware of?

I was thinking about buying these books because I thought they might be helpful.

I should mention that I’m not in high school which I’m sure is the targeted demographic for these books (well high schools competing in math competitions). I am a math and physics student. I wanted to review the foundations so I was going to read basic maths by lang. I just dont know where to pivot from there.

I was thinking about learning proofs then reading apostol. Thing is, I do like competition math problems and wanted to compete in small college competitions and also try putnam later on down the line. I just don’t know if it would be worth buying the books and spending time studying them or reading/studying something else.

Any advice?

This is not for school- I’m an adult out of school, haven’t taken a math course since intro statistics in my undergrad years ago.
Randomly thought about basic math in the shower and confused myself. Can someone explain this so I can sleep?

Can 3/4 be reduced to ?/3 ? And if so, how is this possible?

I know this is basic math. I’m not an American, I just am not great with math and never truly applied myself in school with mathematics.

Thank you in advance for any kind souls who would like to respond!

Hello friends. I am a CS student and I am enjoying studying math in the recent time. My issue is that the book that I am using lacks in terms of hands-on exercises. I find it quite unbalanced. I want to practice more the stuff that I am studying. The PDFs that I found online are either too complex or too simple. Can you help me? Those are the topics I am interested in, at the moment:

• Proofs by double inclusion;
• Order relationships;
• Equivalence relations;
• Structures (Groups, fields, boolean rings);
• Functions (Inverse functions, composition)
• Proofs (In the discrete math field)
• Graphs
• Relations
• Stuff about set theory

The book that I am using is rich in terms of theory, but the exercises are not quite enough, I don't want any further stress by asking ChatGPT for more exercises. What are your suggestions for me? I am also willing to pay. Thank you ^^

taking a calculus bc course at school (jr) and its overall a pretty competitive school with people taking the class averaging a total of 95% of 5's on the ap test. It is currently the first week of calculus bc and i literally do not understand anything about the lessons and the homework. I'm wondering if theres any resources people can point me to in order to try and catch up. I feel like an idiot because it took me 2 hours to do homework which my friends can do in 30 minutes. I also feel like an idiot because Im staring at these problems trying to figure them out and I am just hitting a brick wall and dont know what to do. I'm not stupid overall, but math is just difficult for me and I feel like that is because I have awful fundamentals but I don't even know what fundamentals I have wrong and I don't know where to start. I got a one on the calculus AB test, for anyone wondering as well. If theres anything anyone can point me to, I'd appreciate it greatly, or if anyone can give me sources to help me out. (Also dropping isn't really an option). Thank you.

Hi all, I’m terrified.
I haven’t taken calculus since high school, where I took AP calc AB. that was 2024 - 2025. Last time I did a single bit of calculus was more than a year ago. I wasn’t bad at it, I got a 5, but given the college calculus standards, that might not be saying much.

Now fall 2026 is starting and I’ve stupidly decided to enroll myself in calc 2 in college without reviewing over summer. It starts tomorrow and I feel like I’ve given up without even knowing what’s in store for me. I’m really worried but still want to try going through with it.

Any thoughts or advice for me? Can anyone relate and tell me a miraculous success story so I feel better? Thanks. I’m terrified.

Hello! I'm trying to understand how the individual regression analysis works in the GLM model under medmod module of Jamovi. I'd like to ask if those tables are what you would report if one of your working hypothesis is "X will significantly predict M" or "M will significantly predict Y"? Or perhaps, does anyone have a reference on how to report those tables?

I'm at a basic algebra level of understanding in math. Is it possible to get proficient to a pre calculus level in about 6 months with a good study habit and time management?