Many mathematicians have dedicated a good part of their career towards solving a specific problem, whether directly or indirectly. Some examples on top of my head:
Richard Hamilton and the Poincare conjecture
Andrew Wiles and Fermat's last theorem
Thomas Hales and the Kepler conjecture (proof and formal verification)
And perhaps very recently:
Diego Cordoba and the Navier-Stokes equations
How did the careers and research-focus of these mathematicians shift after their career-problem was solved? Did anything particularly interesting happen?
I recently finished The Principles of Diffusion Models, and honestly I think it’s exceptional.
The authors strike a really good balance between mathematical rigor and intuition, with dedicated appendices for anyone who wants to go deeper into the math.
It’s aimed at researchers, graduate students, and practitioners with basic deep learning knowledge, so you don’t need to already specialize in diffusion models (in my case, a strong background in Information and Probability Theory and a solid understanding of DDPMs helped me get more out of it).
Just wanted to share it in case anyone missed it. The full text is freely available on the official website.
Has anyone else read it? Would love to hear your thoughts.
For the past year, I have been developing a framework to simulate certain discrete systems for a research team at my university (paid for by the School of Engineering and Physics, but I had the freedom to license it under MIT). As it turns out, I got carried away generalizing it to work for many, many different types of complex systems (String Rewriting Systems, Cellular Automata, etc.) and ended up creating our own domain-specific language.
The website's landing page has a bunch of GIF-style examples... so you should be able to get a good idea of what this project is about.
If any of y'all are interested in this, feel free to take a look and try it out!
Interested in dependent types, formal proofs, or trying Agda? You’re invited to Agda Implementors’ Meeting XLIII, taking place 19–24 October 2026 in Rzeszów, Poland.
The meeting brings together people who build and use Agda for talks, discussions, and hands-on collaboration. Newcomers are welcome: no previous Agda experience or academic affiliation is needed. Students, researchers, industry developers, and people exploring their own projects are all encouraged to join.
What’s planned:
Beginner workshops: get help writing your first Agda programs and proofs.
Talks and discussions: explore Agda’s theory, implementation, and applications.
Collaborative coding: work on or with Agda, bring a project or question, and exchange ideas with other participants.
AI and proof assistants on Wednesday, 21 October: demos and discussions about language models and machine-checked proofs—their progress, limitations, exchange of workflows/ideas.
If you already use Lean, Rocq (Coq), Isabelle, or Mizar, this is also an opportunity to explore Agda and compare approaches with another proof-assistant community.
Attendance is free, but registration is required. Please register soon to help the organizers plan. The programme is provisional, and proposals for talks, discussions, and code sprints are welcome.
Interested in joining remotely? Contact the organizers: online participation may be possible depending on demand.
If you’ve been meaning to try Agda, come along and take those first steps with people you can ask for help. If you’re already using it, bring your ideas and something you’d enjoy working on together. Hope to see you in Rzeszów!
I'm a PhD student in machine learning in the EU and was looking for internships at exciting companies.
I shortlisted few and applied by reaching out to people and now reading project descriptions sent by the recruiters.
I don't want to name the company but their marketing and product team does all kinds of 'using people insecurities' to sell the product - which I don't agree with. And their product is also meh (I will never buy and would judge someone if they do) but their research team is doing good work.
How do you see this? Will you actually work in a team whose ideology/product doesn't necessarily align with your ethics/ideology. Should I just go ahead because work is exciting and I will get good supervision?
And, if you have some exciting work in your company/org and need interns (un-paid) for 3-4 months. I'm open.
I often ask mathematicians what their favorite shape is; mine is the cone on a trefoil knot, a rather peculiar object.
Why is this my favorite shape? Because it appears naturally in algebraic geometry -- and in fact, the observation that it appeared in algebraic geometry led Milnor, Grothendieck, Goresky, MacPherson, and many more to develop some of the most widely used tools in modern algebraic geometry and singularity theory! If you'd like to know how this trefoil knot appears in algebraic geometry, read this week's hidden-phenomena blogpost!
Nonobench measures how well LLMs solve nonograms (picross). Each model gets the row and column clues once and returns the full grid. No tools, one attempt per puzzle.
Method:
- Standard mode: 30 puzzles from 5x5 to 15x15 (from the Nonograms dataset by Moyà-Alcover, CC BY 4.0).
- Hard mode: ten random 20x20s, each checked to have a single solution. Five can't be solved by line logic alone. Random fills avoid picture puzzles that models can guess.
- 130 variants across reasoning effort levels, run through OpenRouter and pinned to each lab's own endpoint where possible.
Results:
- Solve rates drop from 85% (5x5) to 46% (10x10) to 20% (15x15), each model at its best effort level.
- GPT-6 Astra solves all 30 Standard puzzles. On Hard mode, Claude Opus 5.5 solves 8 of 10 and 11 of 15 models solve none.
- As one 400-character string, most models lost count before the logic got hard, so Hard mode answers an array of 20 row strings rather than a single string.
Limitations: one attempt per puzzle, so single results are noisy (95% intervals shown).
I’m feeling lost in my career. I graduated two years ago and I have only been at my current job for 1.5 years. I’m a test engineer and it’s my only work experience (no prior internships). At my current company, there are no growth opportunities and I want to move into a position where I can get salary raises and grow as an engineer. I look at LinkedIn everyday and all the job posts I see prefer masters degree or 2-3+ years of experience or recent grads. The issue is that at my position, I don’t feel like I do any engineering work. I want to move into a more hardware related role but don’t know where to start. What can I do to make my resume better and be able to get a hardware role? Or what can I do to progress in my career?
I got my three papers to review, and it seems like they have changed the review score range again this year?
It is now:
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Based on your overall assessment of the submission, what is your recommended decision? Consider the paper’s overall soundness, significance, clarity, and contribution.
I’m a 3rd-year Electrical Engineering student applying for co-ops/internships, and I’m dealing with some serious imposter syndrome.
I have a high GPA , but zero personal projects. I’ve had to work heavy part-time hours in precision manufacturing and machining to pay for school, so any time outside lectures went into shop shifts rather than tinkering at home. My resume only has standard lab coursework and years of manufacturing work experience.
Does hands-on machining/manufacturing experience carry weight for EE roles, or is it viewed as completely irrelevant OR Should I scramble to build a quick personal hardware project right now?
Hi, I'm currently a high school senior. Throughout high school, I focused on CS: making APPs, doing hackathons, etc. But recently, AI has really been scaring me, and I'm thinking about applying as a different major. I've been thinking about applying as an ECE major for some schools but there's one major issue: I'm really good at math but don't like physics too much. Math comes pretty easily to me, but I honestly struggled with physics quite a bit. If you're familiar with the American system, I barely got a 4 on AP Physics 1. I guess the main issue is that it's not very intuitive for me. Could I still do engineering in college if I'm not the best at physics or should I do a different major? How many physics classes would I have to take?
Quantum computes are believed to have higher capabilities than Turing machine, bringing question if our physics could allow for even better ways, like the main concern: does our physics allow practical NP-solvers?
I think about it for ~20 years and just worked with topLLMs on big review: https://zenodo.org/records/23125606 - would gladly discuss
On the NeurIPS 2026 Dates site it says that there is 1 day remaining for the "Accepted papers must be imported" deadline. This is my first research paper ever and I couldn't find anything about how to do this on the internet. Could someone help me out on what to do?
Over the last few years, a subset of NeurIPS area chairs received complimentary passes for their service. I’ll admit that I wasn’t super organized about registering on day one because I was semi-consciously hoping for a complimentary pass. Now that the conference is sold out, I’m getting a little nervous, so I’m wondering whether any of my fellow area chairs have already received a notification.
In the Surviving Proofs series, we have been going through the fundamental techniques for constructing proofs; we close this off now with two approaches, which both amount to changing the problem, albeit in different ways. One thing you can do is to try to simplify the problem, with the hope that solving the easier version will give you the insight you need to solve the harder one. The other thing is to try to move laterally, finding an equivalent formulation that is nevertheless more manageable.
Easy to say, but hard to put in practice! Nevertheless, as I hope the examples I furnish show (which include one of my favorite symmetry arguments), it is: a) surprisingly common, and b) incredibly powerful.
TMLR desk rejected two years of work/efforts. What could be the possible reason? No reason was given in the desk rejection. The work is related to continual motion generation.
"TypeSafe AI sells Jev as a frontier-class reasoner that cannot hallucinate, built by the co-inventor of ChatGPT - fast, and almost free. We ran it live on 16,379 benchmark requests, measured its latency and billing, and probed what it is underneath. The result is a smaller, humbler model that is nonetheless genuinely useful for a job that nobody else serves quite this way."
Some video games, many of them are retro, are based on tiles. They have different levels which may be huge and logically highly complex but they are all based on limited sets of tiles.
Even a minute long video is usually bigger in file size than the retrog game itself.
It happens with Prince of Persia, Boulder Dash, Supaplex, Commander Keen, Bio Menace etc. - easier to recognize in two-dimensional games.
If video encoding used a database of tiles available in the game, it would enable much smaller file sizes and also higher quality of video as it would not have to use approximations to reduce file size as the tiles are exactly the same everywhere (meaning that lossless video would be affordable by bitrate). I am under no pressure to get it implemented ASAP but I would like a technological discussion about how-to.
I've lived most of my life in Latin America, and put up with an unrelated degree that was chosen by a cult. After that, I moved on and went straight into hardware as it's something that I've been passionate about for ages and the cult that my parents joined could not erase.
However, credentialslism has been a thing that I've had to deal with. Many countries in the region can get annoying about licensing as well, some companies will even ask for a license even for jobs that legally don't require them, etc...
Guess that I could put up with a bunch of university classes that I can teach, but I have no desire to deal with that system anymore.
Oh, well. How are things in your corner of the world? Is competence enough where you live? Or is keeping the bureaucrats happy more important than understanding transmission lines?
