beyonddream

Current and future mathematicians can now spend most of their time coming up with problems/conjectures and theories that are hard for a future model versions (6 to 1 year out) to solve them and by itself it can be a new major sub branch of mathematics - “Theory of perplexing frontier models” and who knows it can even open up new dimension of mathematics for mathematicians to explore by themselves (because AI by definition cannot help them here). Now is the time to be excited for mathematics!

When the user is understood as yet another human who doesn’t know what they want, the insanity returns! Because an average customer usually doesn’t have practically grounded wants.

What can be done to prevent hostile take over of scientific research from humans by AI ? I hear lot of complaints and hue and cry (fair enough) but are there positive ideas on what to do about this ? (Regressing back to being secretive about one’s scientific endeavor is not the answer)

I don’t know why you got downvoted but you have a point. It looks as if OP doesn’t write for readership and his posts contents have similar characteristics of reckless abandon for conventional norms for a tech post. Too many cross references and link-backs to his own other articles that makes it really hard to follow the main thread of the essay.

Answer is, you do comprehensive unit testing irrespective of Microsoft or any other company doing it. Also, as the OP of your comment posted, you are over estimating the software quality of these big name corporate companies. It can’t be the bar against which you would want measure your own company standards.

I wish they took some time to reflect on how best to name a model. Like, would it make sense to add the model version at the end like every other artifacts labelled in software engineering!

Why ?

The recent breakthrough of llm’s solving major open problem’s in math is a direct contradiction to the article.

But, there is some truth to the article and perhaps it is more true in chat based interactions. The agentic, hands-off mode might tell a different story.

Nice find! The final paragraph of the Conclusion is amazingly prescient!

"Significantly, we found that translation quality as indicated by BLEU score continues to improve with increasing language model size, at even the largest sizes considered. This finding underscores the value of being able to train and apply very large language models, and suggests that further performance gains may be had by pursuing this direction further."

You should read that essay! The model is capable of producing phd level research on it's own with minimal set of prompt's. I was sad because of this paragraph:

"That view is that there is still a great deal of value in struggling with a mathematics problem, but that the era where you could enjoy the thrill of having your name forever associated with a particular theorem or definition may well be close to its end. So if your aim in doing mathematics is to achieve some kind of immortality, so to speak, then you should understand that that won’t necessarily be possible for much longer — not just for you, but for anybody."

He may seem to imply the end is only for some subset of reasons but if you read the entire essay he is just trying to give hope where the rest of the essay is really damning!

I am glad to see this today - after reading Tim gower's recent post on chatgpt 5.5 pro's phd level research ability I was feeling slightly sad about the future of math research.

Interestingly enough, the moment I saw the title I thought of Bill Thurston's famous article "On proof and progress in mathematics" and the top comment on the OP's thread is from him! Reading his reply sort of gave me the antidote to the temporary blues I felt yesterday.

.claude has become the new dotfiles. And what do people do when they want to start using dotfiles ? they copy other’s dotfiles and same is happening here :)

“Internal server error

Sorry, there seems to be an error. Please try again soon.”

Never thought I would ever see this on a google owned websites!

He is talking about IMO (math olympiad) while he got gold at IOI (informatics olympiad) :)

Try mimalloc. I have prototyped a feature on top of mimalloc and while effort was a dead end, the code (this was around 2020) was nicely written and well maintained and it was fun to hack on it. When I swapped jemalloc in our system with mimalloc, it was on par if not better when it comes to fragmentation growth control and heap usage perspective.

My original question is to understand why it is considered as huge tolerance and what should be considered low tolerance. I am suspecting the paper’s intention is not to compare apples and oranges. They are trying to optimize fp32 baseline by sometime resorting using fp16 as long as the resultant solution’s numerical accuracy is within thr tolerance level. They are going for the “low hanging fruits” type of optimization.

Why do you think it is a huge tolerance ? (Just curious since it is not clear to me if that will lead to too much of reduction in numerical accuracy compared to the speedup)

what is the GED you are referring to here ?

Yeah no idea what it is, so I asked copilot, and it says CLP stands for Calculus Learning Project. Makes sense but don’t know if it is accurate :)

This needs 2014 in the title.

I liked and recommend - Statistics Unplugged by Sally Caldwell

I haven't read the article yet but the moment I saw the writer is "Jordana Cepelewicz" I knew it is going to be great! I have read few of her past articles and they were excellent think pieces.

Thanks for sharing!

I have been programming in C professionally for the past ~4 years on a multi-threaded application in the ads industry and that is central to the business. C has lot of documented "foot-guns" but most of it (if not all of it) can be safeguarded against mis-use using "support structures" around the codebase like having standard code style (enforced via tools as much as possible), static code analysis (via compiler and external code scanning tools), dynamic code analysis (via Asan, Ubsan etc), having small, medium and large tests with right amount of code coverage etc. In addition to that, having a standard set of libraries (c modules for high performance data-structures/algorithms, macro based templates to work with types) and threading model goes a long way in reducing the pain to a very bare minimum. On the plus side, you enjoy a "simpler" language syntax that is easy to learn and with the above “support structures” one can become productive in no time. Plus there are newer books in the market that can teach you C properly, one I have read and recommend is "Effective C by Robert C. Seacord" - the author is one of the C standards committee members so you can't go wrong with the choice.

Do you suggest any book that does disambiguate between polynomial and polynomial function (i thought they were equivalent!) ?

amazing to see this JS library uses minimal direct dependencies and even a separate devDependencies that are not needed for runtime - https://github.com/cloudflare/speedtest/blob/main/package.js...

Ingress can also be costly especially if there is a steady state of high load traffic sent from on-prem machines to machines inside cloud (not sure about aws but have experienced this with azure where we had to resort to buy their expressroute which was very costly and ultimately unsustainable for us)

This looks really interesting! Tangentially related if anyone is interested, I recently wrote[1] a pure C (no external dependency) version of coordination free, k-ordered 128-bit UUID Generator library which is inspired by snowflake but has bigger key space and few nifty features to protect against clock skew etc. The 128 bits are split into

  {timestamp:64, worker_id:48, seq: 16}

where the seq is incremented if the unique id is requested within the same millisecond.

[1] - https://github.com/beyonddream/snowid

Oh this! I suffered learning this during college ;)

I am curious to know what are these “formalized architectural decision making methodologies” ? Any books that u know of that cover these topics ?