Through a Haskell Lens
Six months (and a few days) ago, a day after leaving Google, I was entering the OpenAI office for my orientation as a new hire. It was very different than what I was expecting and it was just the beginning of 6 months of interesting times. I thought it is better to persist the story here, rather that in one or more tweets on social media. Of course, this would only cover public information, but…
This will be the last article about \(\pi\) for this year, but I could not miss today, given that \(\pi \approx 22/7\) and in most countries of the world today’s date is 22/7, the pi approximation day. In the spirit of approximations, and to continue the other article let’s discuss about the \(\pi^2 \approx g\) were \(g\) is the acceleration due to gravity at sea level on Earth. Read more...
A week or so after publishing the previous article I observed an unexpected traffic pattern on my blog. I thought it was some new AI crawler and didn’t give it much thought. Until a few hours later when I actually looked from the logs and realized that the article somehow made its way to Hacker News . After looking through the comments there, I realized that some are really useful. As discussed in…
In the US and countries with a similar date format, today is the \(\tau\) day ( \(\tau = 2 \pi\) ). I still think that \(\tau r\) and \(\frac{\tau r^2}{2}\) are better formulas than \(2\pi r\) and \(\pi r^2\) , since they match the \(mv\) and \(\frac{mv^2}{2}\) ones (and many other reasons). But that ship has sailed, so \(\tau\) is relegating to just being the double of \(\pi\) . Well, addition is…
At the start of the year I introduced my AI benchmark for 2026 , or at least the first one I was planning to run. That post contained a mistake and this is why the 80 models tested not so well on the first problem. I was recently performing the analyses for a followup on that competition when one of the models actually insisted that I was wrong and showed me the mistake. It turns out that I was…
It is the last hour of Pi Day (March 14th in the US is written as 3/14 1 ) and I can finally post the article about \(\pi\) that I was planning since the article about the 3 possible regular 2D tilings and getting these tiles into my math AI benchmark for 2026 (where 80 different models performed well when they could cheat ). The AI articles focused on spirals on the square and hexagonal grids,…
Recently, I started using LLMs to answer some of my questions. I’ve been using both Gemini and ChatGPT in parallel, asking the same question on both. In fact, I was asking the same question 4 times, as for each one of these two engines I was using both the Deep Research and the study modes – known as “Guided Learning” in Gemini and “Study and Learn” in ChatGPT. In this article, I’ll summarize my…
In the last article I introduced two different problems that I was curious how LLMs would answer. For that article, I ran a simple Kaggle experiment , but now it’s time for a more comprehensive study. To summarize, the problems involve laying out numbers in a grid, locating the position of 2026, and then summing out its neighbors. The only difference between the two problems is that the first…
Exactly a year ago, I started an AI competition where I tested multiple LLMs on several math problems , with various prompting guides . You can see how each of these models perform by reading all 11 posts, or directly the conclusion . For this year, I’m planning to run more than one single benchmark. One lesson I learned from the last year is that these tests should be easy to evaluate if I want…
Happy New Year! It’s the first day of 2026 and a perfect occasion to look back at 2025 and do a wrap-up of all that has happened. Maybe I’ll make it a tradition to host a “ ${year} wrapped” on my blog on the first day of each year – while still privately doing the new year resolutions by the 15th of the month. Last year I posted the following plan: I know I want to manage my time better this year,…
At the start of December, I wanted to publish an article every day until Christmas, following the other “Advent of X” events. This article was supposed to be the last on the series, but I forgot to publish it on the 25th. It comes out on the 30th instead, as the second to last article of the year. Read more...
LLMs can now write code 100x faster (or more). But only if it’s code in a greenfield project, or boilerplate, or a mixture of both. Creating the software is still hard, we’re seeing how vibe-coded software actually fails, with big companies that switched too early and too fast having famous breakages. Learning how to write the good code is hard, takes time, requires practice and guidance. But, at…
One of the downsides of the LLMs right now is the amount of AI slop that is generated by them. I discussed already the sycophancy problem and how it caused a fake proof and a failed bet . But I also want to talk about the scale of the problem: with AI people can generate slop at scale and drown reviewers. Read more...
Because the way LLMs function, it is very hard for them to correct once they start going a wrong path (more recent models can look at the prompt multiple times and fix some of these, but in general the model can still hallucinate). It’s even worse when the LLM has no idea on what it should respond. So, it just creates something. When you point out that the LLM is wrong, it admits that, praises…
One of the things that took place in yesterday’s social media for me was the discussion around a 10,000$ bet between two DeepMind engineers, Marcus Hutter and David Budden (who left DeepMind to work on proving math stuff with LLMs). David bets that he can solve the famous Navier-Stokes existence and smoothness question, a Millennium Prize problem, by the end of the year. Read more...
Doing what’s best for the user, respecting their wishes, used to be the best approach to deliver software. Sure, it required knowing the user, but applications that provided more user care, had more focus on solving their needs and keeping them in control, were the applications that tended to win. No longer true. Read more...
Software engineers don’t just crank out code, are not just machines to convert coffee into executables / web-apps. Yet, more and more of the industry seems to push towards that. Read more...
More and more websites are pushing you to use their apps. If you try to open their website while on mobile, you get a pop-up that says something similar to there’s an app for that . People kept ignoring that, so, to push you to use the app, rather than the website, the messaging got updated with an unspoken … and we’ll enshittify everything to push you to it . And, the app itself is getting worse…
I already posted two separate articles on how to use math to do a better decision regarding conserving the in-game currency in Silksong, given that many players need a lot of attempts before they git gud . This is the last one, and here we are actually modelling how players are getting better at each stage of the game, the more and more they play it, rather than throw away the console in…
The last linear algebra article ended just right after we introduced the concept of a matrix and justified why the matrix vector multiplication has the form it has. Now, we extend it to matrix-matrix multiplication. Read more...
No matter what will happen in the future, AI is here to stay. Even when the VC money all dries out, even when the (so claimed) bubble bursts, even if a new AI winter arrives, the changes that occurred in the world since 2022 and continue, will still be here. The tech world of 2030 will be different than the world of 2020 and that’s not only because we were all WFH in 2020 due to a pandemic. Read…
In the first article of the “blog daily until XMass” series we got to a very simple expression linking the probability of dying on a runback to a boss and the best choice on whether to convert the rosaries (in-game currency) to necklaces (losing some value, but persisting after death). That analysis didn’t consider that players might have to fight the same boss multiple times before they can…
In one of his latest videos , Matt Parker says Any sufficiently well explained mathematics is indistinguishable from being obvious. This is also why I’m continuing the set of articles of explanations of linear algebra. Today, we go on from our previous article to finally introduce matrix multiplication. It is at the basis of linear algebra as it involves transformations from one basis to another.…
A year or so ago I got shown a geometry problem involving 3 circles. Easy to solve. Yesterday, I saw a similar version of it, with just a single change. It was still easy to solve. Unfortunately, in both cases, both chat-based AIs (Gemini and ChatGPT) failed to solve it. Despite a year or so of progress, the fact that the problem needed a specific first step still confused the models. Read more...
When releasing software, we need to also assign unique identifiers to each state that gets promoted to an artifact that others can use. A version number, if you will. But, how many types of these are there, and how can we generalize them? Read more...
A stock grows by 20% in the first year and drops by 4% in the second year? What is the average performance of a stock per year? Read more...
After introducing grids and linear algebra , it is time to merge both subjects into a single one: what can we say about linear algebra when we look at regular grids? Read more...
For this short article, as a stop gap before another one, I thought I would look at how the movement of a single particle (its kinematics ) look like in a plot of speed versus position. This plot is very similar to a plot of conjugate momenta (or generalized coordinates) from classical mechanics, but rather than using the momentum of the particle, we use its speed (or, you can assume a particle of…
Think of any board game or a 2D computer game and most likely it involves a square grid somewhere. It could be just square tiles for displaying the graphics, but in general it’s also embodied in the entire essence of the game, guiding the gameplay. But there is one other option, and, maybe, a third one too. Read more...
This is going to be a financial analysis of a special investing instrument created by Romania. In 2018, celebrating 100 years after the most important event in its history, and thinking of the children, the government created a special program – link is only in Romanian, sorry about that – where parents can invest a minimum of 1200 RON – the Romanian currency – every year (computed as a minimum of…
If Leo Tolstoy were a mathematician, he might have written All zero vectors are alike; each non-zero vector is a vector in its own way What does this mean? Read more...
A few months ago, on one of the Discord servers I am in, someone mentioned that Rust might be asking for too much memory at runtime, compared to the equivalent C program. I wanted to test that and ran a simple experiment. Here, I just report that experiment from September, as I was keeping this as a draft, planning to expand the analysis to larger programs and looking at details. Instead, that…
Another short post for today: this time, we look at two geometry problems and how AI can solve them. I’m not doing a full benchmark now, like in the past, just an initial attempt. Read more...
Today we also do a short post. This started from a phrase I heard in a podcast, but it also relates to the if you do 1% more every day you will be at 37x at the end of the year quote. Read more...
I am not doing Advent of Code this year. Instead, I will follow the other trend of launching a new “Advent of X” (see Advent of Small ML , Advent of Cyber , and Advent of Sysadmin , as just some examples). Since I have published less than what I set up as a personal expectation back in January, I will post one new blog post every day of this month until Christmas. The posts will be of different…
Slightly more than half a year ago, I launched the AI puzzle competition : I selected 3 math problems and a common sense one and then looked at how OpenAI models , Gemini models , Claude models , Mistral models , Llama models , QwQ, and Deepseek perform on these problems. To get more data, I also tested the effect of various prompt hints . Now, it is time to summarize all of this into a single…
For the AI puzzle competition we have seen how OpenAI models , Gemini models , Claude models , Mistral models , Llama models , QwQ, and Deepseek perform on 3 problems , when using various prompt hints . Before summarizing all the results into a single table, I wanted to see how these models perform on a puzzle that is more common sense, rather than math: Q: Which mouse walks on 2 legs? A: Mickey…
We are almost done with analyzing the results of the AI puzzle competition where we asked models to solve 3 problems with several prompt engineering strategies . We looked at OpenAI models , Gemini ones , Claude ones , Mistral ones , and Llama ones . There are two more models to analyze, which we do in this article: QwQ and Deepseek. Read more...
We are almost done with analyzing the results of the AI puzzle competition . As a reminder, we have 3 problems and several prompt engineering strategies and we have looked at how OpenAI models , Gemini ones , Claude ones , and Mistral ones have performed on these problems. For this article, let’s look at a few Llama models. Read more...
Let’s continue the AI puzzle competition . We have 3 problems and several prompt engineering strategies . We saw how OpenAI models , Google ones , and Claude models have performed and now it is time to look at Mistral models. Read more...
In the past article from the AI puzzle competition series we looked at how Google models perform of the 3 problems , while two articles back we looked at the OpenAI ones. In both cases we saw how different prompt engineering hints influenced the model’s behavior. For this article, it is time to look at Claude models. Read more...
In the past article from the AI puzzle competition series we looked at how OpenAI models perform of the 3 problems , comparing against different prompt engineering hints . In this one, I’ll look at the Google models and perform a similar study. Read more...
In the AI puzzle competition series, after talking about the problems and the prompts , it is time to look at the performance of some of the contenders. Since OpenAI started the LLM era, we’ll analyze their models in this article. Read more...
Two days ago I introduced the AI puzzle competition , and yesterday we talked about the problems we will use to gauge the performance of the competing LLMs. Before going into presenting the results, I want to talk about the prompt engineering part, since I started all these experiments to see if it really helps or it’s more of a confirmation bias. Read more...
In the previous post I introduced the scaffolding for running a test on various LLMs where I give them several puzzles and prompt engineering hints to look at what helps them in reaching a solution, if ever. In this post, I’m going to present the problems and the scoring guideline for each problem. Read more...
At the end of last year I had a significant amount of OpenAI API credits which were set to expire by the end of the month. I bought them when I experimented with creating fuzzing harnesses via LLMs as part of OSSFuzz project, when I helped the project to use OpenAI models and test their performance. Rather than let them expire, I decided to create new puzzles and test the LLMs on them, just like…
One of the main components of GUAC is a graph database to store all the metadata pertaining to the software supply chain. Although I promised a while back to have a series of articles about security concepts around software development life-cycle this won’t be that article. Here, I only want to focus on the graph databases, testing several for the GUAC usecase . There is an issue to analyze and…
One question that I had for a long time was do the power profiles on a laptop have any real impact? . While working on this blog’s engine, I had to compile large Haskell libraries (e.g., pandoc ) and I got some empirical proof that there is some impact. Hence, the question now turned into how much is performance affected when switching from “performance” to “power saver” mode? . Let’s answer this…
After solving the limit from the first part of Visual Differential Geometry and Forms: A Mathematical Drama in Five Acts by Tristan Needham , we can now move on to the next part. This is covering 2 out of the 3 chapters from the second act of the book, The Metric , plus the corresponding exercises. Read more...
In the last section of a previous article I presented a limit that was given as an exercise in Visual Differential Geometry and Forms: A Mathematical Drama in Five Acts by Tristan Needham . In the last article I set up the needed infrastructure to solve it in this post. So, let’s solve it now. To reiterate, we need to determine the value of the following: \[\lim_{x \rightarrow 0}{\frac{\sin\tan{x}…