An OpenAI model solved the Erdos unit distance problem. Erdos roughly said, “The number of edges of the same distance between N points can’t compound faster than close to 0%.” The model found a method of placing points so that it compounds at about 1.4%. This visualization is a crude way of visualizing how that works.
In Panchayat Season 1 Episode 7 Ladka Tez Hai Lekin…, at around 17:00, Pradhan asks Abhishek to solve problem 42. 42. A takes 5 days more than B to do a certain job and 9 days more than C. A and B together can do the job in the same time as C. How many days would A take to do it? (a) 16 days (b) 18 days (c) 15 days (d) 20 days The correct answer is (c) 15 days. But interestingly, ChatGPT got it wrong the first time too. It said (a) 15 days instead of (c) 15 days, and required a fact-check to correct itself. ...
Terence Tao said, “We haven’t done many experiments … large-scale studies where we take a thousand problems and just test them.” So I told Claude: You know my style. Suggest some innovative experiments I could run. The first suggestion was cool! The Polya Audit. Polya’s How to Solve It lists 20 heuristics (work backwards, induction, analogy, etc.). Mathematicians treat these as wisdom. Nobody has ever measured which ones actually work, and on what problem types. ...
This week, I learned: Timsort is one of the fastest sorting algorithms. Switching from bat to moor as a pager, since bat doesn’t support wrapping via keyboard shortcuts. Gemini “Use (some-command) --help to …” is an efficient prompt prefix that tells agents to read the docs and use a CLI tool to solve a problem. For example, “Use uvx rodney --help and ffmpeg for a demo video of GitHub PRs”. As agents improve, we’ll have more mediorce output (e.g. dashboards) since people won’t know to ask for better, or validate the result. They’ll hire experts who know to ask better and verify better. Claude Opus 4.6 solved a problem Knuth was working on! Knuth Cognitive debt is what Simon Willison calls it when we build (or, in my case, say/write) stuff we don’t understand. The debt framing is apt. One solution is to generate a version intended for AI to read, and another for us. # How can an innovator learn accountability? “I’m wired to start fires. Should I learn to also run the fire department, hire someone who does, or just stay a fire-starter and let others deal with the mess?” ANS: First, accountability is high value, so do it! Second, prefer a partner over building muscle. Build muscle only if output is checkable, has value, and customers will pay. Claude | ChatGPT | Gemini Commit publicly. Put your name on the output. Commit to process (or narrowly defined output) rather than outcome. Optimize with data, code, checklists, workflows, culture, etc. OpenAI released gpt-realtime-1.5 and gpt-audio-1.5. Buth are ~20% cheaper than the 4o versions, but 6.7x more expensive than gpt-realtime-mini. 1 second is about 10 tokens, so an hour of audio input at $32/MTok is about $1.15. The “Effort” setting for AVIF files on Squoosh doesn’t reduce file size - it increases quality slightly (for a tiny increase in file size). So, set the quality to whatever file size you need and increase the effort for a slightly better quality. Polya believed in teaching problem-solving rather than solutions, i.e. teach How to Solve It, not just what you get at the end. To me, this includes: Understand the problem (from different perspectives) Plan (with different mental models) Execute (the easy bit) Look back (post-mortem, retrospectives, etc.) Browserless lets you run browsers via an API. Useful when you don’t want the overhead of setting up a browser infrastructure, or for multiple browsers in parallel. Scraping, testing, web app automation, PDF/screenshot/video generation, etc. are all possible. Gemini OpenAI has a Websocket mode GitHub Agentic Workflows lets you “compile” a Markdown file into an agentic GitHub action. Useful as a sceptical reviewer, issue-to-prototype builder, data to story generator, automated code migrator, etc. Gemini Claude Questions I was asked Week ending 15 Mar 2026 ...
When I was in class 8 or 9, our English teacher told us a story I’ll never forget. There was a poor farmer who lived in a village. He owed the zamindar (landlord) of the village a lot of money. The zamindar had an eye on his daughter. “Marry your daughter to me, and I’ll forgive your debt,” he said. The farmer was reluctant. “Please, sir, what will the village say about your marrying such a young girl?” he asked. ...
I have this feeling that the skills we need for the AI era might be found in video games. (Actually, no. I just want an excuse to play games. Self-improvement is a bonus.) I asked the usual LLMs (Claude, Gemini, ChatGPT): What are mobile phone games that have been consistently proven to be educational, instructive or skill/mental muscle building on the one hand, and also entertaining, engaging and popular on the other? ...
This year, I created a series of tests for my course at IITM and to recruit for Gramener. The tests had 2 interesting features. One question required them to hack the page Write the body of the request to an OpenAI chat completion call that: Uses model gpt-4o-mini Has a system message: Respond in JSON Has a user message: Generate 10 random addresses in the US Uses structured outputs to respond with an object addresses which is an array of objects with required fields: street (string) city (string) apartment (string) . Sets additionalProperties to false to prevent additional properties. What is the JSON body we should send to https://api.openai.com/v1/chat/completions for this? (No need to run it or to use an API key. Just write the body of the request below.) ...
One problem I’ve had in Markdown is rendering a content in columns. On Bootstrap, the markup would look like this: <div class="row"> <div class="col">...</div> <div class="col">...</div> </div> How do we get that into Markdown without writing HTML? On Python, the attribute lists extension lets you add a class. For example: This is some content {: .row} … renders <p class="row">This is some content</p>. But I can’t do that to multiple paragraphs. Nor can I next content, i.e. add a .col inside the .row. ...
From what I’ve seen, puzzles and exam questions share two un-real-worldly characteristics. Firstly, you are guaranteed that a solution exists. Secondly, you are given that all the information provided to you is relevant. (Well, not always. Some case studies I’ve seen have had their share of contrived irrelevance. But that’s often what it is, I think. People fill in the relevant stuff, and then try and distract by adding irrelevant material in the hope of making it more real-world-like. But that’s just a guess). ...
How would you solve this multiple-choice problem: What is 12345 x 45678? 201932843 563894910 402394820 384718349 938491834 It always amazes me when people try and multiply the two numbers. In any objective-type test (multiple choice question), the aim is not to solve the problem – it is to pick the correct answer! Most people don’t seem to realise the difference. If I had to solve the problem, I’d look for shortcuts. For example, ...
I’ve seen many proofs that 1=2. Here’s a classic. The (not-so-subtle) error in the above proof is that we’re cancelling (a-b) on both sides, when (a-b) equals zero. That is, we’re dividing by zero on both sides. That completely invalidates the equality. Another proof uses the fact that the square root of a number can be both positive or negative. ...
What programmers do.
O’Reilly hacks.
Over my last few years as a consultant, I’ve seen many interesting ways in which markets have emerged where they shouldn’t have, creating havoc in pricing and scarcity. Fixed prices fluctuate, free goods acquire a value, and non-tradeable goods are traded. I’ll share a few of these examples over the next few weeks. Once, a fan manufacturer asked us, We did an analysis and found that our wholesalers’ margins fluctuate. How could that happen, when we are fixing their buying and selling prices? ...
Think like a genius.
10 steps for boosting your creativity If you’re stuck for an idea, open a dictionary, randomly select a word and then try to formulate ideas incorporating this word. You’d be surprised how well this works. The concept is based on a simple but little known truth: freedom inhibits creativity. There are nothing like restrictions to get you thinking.
Realistic lateral thinking puzzles.
It’s been long since I solved lateral thinking puzzles. Hartman’s site has over a hundred (with answers).
First Round On Saturday (25th November 2000), I dress up in my best suit (only suit, really), and find my way to the Green Park station for an interview with the Boston Consulting Group. Of course, being terribly conservative, I arrived an hour early, so it was time to walk around Green Park and have a look at the Buckingham Palace, while singing “I have confidence…” from Sound of Music. The walk did lift my spirits a bit. There was this tiny poodle that was busy licking a bulldog. The bulldog didn’t seem to mind, though it was large enough to eat up the poodle. Then the poodle’s owners picked it up, and walked away. The poodle was reluctant though. It just hadn’t finished licking the bulldog. After about 5 minutes, the bulldog (and owner), were about half-a-kilometer away, when the poodle was finally let down. Being the determined creature that it was, it ran ALL the way to the bulldog, and proceeded to lick. The bulldog, right through, was wearing a puzzled expression on its face, as if to say, “Are you sure you don’t want me to smack this little white fluff?” ...