Today's Hook
A math problem that stumped experts for 80 years. An AI solved it in a weekend.
In 1946, a mathematician named Paul Erdos asked a deceptively simple question: if you scatter points on a flat surface, how many pairs can sit exactly one unit apart?
Mathematicians spent decades assuming grid-like patterns were basically the best answer.
Last week, OpenAI announced that an internal reasoning model did not just answer the question. It proved the whole conjecture was wrong.
The model found a new family of point arrangements that blows past the old ceiling. Then Princeton mathematician Will Sawin sharpened it further, confirming the result holds at massive scale.
Why you should care even if math makes your eyes glaze over:
Mathematical proofs are one of the few places where AI cannot fake its way through. Either the logic holds under expert review, line by line, or it does not. This one held.
As TechCrunch noted, OpenAI had a shaky Erdos claim once before. This time, outside mathematicians, including some past critics, signed the companion remarks.
Translation: the haters became validators.
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Today's Ai Tip
Stop Letting Your AI Forget What Done Looks Like
Here is the most common reason long AI tasks fall apart: the model loses track of what it was actually trying to accomplish.
You ask it to audit a document, refactor a codebase, or clean up a report. It starts strong, drifts, and hands you back something half-finished with a confident tone.
OpenAI's Codex has a fix for this: the /goal mode.
It works like a mini contract you hand the model at the start. You define the outcome, the constraints, and the tests. The model keeps checking itself against that contract as it works.
When to use it
Reach for /goal any time your task has more than three steps. Migrations, audits, bug sweeps, multi-section edits, report generation. Basically anything where "just do it" is not a complete instruction.
Note: If /goal does not appear in your Codex interface, enable it by adding features.goals = true to your config.toml or running codex features enable goals in the terminal.
Prompt Station
Give Your AI a Definition of Done
Paste this into Codex or any AI agent handling a multi-step task:
/goal Audit this project for newsletter draft readiness. Definition of done: 1. Every section has the required header. 2. Every hyperlink is attached to a short, natural anchor. 3. No Treats or Around the Horn bullets use bold text. 4. Every technical term has a plain-English parenthetical on first use. 5. Return a short report with pass/fail status and exact fixes made. Before editing, make a checklist. After editing, run the checklist again and show me what changed.
Bonus image prompt: LEGO Brand Products
Turn any product into a viral-worthy LEGO photo shoot. Use this in your favorite image AI (Midjourney, DALL-E, Ideogram):
Create a professional product photography image of a [PRODUCT] reimagined entirely in LEGO bricks. Construct the iconic shape using LEGO elements in brand-appropriate colors. Include the official brand logo in pixelated LEGO mosaic style. Use high-end studio lighting, professional depth of field, vibrant brand colors, and a 4:5 vertical format. The product should look fully functional, three-dimensional, and unmistakably made of LEGO. Style: photorealistic 3D rendering, premium studio setting.
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