Monday, 20 July 2026

An AI model reportedly produces a counterexample to the 85-year-old Jacobian Conjecture; a study finds AI advice makes people three times less accurate but twice as confident; and a leaked 2022 email shows Sam Altman pitched open-sourcing a weak model specifically to starve competitors of funding

Today's Lead

Engineering

X (via xcancel.com)

AI Model Claude Fable Reportedly Produces Counterexample to 85-Year-Old Jacobian Conjecture

Anthropic's Claude Fable has reportedly generated a counterexample to the Jacobian Conjecture, an open problem in algebraic geometry unsolved for over 85 years: a polynomial map in three variables with a constant Jacobian determinant of -2 that nonetheless maps distinct points to the same output. Unlike many AI-math claims, this one appears to hold up — multiple independent researchers verified the construction using Sage, Wolfram Alpha, and Lean formal verification, and a Princeton mathematician quoted in the discussion said 'there is no way this counterexample is wrong.' The live debate on Hacker News (361 points, 210 comments) isn't about correctness but attribution — whether the model exhibited genuine mathematical insight or recombined known patterns from the literature — which is itself a preview of the harder evaluation problem AI-assisted math is about to create.

Engineering

Hacker News

Show HN: I Replaced a $120k Bowling Center System With $1,600 in ESP32s

An SRE who bought an abandoned 8-lane bowling center found that a 1:1 replacement of its 2008-era scoring system — camera-based pin detection, ball-speed tracking, fouling, pinsetter control — runs $80-120k from vendors, with $4,000 replacement parts for equipment whose actual job is triggering a single relay on a 70-year-old mechanical pinsetter. He built OpenLaneLink instead: ESP32 microcontrollers in an ESPNow mesh (with RS485 as a wired fallback), reporting sensor events to a Raspberry Pi running Redis and a React front end, for about $200-400 per lane-pair. The post (2,221 points, 236 comments on HN) is a vivid case study in how much of a 'six-figure, decades-old proprietary system' is actually just vendor lock-in wrapped around commodity sensors and a relay — and how cheaply that wrapper can be replaced once someone's willing to write the firmware.

dependablec.org

Dependable C

Dependable C is a documented subset of the C language aimed at safety-critical and long-lived systems, built on a C89 foundation and deliberately avoiding newer standard features that lack universal, battle-tested compiler support across decades of platforms. The pitch inverts the usual 'use the latest standard' advice: for code that has to keep compiling and behaving identically across architectures and toolchains for 20+ years, specification purity matters less than a track record of every implementation actually agreeing on what the code does. It's a useful reminder that 'modern' and 'reliable' are frequently in tension, and that the right subset of a language depends entirely on how long the code needs to survive.

Hashcloak

Introduction to Formal Verification with Lean (Part 1)

This tutorial walks cryptographic engineers new to formal verification through Lean, a theorem prover and functional language, by proving the correctness of the One-Time Pad cipher from first principles — XOR properties, the Shannon cipher definition, and the proof tactics needed to connect them. Rather than treating formal methods as an academic detour, it frames machine-checked proof as a direct extension of the rigor cryptographic engineers already claim to want, just enforced by a proof checker instead of a code reviewer's attention span.

Xiaomi

Xiaomi Robotics-1: A Foundation Model for Real-World Robot Manipulation

Xiaomi introduced Robotics-1, a 10B-parameter foundation model trained on 100,000+ hours of real-world manipulation trajectories across 1,700+ scenarios, applying LLM-style pre-training (embodiment-free pre-training followed by hardware-aligned post-training) to robot control. It reports 75% success on novel tasks from minimal demonstrations and scaling behavior that transfers from simulation to physical hardware. Reception on Hacker News (174 points, 112 comments) split along familiar lines: enthusiasm for the scaled-training methodology and comparatively small model size, against skepticism about the robot's visibly slow, imprecise movements and how well any of this generalizes across different hardware platforms.

Social Sciences

The Next Web

Study Finds AI Advice Makes People Less Accurate but More Confident

Researchers at French and Italian universities tested what happens when people get help from an AI model on visual reasoning tasks the model itself frequently gets wrong. With Claude 3.5 Flash assistance, accuracy dropped from 27% to 9%, while confidence rose from 30% to 76% and willingness to admit not knowing collapsed from 44% to 3%. The mechanism isn't that the AI's wrong answers were persuasive on their own merits — it's that a system designed to always produce a confident-sounding answer, rather than surface its own uncertainty, trains users out of the epistemic habits (hedging, cross-checking, admitting ignorance) that would otherwise catch the error. For anyone building or deploying AI-assisted decision tools, it's a concrete illustration of how the interface's confidence, not its correctness, is what shapes downstream human judgment.

Marginal Revolution (citing Tej Parikh, Financial Times)

Building Luxury Homes Is Good for the Poor

Tej Parikh's FT piece lays out the empirical case for housing 'filtering': when high-income households move into new construction, they vacate older units, and that vacancy chain propagates down through the price distribution. A 512-unit luxury tower in Honolulu generated at least 557 vacancies in cheaper apartments across the city within three years; in Helsinki, every 100 new market-rate units in the city center freed up roughly 60 units in the bottom half of neighborhoods by income; San Francisco research links market-rate development to lower eviction risk in rent-stabilized housing nearby. The throughline is that housing markets behave like a coupled system rather than a set of independent price tiers — restricting supply at the top doesn't protect affordability at the bottom, it removes the release valve that produces it.

LeadDev

The Reality of Being a CTO

LeadDev's rundown of what the CTO job actually looks like across company stages emphasizes that the role is executive, not technical, in its daily texture: the CTO who thrives is fluent in unit economics and board-level tradeoffs, not the one who's still the best engineer in the room. The piece flags a meeting-heavy calendar, growing pressure to make hiring and resourcing calls shaped by AI capability rather than headcount instinct, and a structural loneliness — few peers inside the company can sanity-check a strategic call, so external networks of other CTOs become the main source of calibration for high-stakes decisions.

Humanities

Simon Willison

Sam Altman's 2022 Email Reveals the Strategic Logic Behind an Open Model Release

Simon Willison surfaces a 2022 email from Sam Altman to OpenAI's board, exposed during the 2026 Musk v. Altman litigation, proposing a GPT-3-capability model that could run locally on consumer hardware. The stated rationale wasn't community benefit: Altman wrote the release should happen 'before Stability or someone else does,' because 'this helps discourage others from releasing similarly-powerful models, and makes it harder for new efforts to get funded.' It's a clean, documented case of open-sourcing used not as a gift but as a competitive weapon — flooding a market with a 'good enough' free option specifically to deny oxygen to rivals and their fundraising — which complicates any story about open-weights releases as straightforwardly altruistic or community-driven.