Promptings

Inside a new Freedman paper: a Googol hidden in 100 tokens, and why mathematics is a three-thousand-year AlphaZero run. In March this year, Michael Freedman, who won the Fields Medal back in 1986, published a paper with a few collaborators. The title is brash: Compression Is All You Need: Modeling Mathematics. I am borrowing it for this essay, because once you see what they measured, no other title does the job. They did something that sounds dull at first. They took MathLib, the Lean 4 library with roughly half a million theorems, definitions, and lemmas, turned the whole thing into a dependency graph, and measured two numbers for every element. One they call wrapped length: how many tokens you write in the Lean source to state this thing. The other is unwrapped length: if you recursively expand every reference down to the base axioms, how many raw symbols do you end up with. Then they went looking for the deepest element in MathLib. They found a theorem in algebraic geometry called AlgebraicGeometry.Scheme.exists_hom_hom_comp_eq_comp_of_locallyOfFiniteType. Wrapped, it takes about 100 tokens. Fully unwrapped, it contains around $10^{104}$ raw symbols. ...

Last year, the AI coding conversation had a clear hero: Spec-Driven Development (SDD). This year, people are talking about harness engineering instead. That looks like a trend. It is a signal that the bottleneck moved. SDD is about making intent explicit so an agent can start in the right direction. Harness engineering is about building the environment, constraints, feedback, and governance that keep the agent on track after the 50th or 100th step. If you have ever watched an agent do impressive work for 20 minutes and then slowly degrade into a mess, you already understand why the vocabulary changed. TL;DR SDD helps agents start correctly Harness engineering keeps them correct over time The bottleneck moved from generation to verification Long-running reliability is now the real problem The SDD moment: why it caught on Early “agentic coding” had a predictable failure mode. You’d say: “Add user auth,” or “Make a dashboard,” or “Fix onboarding.” The agent would produce something that looked plausible. It might even compile. Then you’d try to use it, and realize half the work was guesswork. ...

Why a concept called epiplexity may explain where intelligence really comes from. Intelligence, at its core, is a compression problem. Humans cannot track every falling apple, so we invent gravity. We cannot memorize every chess position, so we develop strategy. We cannot remember every sentence we’ve ever read, so we acquire grammar. In each case, intelligence emerges from the same constraint: we cannot brute-force the world. When computation is limited, discovering structure becomes essential. A recent paper from researchers at Carnegie Mellon and NYU introduces a concept that captures this idea precisely. They call it epiplexity — the portion of information that a computationally bounded learner can actually extract. The idea helps explain several puzzles about modern AI, from AlphaZero’s superhuman chess ability to the surprising effectiveness of reasoning-based models. More importantly, it reframes a deeper question: Where does intelligence actually come from? The Static vs. Euclid Problem Consider a simple thought experiment. You have two things in front of you. One is a terabyte of television static — pure noise, every pixel random. The other is a copy of Euclid’s Elements, the geometry text that shaped two thousand years of mathematics. ...

Not long ago, Notion founder Ivan Zhao published a widely shared essay, Steam, Steel, and Infinite Mind, using the Industrial Revolution as a metaphor for understanding AI. In his framing, AI is an “infinite mind” that will fundamentally reshape the structure of knowledge work. He also invoked Marshall McLuhan’s “rearview mirror” idea, arguing that we are still embedding AI chat boxes into existing workflows, far from touching the deeper structural shift. This essay takes a different route. Instead of relying on industrial metaphors, it picks up McLuhan’s core toolkit — “the medium is the message,” extension and amputation, hot and cool media, the rearview mirror effect, and the tetrad of media effects — and applies it directly to AI. Industrial metaphors are good at analyzing productivity and economic organization. McLuhan’s framework goes deeper. It asks how AI is altering perception, cognition, and understanding itself. I. “The Medium Is the Message” | AI’s Real Impact Is Not What It Produces McLuhan’s most famous line comes from Understanding Media: “The medium is the message.” He elaborates: “The personal and social consequences of any medium — that is, of any extension of ourselves — result from the new scale that is introduced into our affairs by each extension of ourselves, or by any new technology.” ...

People often treat prompting as a trick. A clever sentence. A secret template. A magic phrase. That mindset misses the point. Bad Prompts Reveal Confused Thinking When a prompt fails, it usually fails for simple reasons: The goal is unclear The context is incomplete Success is undefined AI reflects the quality of your thinking back to you. Prompting as Externalized Thought Good prompting forces you to: Name assumptions Clarify constraints Decide what matters This is why prompting feels exhausting at first. You’re not writing instructions—you’re organizing your mind. Why Templates Only Help So Much Prompt templates are useful, but limited. They work best once you already understand: The structure of the problem The type of output you want The trade-offs you’re willing to accept Without that understanding, templates just produce confident nonsense. Collaboration, Not Control The most effective prompts treat AI as a collaborator: Ask for alternatives Invite critique Explore uncertainty Prompting isn’t about controlling AI. It’s about becoming precise with yourself.