The Frontier and the Froth

OpenAI’s Erdős breakthrough shows the ceiling is rising. Enterprise AI adoption shows the floor remains stubbornly human.

A tale of two realities

OpenAI just disproved a central conjecture in discrete geometry, connected to a problem Paul Erdős posed in 1946.

The original problem is deceptively simple: given n points in a plane, how many pairs can be exactly one unit apart? For decades, the prevailing intuition was that the best arrangements would look roughly like square grids. OpenAI’s model found an infinite family of constructions that beat that intuition, using ideas from algebraic number theory to make progress on a problem that had resisted human mathematicians for nearly 80 years. This was cross-domain reasoning, not a brute-force computation, a Lean formalization, or a known proof recovered from training data. Outside mathematicians reviewed the proof, and Fields Medalist Timothy Gowers called it “a milestone in AI mathematics.”

So yes, this is a big deal.

At the high end, models are moving from autocomplete to discovery. They are proving things, designing experiments, writing software, and beginning to perturb the frontier of knowledge itself. You cannot look at a model helping overturn a long-standing mathematical conjecture and conclude that this technology is fake, trivial, or overhyped.

And yet.

You can believe the technology is profound and still think much of the implementation layer is a mess.

That distinction is where a lot of the current AI debate goes wrong. The conversation keeps collapsing into two bad camps. On one side: AI is a bubble, a scam, a spreadsheet hallucination wrapped in NVIDIA capex. On the other: every deployment is progress, every usage number is adoption, and every chatbot shoved into a product surface is proof of inevitable productivity gains.

Both views are lazy.

This is the uncomfortable middle of AI: the technology is profound but much of the implementation is mediocre. Both facts are true, and much of the current debate is just people choosing whichever half flatters their priors or furthers their agenda.

The frontier is moving. The rollout is messy. The next several years of AI will be defined by the gap between those two facts.

Take Starbucks. The company rolled out an AI-powered inventory counting tool across more than 11,000 North American company-owned stores in 2025, with the promise of faster stock checks and better product availability. Nine months later, they are scrapping the system after persistent inaccuracies, including problems distinguishing similar milk types. The company is going back to manual counting and daily replenishment.

That does not prove AI is useless. It proves operations are hard.

A model can be impressive in a benchmark and still fail in a stockroom. Real-world deployment involves edge cases, employee workflows, incentives, training, accountability, and the quiet rage of the person who now has to fix the machine’s mistakes while also doing their actual job. The demo usually ends before this part.

You see the same problem in software development. “Anyone can code” does not mean anyone can build software. A senior engineer with taste can use AI like a power tool. A novice without judgment can use it like a leaf blower in a china shop. The difference shows up later, when the prototype becomes production and the company discovers that “AI-generated code” is not the same thing as maintainable software.

This is where bad metrics become dangerous. If companies make “percentage of code written by AI” the goal, people will optimize for that goal. Software teams spent the last twenty years learning that more code is not inherently good. Now some companies are rediscovering that lesson with GPU assistance.

The problem is not AI coding. The problem is confusing code volume with engineering output.

The same stat-padding is happening at company level. Open Instagram and try to search for an account. Increasingly, you get AI-generated summaries and AI-mediated discovery surfaces jammed into what used to be a simple navigational action. This is the new growth hack: put AI in the path of an existing behavior, then count the collision as adoption.

This is not unique to Meta. Across software, companies are routing existing workflows through AI features, bundling AI into existing contracts, subsidizing adoption, discounting core products if customers try the AI module, and then reporting usage numbers that sound impressive on earnings calls. Some of that usage is real. Some of it is the unavoidable result of putting the AI feature directly in the path of something the user was already doing.

When a public company says millions of people are using its AI product, the useful question is what kind of usage it represents. Did the user choose it? Did it make the workflow better? Did it save time, improve quality, reduce cost, increase retention, or change behavior? Or did the user merely pass through an AI surface because the company placed it there and then counted the encounter as engagement?

A lot of AI metrics right now are like adjusted EBITDA. Not necessarily meaningless, but you do want to read the footnotes.

This is the heart of the adoption problem. Capability does not automatically become productivity. Technology has to pass through incentives, politics, procurement, org charts, and the competence level of the people implementing it.

This is why the most important AI work inside large enterprises is not buying new tools or laying off employees, its training senior leadership.

Many of the people setting AI mandates do not use these tools deeply themselves. They have seen the demos. They have read the strategy decks. They may have asked ChatGPT to summarize a board memo and found the experience spiritually moving. But they often lack the hands-on fluency to distinguish a useful workflow from a clever demo, real productivity from metric theater, and thoughtful implementation from an internal science fair.

When leaders cannot tell the difference between real AI leverage and AI theater, the organization quickly learns to optimize for theater. The grifters get promoted. The builders get cleanup duty.

The firms that benefit most from AI will not be the ones with the loudest mandates or the highest internal usage numbers. They will be the ones that redesign workflows, train people properly, set real standards, measure actual output, and have leaders who understand the tools well enough to ask non-stupid questions.

OpenAI’s geometry result tells us the ceiling is rising. Enterprise implementation tells us the floor is still sticky.

The next phase of AI will be defined by the gap between those two realities. At the frontier, models are beginning to surprise mathematicians. In the enterprise, many companies are still trying to figure out whether their AI tool can correctly count oat milk.

That is the market right now. The technology is extraordinary. The implementation is still human.

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