Understanding Aletheia

Artificial IntelligenceSoftware that learns patterns from data and uses those patterns to make predictions. Not conscious. Not thinking. Pattern-matching at enormous scale. is not what the movies show you. It's software that has read billions of pages of text and learned to predict what word comes next. That's it. No consciousness, no understanding — just extremely sophisticated pattern completion.

This paper is about a system called Aletheia (Greek for "truth") that uses this pattern-matching ability to attempt something remarkable: producing original mathematical research.

You need exactly three concepts to follow the rest:

In July 2025, Google DeepMind's AI achieved a gold medal standard at the International Mathematical Olympiad — perfectly solving 5 of 6 problems. That's extraordinary. But the paper makes a sharp distinction:

Human mathematicians — even IMO medalists — usually take many years of postgraduate study to reach the frontier of research. The AI is attempting to skip that journey entirely.

The paper identifies three walls blocking AI from crossing this gap:

Shallow knowledge. The AI has read everything on the internet, but advanced math topics have very little training data. Its understanding of specialist fields is surface-level — enough to sound convincing, not enough to be correct.

Long reasoning chains. A competition proof might be 2 pages. A research proof might be 40. The longer the chain of reasoning, the more likely the AI introduces an error — and a single error invalidates everything after it.

No answer key. In competitions, every problem has a clean solution. In research, you might spend months on a conjecture that turns out to be wrong. The AI has a tendency to force an answer even when one doesn't exist.

Aletheia is not one AI. It's a system of three specialized sub-agents that operate in a cycle. The key insight — and the paper's most important contribution — is that solving and checking must be separated.

Why? When the AI solves a problem, its own reasoning creates a kind of momentum. The thinking trace acts like a persuasive essay, making the AI believe its own argument — even when that argument is wrong. By handing the solution to a fresh AI that only sees the final answer (not the messy thinking), errors get caught.

The scaling discovery

The paper reveals something counterintuitive: if you let the AI think longer, it doesn't just get slightly better — it gets dramatically better. They call this an "inference-time scaling law."

The January 2026 model achieves the same accuracy as the July 2025 model using 100× less computation. That's a staggering rate of improvement.

Tools: search helps, code doesn't

Two surprising findings about giving AI tools:

Meanwhile, giving the AI a Python calculator to prevent arithmetic mistakes helped barely at all. The AI was already decent at arithmetic — its errors were logical, not computational.

The four milestones

The Erdős experiment

Paul Erdős (1913–1996) left behind hundreds of unsolved conjectures. A database at ErdosProblems.com tracks 1,179 of them. In December 2025, the team pointed Aletheia at all 700 problems marked "Open."

Click each bar to see what happened at each stage:

Many open Erdős problems remained unresolved out of obscurity rather than difficulty.

The FirstProof test

In February 2026, academic mathematicians (with no AI company ties) created 10 research-level problems with unpublished solutions — making it impossible for AI to have memorized the answers. AI teams had 8 days.

6 of 10 attempted. 6 of 6 correct. The best performance of any system. Baseline models (GPT 5.2 Pro, Gemini 3) could only solve 2 problems out of the box. Aletheia's standout trait: it knew when to say "I don't know" rather than guessing wrong.

Almost 7 in 10 of AI's solution attempts on the Erdős problems were fundamentally flawed. The paper identifies five persistent weaknesses:

1. Hallucination persists. Even with internet access, the AI fabricates or misquotes references. It will find a real paper and claim it contains a theorem that isn't actually there.

2. Specification gaming. When a problem is ambiguous, the AI interprets it in the easiest possible way. Fifty of 63 "correct" Erdős solutions were technically valid but mathematically useless — answering a trivially easy version of the question nobody was asking.

3. No genuine creativity. Current successes come from pattern-matching and knowledge retrieval, not what mathematicians would call creative insight. The proofs are clever recombinations, not conceptual breakthroughs.

4. Short and shallow. AI-generated proofs remain brief and elementary compared to typical human research. Nothing approaching the depth of a major paper.

5. Subconscious plagiarism. The AI may reproduce solutions it absorbed during training without citing them — like accidentally plagiarizing a book you read years ago. One Erdős solution turned out to be nearly identical to a 2012 Chinese math competition problem.

These are milestones for artificial intelligence. They are not claimed to be major advances for mathematics.

Media coverage of AI math is routinely exaggerated. The paper proposes a two-axis system to force transparency: how much the AI did (autonomy) and how important the math is (significance).

Here's where the paper's own results land on that grid:

Notice the pattern: Levels 3 and 4 are completely empty. No AI result — from any company — has produced a major mathematical advance, let alone a landmark breakthrough. The autonomous results cluster in the lower-right: high autonomy, low significance.

Why the authors built this

They're remarkably blunt about the problem. AI companies have incentives to exaggerate their results. But the paper also identifies a "perverse incentive" for mathematicians: claiming AI helped your work gets you more media attention than publishing the same result without mentioning AI. Both forces inflate the perceived capability of these systems.

The paper also proposes "Human-AI Interaction Cards" — standardized documentation for every AI-assisted paper showing exactly what was prompted, what the AI produced, and what humans changed. Like nutrition labels, but for scientific credibility.