Let's Talk About AI's Progress, From Word Games to Doing Its Own Research
From solving elementary school math problems, to winning International Olympiad gold medals, to independently proving conjectures that have stumped the math world for decades—AI's "cognitive evolution" might be happening much faster than you think.
Why Start With Elementary Math
Early large language models (the ChatGPT type) are essentially statistical word-prediction machines. You give them a sentence, they guess the next most likely word based on probability. This works fine for writing, but try asking for logical reasoning: "A rope measures 30 centimeters. How many decimeters is that?"—early models often produced confident nonsense.
Why? Because they lacked deterministic logic—the hard rule that "1+1 must equal 2," not "probably equals 2." Human children learn through the same progression: first size comparison, then measurement, then arithmetic and unit conversion. You can't skip steps. Neither can AI.
Without mastering fundamental logical operations, advanced reasoning is impossible. So the first transformation had to be: from a "probabilistic word-guessing machine" into a "logical reasoning engine."
Deep Research: AI Learns to Conduct Its Own Investigations
Once basic logic was in place, AI did something more striking—it learned to research autonomously.
In February 2025, OpenAI launched "Deep Research." Unlike chat mode, it works like this:
- It clarifies what you actually want—asking clarifying questions before diving in.
- It decomposes the problem—breaking a large task into a tree of subtasks, building the framework before filling details.
- It searches extensively—running dozens of queries online, adjusting keywords as it goes, finding workarounds for paywalls, and pivoting when results are unhelpful.
- It performs deep analysis—reading web pages, parsing PDFs, analyzing charts, writing Python code for data analysis.
- It writes a report—synthesizing everything into a structured document with citations and clear logical flow.
In practice, it accomplishes in 30 minutes what takes a human researcher 6–8 hours. After blind review, one professional called it "better than what an intern would write." An architect used it to generate a 15,000-word building code compliance checklist—synthesizing 21 different sources and saving roughly 15–20 hours of manual work.
The system has built-in limits on searches, runtime, and iterations. If it hits a limit before finishing, it submits an honest "progress report" rather than pretending it found everything.
Google's Complementary Approach
Google's Gemini Deep Research takes a different path: deep integration with corporate infrastructure.
While OpenAI scrapes the public internet, Gemini directly accesses your Gmail, Drive, Docs, Sheets, and team chats. For competitive analysis, it pulls public market data while simultaneously reviewing your company's internal strategy memos and product comparison sheets. The resulting synthesis bridges public and private intelligence.
In practice, work that once took a team several days requires a single prompt. A new employee needs to ramp up on a project? Gemini extracts relevant emails, documents, and chat logs to produce a project summary in five minutes.
The Difference in Practice
- OpenAI: A rigorous independent investigator, adept at deep dives through public information and large-scale logical inference.
- Google: A tightly integrated corporate assistant, skilled at connecting internal knowledge with external intelligence.
On the "Human-Level Evaluation" benchmark (an exceptionally difficult multi-disciplinary reasoning test), OpenAI scored 26.6%. Google later reached 46.4%. These low numbers reflect the test's design: it pushes AI to its absolute limits.
From Synthesis to Creation: AI Proves Mathematical Theorems
Deep Research, however impressive, still amounts to organizing and synthesizing human knowledge.
What happened next was fundamentally different—AI began to create new knowledge.
The mathematics community provided the ultimate test: make AI prove theorems. In pure mathematics, memorization is useless; only logical deduction works.
AlphaGeometry: Neural Networks and Symbolic Reasoning Working Together
Google DeepMind built AlphaGeometry to solve International Mathematical Olympiad geometry problems. Its architecture elegantly combines two reasoning systems:
- Neural Network (Intuition): Proposes candidate moves—"What if I add an auxiliary line here?"—much like a mathematician's flash of insight.
- Symbolic Reasoner (Rigor): Verifies each step with cold logic, leaving no gaps.
They alternate: the symbolic engine deduces as far as possible, then passes to the neural network when stuck. The neural network suggests an auxiliary construction, and the symbolic engine resumes. This continues until a proof emerges.
The results speak for themselves. AlphaGeometry solved 25 of 30 IMO-level geometry problems, versus 10 for previous methods. It even discovered a more general version of a 2004 IMO theorem—effectively inventing a new theorem.
July 2025: AI Wins IMO Gold
In July 2025, Google DeepMind announced that Gemini equipped with "Deep Think" had achieved gold medal standard at the IMO: 35 out of 42 points, solving 5 of 6 problems across algebra, combinatorics, geometry, and number theory.
The IMO president and coordinators independently reviewed the solutions by the same standards applied to human contestants, calling them "stunning," "clear," and "precise."
This breakthrough differed fundamentally from prior attempts. Previously, human experts spent days translating problems into formal language before AI could begin. This time, Gemini read the original problem text and wrote a complete proof within the official 4.5-hour window—entirely autonomous, no human translation.
How? DeepMind attributed success to three strategies:
- Parallel Exploration: Rather than following a single path, it explores multiple solution routes simultaneously, like a multi-core CPU.
- Deep Reinforcement Learning: Trained on massive amounts of mathematical reasoning, it learned to sustain long chains without distraction or premature surrender.
- Expert Knowledge: The model was seeded with curated high-quality solutions and techniques, teaching it to reason like a top mathematician.
Yet it scored zero on problem 6, the most difficult. Where genius-level insight is required, AI still has blind spots.
Aletheia: Autonomous Mathematical Research
Winning an IMO gold medal is impressive, but Olympiad problems are designed with guaranteed solutions within bounded scope.
Real research is entirely different: no guarantee of solvability, no clear direction, problems spanning multiple fields, exploration of genuinely unknown territory.
To tackle this challenge, DeepMind built Aletheia—named after the Greek goddess of truth. This is a complete autonomous research agent, not a problem-solver.
Testing Against 700 Unsolved Problems
In December 2025, Aletheia confronted 700 unsolved conjectures in number theory and combinatorial geometry from Bloom's Erdős database.
- Aletheia identified 212 problems it believed solved.
- Initial human review left 63 as plausible.
- Expert confirmation: 13 were correctly solved.
These 13 breakthroughs fall into four categories:
Fully Autonomous (2)—True creation. Erdős-1051, a heavyweight milestone, exemplifies this: Aletheia bridged theoretical frameworks to solve a decades-old problem.
Partial Progress (2)—Successfully cracking key components of complex multi-part conjectures.
Independent Rediscovery (4)—Pure logical derivation of correct proofs later found to exist in obscure literature. The AI reinvented known results through reasoning alone, paralleling how top mathematicians think.
Database Correction (5)—These "unsolved problems" were actually solved earlier but mislabeled. Aletheia helped the academic community perform housekeeping.
The FirstProof Challenge
Aletheia also competed in the inaugural FirstProof Challenge, facing 10 frontier problems lacking human consensus. It autonomously solved 6 (problems 2, 5, 7, 8, 9, 10).
For problem 8, even expert judges disagreed sharply. This matters: AI reasoning has reached boundaries of understanding for some human experts.
AI as Academic Author
Everything described so far concerns problem-solving. The next step marks a genuine watershed—AI autonomously wrote a publication-ready academic paper.
The paper "Feng26" was generated entirely by Aletheia without human guidance. It identified a research gap in arithmetic geometry, performed underlying calculations, designed a novel proof, and wrote a manuscript meeting academic standards.
Zero human intervention from problem identification to final draft.
More realistic is human-AI collaboration. In "LeeSeo26," a mathematician and Aletheia tackled a complex problem in interacting particle systems—the AI generated hypotheses and verified logic while the human provided physical intuition and direction.
The "BKK+26" paper emerged after Aletheia solved the Erdős-1051 conjecture. Mathematicians recognized the proof method's elegance and collaborated with the AI to generalize it into broader results.
Real Concerns
Success stories matter less than honest assessment of remaining risks.
Risk of Implicit Memorization
AI ingests massive training data. How do we know a "proof" isn't implicit retrieval from some corner of training data? The Aletheia authors directly addressed this: reviewing reasoning traces confirmed certain solutions were derived through internal reasoning, not literature lookup. But this verification mechanism is immature. The field needs systematic auditing tools to distinguish "truly new proofs" from "sophisticated copy-pasting."
Informal Problem Statements
Aletheia frequently stalled on conjectures because human mathematicians write casually, omitting context and using colloquialisms that AI's logic engine struggled to parse. Human experts had to serve as translators.
Attribution
When AI contributes to research outcomes, how should intellectual property be handled? Current practice uses joint authorship ("Human + System Name") with detailed disclosure of AI involvement at each stage. The academic community is developing more granular standards for classifying AI contributions.
Beyond Mathematics
The same underlying capabilities—massive data processing, rigorous logical reasoning, autonomous hypothesis verification—are transforming other fields:
- Genomics: DeepMind's AlphaMissense scores millions of mutations for pathogenicity, aiding diagnosis of rare genetic diseases. AlphaGenome assesses genetic mutation impact across molecular properties in under a second.
- Earth Science: AlphaEarth Foundations fuses satellite, radar, and lidar data into a unified high-dimensional embedding. It maps land and nearshore areas at ~10×10 meter resolution, accelerating ecological classification and environmental analysis.
- Weather: WeatherNext replaces traditional supercomputer models with AI, running ~8 times faster and allowing evaluation of more scenarios in parallel, improving detection of extreme events.
Each shares Aletheia's throughline: autonomously ingest data, perform rigorous logical analysis, generate scientific conclusions beyond human processing capacity.
The Trajectory
Looking back:
Learn basic logic → Learn to research and write reports → Learn to prove theorems → Learn to conduct independent research and publish papers
This is a person's path from elementary school to postdoctoral researcher. AI compressed decades into years.
The likely future: humans propose the big questions requiring intuitive leaps, set exploration direction, and define ethical boundaries. AI clears technical obstacles—tireless calculation, reasoning, and verification.
Humans will no longer spend vast time on data cleaning, literature review, and intermediate derivations. Our role becomes strategic leadership of an AI research team.
Further Reading & References
Deep Research
- Introducing Deep Research — OpenAI
- How Deep Research Works — PromptLayer
- Hands-on Review: "We Tried OpenAI's New Deep Research. Here's What We Found" — Every
- Gemini Deep Research for Enterprise — Google Blog
- A Guide to Gemini Deep Research — Skywork
- Gemini Reaches 46.4% on HLE — LinkedIn
Mathematical Reasoning & Theorem Proving
- AlphaGeometry Paper — Nature
- AlphaGeometry Community Discussion — Reddit
- Gemini with Deep Think Achieves Gold Medal Standard at IMO — DeepMind Official Blog
- Comparing ChatGPT and Gemini's IMO Performance — Champaign Magazine
Aletheia & Autonomous Mathematical Research
- Aletheia Agent Architecture — arXiv 2602.21201
- Erdos Conjecture Experiments — arXiv 2601.22401 (PDF)
- AI Paper Results Feng26 / LeeSeo26 — arXiv 2601.21442
- FirstProof Challenge — ChatPaper
- BKK+26 Discussion — Reddit r/singularity
Cross-Disciplinary Scientific Applications