Advancing Mathematics Through Artificial Intelligence

Pioneering research at the intersection of AI and mathematical reasoning, developing intelligent systems that can discover, prove, and explore mathematical concepts.

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A New Telescope for Thought

Just as the telescope revolutionized astronomy, Artificial Intelligence is transforming mathematics. This is an exploration of how AI is becoming a new instrument for discovery—not just for calculation, but for reasoning, conjecturing, and pioneering new scientific theories.

The Galilean Revolution

In the 17th century, the telescope turned astronomy from philosophy into an empirical science. By revealing Jupiter's moons and the Moon's craters, it generated undeniable evidence that shattered a millennium of dogma and reshaped our understanding of the cosmos.

The AI Revolution

Today, AI acts as a cognitive instrument for mathematics. It synthesizes vast knowledge, identifies novel patterns, and verifies complex proofs with logical certainty, opening up new frontiers of discovery that were previously beyond human reach.

Three Paradigms of Machine Reasoning

The landscape of AI for math is defined by three core approaches. This research focuses on the synthesis of these paradigms, creating a system that combines intuitive pattern-matching with rigorous, verifiable logic. Click each tab to learn more.

The Future: From Co-Pilot to Creative Partner

Solving IMO problems is just the beginning. The research roadmap envisions AI evolving through three stages, ultimately becoming a true collaborator in pioneering new scientific theories.

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Stage 1: Co-Pilot

AI acts as an assistant, handling tasks like code generation (MATLAB Copilot) and personalized tutoring (Khanmigo), augmenting human workflows.

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Stage 2: Synergistic Partner

In environments like Lean, humans provide high-level strategy while AI manages tactical proof search and logical verification, enabling distributed cognition.

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Stage 3: Pioneer

AI transcends problem-solving to generate novel conjectures and discover new theorems, as seen in knot theory and graph theory breakthroughs.

Research Areas

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Geometry Reasoning

Developing AI systems that can understand and reason about geometric concepts, spatial relationships, and visual mathematical structures.

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Neural Theorem Proving

Developing neural networks that can automatically discover and prove mathematical theorems using deep learning architectures.

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Mathematical Discovery

Using machine learning to identify patterns in mathematical data and generate new conjectures and insights.