Theo Conjecture

Automated mathematical conjecturing

Explore the underlying structure of data to generate plausible relationships for further investigation.

A guided path from “here is my dataset” to “here is a statement worth investigating.”

Automated conjecturing

How it Works

Start with your research domain

Work within established mathematical fields or upload your own structured datasets to explore relationships across known objects and properties.

Define the conjecturing universe

Select the invariants, properties, and targets you want to investigate, guiding the search toward questions relevant to your research.

Explore conjectures with context

Review candidate conjectures alongside their supporting evidence, definitions, and assumptions to evaluate which statements are worth pursuing further.

Theo Conjecture at a Glance

From structured domains to candidate discoveries

How Theo Conjecture Accelerates Research

new descriptors & proof-state predicates

failed statements return as new counterexample rows

01 / Registry

Registry

objects, values, predicates

02 / Search

Theo-Conjecture

relation search

03 / Synthesis

LLM Agent

builds, interprets, revises

04 / Testing

Exact Tests

add counterexamples

05 / Audit

Human-Audited

verifiable proof

Human Mathematical Judgment

Selects meaning, novelty, and defines proof obligations to anchor the loop.

⇢ to Registry — new descriptors & proof-state predicates

⇡ to LLM Agent — anchors each synthesis pass

⇢ to Exact Tests — anchors test obligations for counterexample checks

"Every promoted claim is proved independently of the computational search."

The Output

Candidate conjectures

Every result represents a relationship that survived the selected data and search conditions, providing structured starting points for further investigation.

Inspectable evidence

Inspect the supporting examples, assumptions, hypotheses, and metadata associated with each conjecture to understand why it was surfaced.

Counterexamples surfaced

As new examples are added, identify outdated results, potential violations, and conjectures that may require refinement.

The best research tools are shaped by the people who use them.

More on Conjecturing

Conjecturing

AI system 'Theo Conjecture' solves 35-year-old math conjecture, finds a term no one predicted

An automated discovery system built at FirstPrinciples by Randy Davila has proven a 1989 prediction by Paul Erdős and William Staton linking prime numbers to the Riemann zeta function, and uncovered a second mathematical term that had gone unnoticed for decades.