Mathematicians

Pure mathematicians operate at the theoretical edge, developing new principles or applying complex theorems to fields like cryptography, aerospace, and advanced physics. Their day-to-day involves conceptual wrestling, formalizing abstract proofs, and translating domain-specific problems into rigorous mathematical structures. The primary friction lies in verifying logical bounds, searching through dense academic literature, and meticulously typesetting equations for peer review.

This is an actively hostile market for vertical SaaS or traditional agent sales. With an official workforce numbering in the hundreds, the direct total addressable market is functionally nonexistent. Selling productivity tools to academic researchers or government theorists yields negligible revenue, meaning startups attempting to build software directly for this specific cohort will quickly stall.

The startup opportunity lies in bypass and commoditization rather than empowerment. By pairing LLMs with formal verification languages like Lean, founders can build headless software that delivers pure mathematical reasoning directly to adjacent, high-value industries. This enables services-as-software to perform cryptographic verification, optimize complex logistics networks, or validate algorithmic trading models without requiring a human mathematician on the payroll.