CONJECTURE INDEX

The Conjecture Index is the definitive registry of humanity's unsolved problems, the organisations working on them, and the problems no one has yet claimed.

WHAT IS A CONJECTURE?

In mathematics, a conjecture is a problem believed to be solvable but not yet proven. Some conjectures sit open for decades. Some for centuries. The most famous, Fermat's Last Theorem, took 358 years to prove. We use the same word deliberately. Every problem on this Index is a conjecture. It is believed to be solvable. It has not yet been solved. Some have armies of people working on them. Some have no one.

ON CLASSIFICATION

Biologists have been classifying living things since Carl Linnaeus published Systema Naturae in 1735. His insight was simple and radical: if you could name and classify every organism systematically, patterns would emerge that were invisible to the naked eye. Species that appeared unrelated shared common ancestors. Organisms from completely different environments occupied equivalent ecological roles. The classification revealed structure that observation alone could not.

We are attempting something similar for problems.

The Linnaean system classifies organisms by their characteristics and relationships. We are building a classification system for problems by their characteristics and relationships, to their solvers, to each other, and to the conditions that determine whether they get solved.

Entomology does not just catalogue insects. It reveals how they relate to their environment, what roles they occupy, and what happens when they disappear. The Conjecture Index does not just catalogue problems. It reveals how they relate to their solvers, what structural features determine whether they attract attention, and what happens when they go unclaimed.

The methodology is not yet settled. That is the work of Problem Ecology. But the inspiration is clear: the most powerful thing you can do with complexity is classify it.

A NOTE ON METHODOLOGY

A substantial methodology for classifying and indexing problems is expected by Q4 2026. Until then, the Index operates on working criteria that will be revised as the research matures. This is deliberate, as the alternative (waiting for a perfect methodology before indexing anything) would mean losing the data that the methodology needs to be built on. Problems are being indexed now, imperfectly, because the act of indexing generates the observations that will eventually produce a rigorous classification system.

Every conversation with a founder, researcher, or capital allocator between now and Q4 2026 is data collection. Every problem entered into the Index before the methodology is finalised is a specimen that will inform what the methodology needs to be able to classify. We are running the experiment before we have fully designed it.