Conjecture
Concept · Mathematics, stage 1: Learn the vocabulary
A conjecture is a statement believed to be true but not yet proved. Some are supported by enormous amounts of computation and still remain open, such as the Goldbach conjecture, which has been checked far beyond any doubt a scientist would have and is still unproved. Others are eventually settled: what was called Fermat's Last Theorem stayed a conjecture for over three centuries until Andrew Wiles proved it in the 1990s. A single counterexample disproves a conjecture, but no number of confirming cases proves one.
Why it matters
Conjectures are where mathematics is actually being done, and they show why the demand for proof is not pedantry: belief and proof come apart, sometimes for centuries.
Part of
Sources
- Conjecture Wikipedia
- Millennium Prize Problems Clay Mathematics InstituteSeven problems named in 2000, the standard shortlist of what is currently open.
