A fascinating BBC Horizon program from 1984 looking at the greatest unsolved problems in mathematics including Fermat’s Last Theorem (since solved), The Goldback Conjecture, The Riemann hypothesis, the P=NP Problem, and more. Featuring interviews with many modern mathematicians, this documentary also looks at the history of maths and some of if it’s major players from Euclid to Bertrand Russell.
In discussing the fact that proof requires more than calculated verification reference is made to the Merten Conjecture. A conjecture which was disproved in 1984, despite holding firm for 99 years and having been verified on computer up to the first 10 billion numbers. A fact that makes us think about the things in our own lives which, with far less evidence, we consider to be certainties.