Professor Brailsford explains the concept of the busy beaver game on Turing machines.
Professor David Brailsford
WP: Busy beaver
WP: Turing machine
The scientific method requires an open minded community and freedom of speech to discuss controversial topics. But sometimes there are unpleasant results. Revealing the truth may have effects on someone's reputation. This is where a replacement for the scientific method comes into play: the law.
There are different kinds of logical reasoning, which are used in different situation. Mathematics is deductive, natural science is inductive, and the conclusions of Sherlock Holmes are abductive.
WP: Rigour
WP: Logical reasoning
WP: Abductive reasoning
WP: Deductive reasoning
WP: Inductive reasoning
'Deduction' vs. 'Induction' vs. 'Abduction'
The Mertens conjecture was disproved in 1985.
WP: Franz Mertens
WP: Mertens function
WP: Mertens conjecture
Update (20250808): meanwhile this video is private and not available anymore.
Some background regarding the Möbius function and convolutions:
WP: Convolution
WP: Peter Gustav Lejeune Dirichlet
WP: Dirichlet convolution
WP: Hasse diagram
The Möbius function is a nice tool which is useful in number theory:
WP: August Ferdinand Möbius
WP: Möbius function
WP: Möbius inversion formula