Closing in on the twin prime conjecture
) - "Just months after Zhang
announced his result, Maynard
has presented an independent proof that pushes the gap down to 600. A new Polymath project
is in the planning stages, to try to combine the collaboration's techniques with Maynard's approach to push this bound even lower." [more inside]
In August of last year, mathematician Shinichi Mochizuki reported that he had solved one of the great puzzles of number theory: the ABC conjecture (previously on Metafilter
). Almost a year later, no one else knows whether he has succeeded. No one can understand his proof.
Using computer systems for doing mathematical proofs
- "With the proliferation of computer-assisted proofs
that are all but impossible to check by hand, Hales thinks computers must become the judge." [more inside]
creates numerical fonts
where the amount of ink/pixels for each number is in direct proportion to its value
New math theories reveal the nature of numbers
] - "We prove that partition numbers
are 'fractal' for every prime. These numbers
, in a way we make precise, are self-similar
in a shocking way. Our 'zooming' procedure resolves several open conjectures, and it will change how mathematicians study partitions." (/.
) [more inside]
In September 2006 the largest known prime number, a 9.8 million digit number
, was discovered. If you find one over ten million digits you can win US$100,000
(of which you get to keep $50,000
). No maths is required - just download the software
and you're away. Warning: it takes about a month to run one primality check
so some patience is required. Look out though Cooper and Boone look like they might beat you to it.