Computers are providing solutions to math problems that we can't check
- "A computer has solved the longstanding Erdős discrepancy
problem! Trouble is, we have no idea what it's talking about — because the solution, which is as long as all of Wikipedia
's pages combined, is far too voluminous
for us puny humans
to confirm." (via
Discovering Free Will
, Part III
) - a nice discussion of the Conway-Kochen "Free Will Theorem". [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]
It's Saturday; why not think about the pigeonhole principle
? Here are problems
and more problems
and what you might call a problem with the principle itself
as it is often stated.
Geometrically the irrationality of the square root of 2 means that there is no integer-by-integer square whose area is twice the area of another integer-by-integer square. A visual proof that the square root of 2 is irrational
(not found in previous visual proof post
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]
has always been a haven for geek humor
, but last week's episode "The Prisoner of Benda"
pushed things to the next level. First hinted at in an American Physical Society interview
with showrunner David X. Cohen (previously
), staff writer and mathematics Ph.D. Ken Keeler
devised a novel mathematical proof
based on group theory
to resolve the logic puzzle spawned by the episode's brain-swapping (but no backsies!) conceit. Curious how it works? Read the proof (in the show
or in plain text
), then see it in action using this handy chart
. Too much math for a lazy Sunday? Then entertain your brain
with lengthy clips
from the episode
-- including two of the funniest moments in the series
in the span of two minutes.
Did you know that you can create a simple set of directions to your house that works no matter where the recipient starts from?
After 38 years this remarkable conjecture
has now been proved
by a 63-year old former security guard