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
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]
"Perhaps twenty or thirty people in England may be expected to read this book."
G.H. Hardy's review of Whitehead and Russell's Principia Mathematica
, published in the Times Literary Supplement 100 years ago last week. "The time has passed when a philosopher can afford to be ignorant of mathematics, and a little perseverance will be well rewarded. It will be something to learn how many of the spectres that have haunted philosophers modern mathematics has finally laid to rest."
92 years young, the delightful Raymond Smullyan
is a mathematician, logician, magician, concert pianist
, and Taoist philosopher
- who also pioneered retrograde chess problems
Godel's theorems have been used to extrapolate a great many
"truths" about the world. Torkel Franzen
sets the record straight
in his new book Godel's Theorem: An Incomplete Guide to Its Use and Abuse
. Read the introduction
(PDF). If you want, check out his explanation
of the theorems.
The Logic of Diversity
"A new book, The Wisdom of Crowds
] by The New Yorker
columnist James Surowiecki, has recently popularized the idea that groups can, in some ways, be smarter than their members, which is superficially similar to Page's results
. While Surowiecki gives many examples of what one might call collective cognition, where groups out-perform isolated individuals, he really has only one explanation for this phenomenon, based on one of his examples: jelly beans [...
] averaging together many independent, unbiased guesses gives a result that is probably closer to the truth than any one guess. While true — it's the central limit theorem
of statistics — it's far from being the only way in which diversity
can be beneficial in problem solving." (Three-Toed Sloth)
What Color is My Hat?
I [heart] these mathematical conundrums -- simple, easy-to-state, seemingly obvious logic problems that have solutions that completely defy common sense. Here's another you can spring on a friend: "You want to fry up three pieces of french toast. You have a frying pan that is just large enough to accomodate two pieces of bread at a time. If it takes you 30 seconds to fry one side of bread, and each piece of must be fried on both sides, how long will it take you to cook up three pieces (assuming that the act of flipping a piece or adding/ removing it to or from the pan takes no time). Think about it. Answer inside.