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8 posts tagged with research *and* math.

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## HoTT Coq

Univalent Foundations Redefines Mathematics - "When a legendary mathematician found a mistake in his own work, he embarked on a computer-aided quest to eliminate human error. To succeed, he has to rewrite the century-old rules underlying all of mathematics." (previously) [more inside]

## Math, myths, and Vikings: storytelling and social networks

"An unusual article recently appeared in the magazine of the Royal Statistical Society and American Statistical Association.
It featured web-like diagrams of lines connecting nodes, a hallmark of research that analyzes networks. But each node, rather than being a plain dot, was the head of a burly, red-bearded Viking sporting a horned hat, his tresses blowing in the wind." [more inside]

## A SAT Attack on the Erdos Discrepancy Conjecture

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; previously ;)

## Computerized Math, Formal Proofs and Alternative Logic

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]

## Arthur's Classic Novels, his Love of Mankind and the Internet

Arthur's Classic Novels has 4000 free ebooks, no registration, nicely organized by author and topics: great old Science Fiction magazines l plentiful online education with 650 books for doctors l a vast collection of famous novels l short stories l by women l Buddhist Scriptures, including The Buddhist Bible, a fave of Jack Kerouac l magazines online l stories by Robert Sheckley l The Autobiography of Charles Darwin l huge collection of fairy tales l philosophy l P. G. Wodehouse l vintage technology l Oscar Wilde l Mark Twain l Rudyard Kipling l George MacDonald l the Koran l a collection of eText resource links. About Arthur Wendover. [more inside]

## Virtual Thinking

Correlative Analytics -- or as O'Reilly might term the Social Graph -- sort of mirrors the debate on 'brute force' algorithmic proofs (that are "true for no reason," cf.) in which "computers can extract patterns in this ocean of data that no human could ever possibly detect. These patterns are correlations. They may or may not be causative, but we can learn new things. Therefore they accomplish what science does, although not in the traditional manner... In this part of science, we may get answers that work, but which we don't understand. Is this partial understanding? Or a different kind of understanding?" Of course, say some in the scientific community: hogwash; it's just a fabrication of scientifically/statistically illiterate pundits, like whilst new techniques in data analysis are being developed to help keep ahead of the deluge...

## Tangible Applications of Science

Beyond Discovery - illustrations of the path from research to human benefit

## The Complexity of a Controversial Concept

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)Page:
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