I would like to post this, because it's a really neat result and also it is today's (July 28th) "Theorem of the Day"!

"The Fifteen Theorem", announced in 1993 by Conway and Schneeberger, states that if a positive-definite quadratic form having integer matrix represents every positive integer up to 15 then it represents every positive integer. In its strongest form, if a positive-definite quadratic form having integer matrix represents 1, 2, 3, 5, 6, 7, 10, 14, and 15, then it represents every positive integer. See Manjul Bhargava's article "The Fifteen Theorem, and Generalizations".

## Tuesday, July 28, 2009

## Tuesday, July 21, 2009

### Julia Robinson and Hilbert's Tenth Problem - Trailer

Apparently Julia Robinson first met Yuri Matijasevic at a meeting in Bucharest...

## Thursday, July 16, 2009

### Robinson's theorem in connection with a Putnam problem

Robinson's theorem in connection with a Putnam problem.

*Award-winning poster presentation at the 2007 Joint AMS/MAA Mathematical Meetings held in New Orleans.*## Tuesday, July 7, 2009

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