Original URL: http://www.theregister.co.uk/2010/08/11/the_p_versus_np_problem/

## HP boffin claims million-dollar maths prize

Number nerds demand "real" proof

Posted in Science, 11th August 2010 22:33 GMT

**Update** An HP mathematician claims to have solved one of computer science's thorniest problems and thus bagged a $1m prize for his million-watt brainpower. Fellow number-boffins, however, are saying otherwise.

The million-dollar challenge, one of seven thrown down by the Clay Mathematics Institute (CMI) in its Millennium Prize series, is known as the P vs NP Problem.

It essentially involves figuring out whether or not there are computing problems that have solutions that can be quickly checked after they have been reached, but that are far too complex and multifaceted to be solved without a computer needing, oh, just about forever to arrive at said solution.

Or, as CMI mathematician Steven Cook explains: "The P versus NP problem is to determine whether every language accepted by some nondeterministic algorithm in polynomial time is also accepted by some (deterministic) algorithm in polynomial time."

Got it? Good.

HP's Vinay Deolalikar not only understands Cook's summation, but believes he's found the answer — which, by the way, can be succinctly summed up as "No" — and by doing so has earned the CMI's million-dollar prize.

If you're of a mathematical bent, you'll find Deolalikar's 116-page explanation of his proof, "P ≠ NP" (PDF), a jolly read.

According to the BBC, however, not all number-nerds are impressed by Deolalikar's reasoning. Scott Aaronson, an MIT comp-sci guy, says that before he and others buy into Deolalikar's resolution of the P versus NP problem, the HP boffin's proof must first pass "a sanity test."

Aaronson's definition of such a test is brief and to the point: "[Deolalikar's proof] had better not also prove something that we know to be false." Citing other mathematicians' concerns, Aaronson said the ball is in the HP math man's court: "Everyone agrees, if he can't answer this, the proof is toast."

*The Reg* is rooting for Deolalikar. After all, there are still five more million-dollar challenges out there that Aaronson and his peeps can take on: the Birch and Swinnerton-Dyer Conjecture that puzzled Stieg Larsson's heroine Lisbeth Salander, the Hodge Conjecture, Navier-Stokes Equations, Riemann Hypothesis, and the Yang-Mills and Mass Gap problem.

The seventh Millennium Prize challenge, the resolution of the Poincaré conjecture, has already been met, earning Russian mathematician Grigori Perelman a cool 30.4m rubles ($1m).*

Missed your chance. ®

### Bootnote

For the mathematically lightweight or middleweight, mathematician Ian Stewart provides an explanation of the P vs NP Problem using the familiar computer game Minesweeper. Trust us, Stewart's gloss is far more comprehensible to the layman than Deolalikar's P ≠ NP.

### * Update

*Reg* reader "Stan" has brought to our attention that although Grigori Perelman did, indeed, solve the Poincaré conjecture, he refused not only the $1m prize from the CIM, but also the prestigious Fields Medal, which Stan referred to as "the Nobel prize equivalent in the world of mathematics."