By Anupum Pant
Till the year 2003, there were seven mathematical problems that had not been solved. Then came in Grigori Perelman, a Russian mathematician, who solved The Poincare Conjecture, a problem which was the first one of those seven unsolved problems.
To Grigori Perelman the prize was completely irrelevant. Sir John Ball, president of the International Mathematical Union tried persuading him for 10 long hours to accept the prize. But, he did not attend the ceremony, and declined to accept the medal, making him the first and only person to decline this prestigious prize.
6 problems yet to be solved
One down. Today, six of them still remain unsolved. Each one of those six problems carries a $ 1 Million for whoever solves it. A total of $ 6 Million to be won! For more than a century the solutions to these six problems have eluded mathematicians.
- P versus NP
- The Hodge conjecture
- The Riemann hypothesis
- Yang–Mills existence and mass gap
- Navier–Stokes existence and smoothness
- The Birch and Swinnerton-Dyer conjecture
Today, I’m going to talk about the first and probably the most popular problem among the six millennium prize problems.
P versus NP
The first one and one of the most vexing questions in computer science and mathematics is the P versus NP problem – polynomial versus non-deterministic polynomial. It is quite a popular one and has made appearances in TV shows like The Simpsons and Numbers and in a video game, SIMS 3.
The reason this one interests me more than the other 5 problems is because P versus NP is a problem which is the most likely, among all of them, to be solved by an amateur.
Presently it is not known if P equals NP. The problem if solved could figure which problems can or cannot be solved by a computer. Seems abstract, but if solved it could have great implications. It could dramatically affect our everyday lives.
- Although mathematicians expect it to go the other way, but if it is proved that P = NP, it would make our current definitions of security obsolete. Public-key cryptography could become impossible. We could face problems with online security if wrong people get proper resources to break public key – That means it would become possible for people to break into your bank accounts, communications, emails, encrypted data etc…
- Dealing with optimization problems would become easier. That means everything will be much more efficient. Transportation of will be scheduled optimally. Moving people and goods would become quicker and cheaper. Manufacturing units would be able to improve their production speed and make less waste etc…
- Weather, earthquakes and other natural phenomenon would get easier to predict. We might even find the perfect cancer cure.