Dissecting The Riemann Zeta Function

1 mainThe Riemann Zeta function is an extremely important function in mathematics and physics. It is intimately related to very deep results surrounding the prime numbers. Now why would we want to care about prime numbers? Well, the entire concept of web security is built around prime numbers. Most of the algorithms for banking security, cryptography, networking, communication, etc are constructed using these prime numbers and the related theorems. The reason we do this is because of the inherently sporadic nature of prime numbers. You never know where the next one is going to appear on the number line! So what does that have to do with the Reimann zeta function? If prime numbers are random, what’s the point of looking into them?   Continue reading

What Do You Know About Infinity?

infinityWhat do you think of the term “infinity”? In layman’s terms, infinity is something that has no end, something that is bigger than all the things we know. This is what most people think! Many people who have not seen advanced mathematics do not know about the fact that there are many different types of infinity, some of which are bigger than others. Now how is that possible? Isn’t there just one single infinity which quantifies the essence of uncountability?   Continue reading

P vs NP: The Epic Saga

P vs NPP vs NP problem is one of the great unsolved problems in theoretical computer science. This problem has become broadly recognized in the mathematical community as a mathematical question because it is fundamental, important and beautiful. It is in fact one of the seven Millennium Prize Problems. If you solve this problem, you get $1 million and become really famous among mathematicians and computer scientists. If you are evil, then you can use your proof to become richer than God, then publish your proof, reject the prize money and become extremely well respected in the mathematics community! Wait a minute, really? How can I use this to become rich? Before we answer that, let’s see what exactly is the difficulty in solving the problem. Shall we?   Continue reading

Reimann Hypothesis And Its Connection To Cryptography

Over the centuries, mathematicians have been involved in solving some of most complex problems. But what is the motivation behind that? The pursuit of truth! But The Clay Mathematics Institute thought that there should be a little more than that. So to celebrate mathematics in the new millennium, they established seven Millennium Prize Problems. The prize money for each problem is one million dollars. That’s pretty exciting! These were some of the most difficult problems over which many mathematicians were racking their brains. Reimann Hypothesis is one of them. The interesting thing about this particular problem is that it has far reaching consequences in the field of modern cryptography and internet security. Now how can an obscure and complex mathematical problem affect cryptography and internet security?   Continue reading