What is the greatest achievement of our civilization? In my opinion, it is undoubtedly the linguistic ability that we have developed over the years. Here I take linguistics in its broadest sense, and consider mathematical derivations and set theory as part of it.

 

A spectacular example of clever use of symbols is provided by the four equations of Maxwell. Looking at his equations, without stirring out of his room, he said there should be electromagnetic radiation, and sure enough there was. Science is replete with similar examples like the prediction of bending of light rays and the existence of elementary particles.

 

It is as though Nature dances faithfully to the musical composition we write on paper, so long as the composition conform strictly to mathematical logic. Some scientists are so impressed by this fact that they consider the Big Bang and the Big Crunch as nothing but the cosmic dance of The Creator.

 

What we are talking about here is what is generally understood as physics, mathematics and metamathematics. I consider these as the rational study of visible, visualizable, and ultimate Reality, respectively.

 

The most interesting problem I know in metamathematics is called Continuum Hypothesis, an issue which has occupied the minds of logicians for more than a century. Loosely speaking, continuum hypothesis is an educated guess about the continuity and extent of the physical space around us. The most challenging unsolved problem I know in mathematics is called Riemann Hypothesis, which states that an elegantly defined analytic function called Riemann Zeta Function has all its complex zeroes on a vertical line in the complex plane.

 

Both these hypotheses we will discuss in this site with the hope that any well-motivated novice would be able to recognize the serious issues involved here and contribute towards the resolution of the problems. We will touch upon some other mathematical problems also, including the ones which have assumed importance because of the Internet.