Intellectual Curiosity

The picture is of the prime number counting function. It displays the values of the function up to 100. Note, the x and y axis have different scales. One can use the Sieve of Eratosthenes to verify it's accuracy.

Many of the most interesting and difficult problems of mathematics are spawned by the desire to find a function that estimates pi(x) to within square root accuracy. You don't have to be a mathematician to understand the problem, but you have to be one of the world's most talented mathematicians if you stand a ghost of a chance of solving it.

So, if you are not a brilliant mathematician, why care? Curiosity I suppose.