If one more person asks me why my work on the divisor function is applicable, I am going to scream! I’ve been mentioning Robin’s Theorem (proving a bound on the divisor function is equivalent to proving the Riemann Hypothesis) as an example of what can be done with this, but that is not why I did this research.

If Dali had to justify his paintings to the powerful, we would not have “The Persistence of Memory”. If Beethoven had to justify his works to the elite, we would not have the Moonlight Sonata. The simple act of expression is a reflection of the beauty in the soul.

It is the same with mathematics. I don’t know how significant my result is (though I am sure that it is at least novel and suspect that it has a moderate degree of significance… probably not enough to prove the Riemann Hypothesis), and probably never will due to society’s refusal to accommodate my wish to pursue multidisciplinary training, but I don’t care, because I’ve effectively reduced the amortized time complexity of calculating the divisor function for sequentially-increasing values to O(n) (calculating it the old-fashioned way, by multiplying over the primes, is polynomial) in a most elegant way.

That suffices for me. If it doesn’t suffice for you, I’d say you are, mathematically, at a handicap against those with an innate sense of mathematical beauty. At the very least, you’ll lack the passion that we have.

Oh, and this doesn’t only apply to math. If you only concentrate on application, a whole world of beauty is closed to you.