Discovery or Invention

Jacques Hadamard, who lived from 1865 to 1963, was a French mathematician whose most important result was about the distribution of prime numbers - basically, the bigger the numbers, the more sparse are the primes (the number of prime numbers less than n grows as fast as n/log(n) ). However, he also wrote quite a famous piece on the way in which mathematicians' minds work in the process of uncovering mathematical results.

He says: "The distinction between (invention and discovery) is well known: discovery concerns a phenomenon, a law, a being which already existed, but had not been perceived. Columbus discovered America: it existed before him; on the contrary, Franklin invented the lightning rod: before him there had never been any lightning rod."

Hadamard says that artists' creations are generally inventions, whereas scientists work is mostly concerned with discoveries. Mathematicians are often caught between these two worlds: Hadamard's prime number result is a discovery. But is the square root of minus 1 a discovery or an invention?

Is the new knowledge you are uncovering in your thesis a discovery or an invention? Which sort of new knowledge best advances humankind?