But then Andrew Wiles was able to solve it in 1994. The continuum hypothesis is a problem of a very different kind; we actually can prove that it is impossible to solve it using current methods, which is not a completely unknown phenomenon in mathematics.

Who proved the continuum hypothesis?

The continuum hypothesis was advanced by Georg Cantor in 1878, and establishing its truth or falsehood is the first of Hilbert's 23 problems presented in 1900.

Is the continuum real?

The continuum hypothesis (under one formulation) is simply the statement that there is no such set of real numbers. It was through his attempt to prove this hypothesis that led Cantor do develop set theory into a sophisticated branch of mathematics.