Margaret Wertheim in the Los Angeles Times:
A baker knows when a loaf of bread is done and a builder knows when a house is finished. Yogi Berra told us “it ain’t over till it’s over,” which implies that at some point it is over. But in mathematics things aren’t so simple. Increasingly, mathematicians are confronting problems wherein it is not clear whether it will ever be over.
People are now claiming proofs for two of the most famous problems in mathematics — the Riemann Hypothesis and the Poincare Conjecture — yet it is far from easy to tell whether either claim is valid. In the first case the purported proof is so long and the mathematics so obscure no one wants to spend the time checking through its hundreds of pages for fear they may be wasting their time. In the second case, a small army of experts has spent the last two years poring over the equations and still doesn’t know whether they add up.
More here.