Hah, now that's quite nice that I can finally write 'bout something I really understand.
To singuarities then. Einstein, as we all know, authored the General Theory of Relativity, and sixty years later Hawking & Penrose showed that if Einstein's theory is true, than the universe must have begun once by explosion from a singularity. Meaning the big bang.
Einstein's theory is a milestone and considered the most true of all true ones
, therefore it is a really hard nut to crack for people that were opposing the idea of singularities; as Hawking gave straight mathematical proof of his theory, leaving no backdoor for mistakes.
What singularities are? They are (theoretically) points in the universe, where the gravity is equal to infinity, and as such, all the laws of physics are useless there. As well as mathematical description, as mathematicians tend to avoid infty's where they see one:)
There is a popular theory stating that a singularity is placed in the center of each of them black holes, if You remember such things (those are collapsed stars).
A given star, if it is heavier than certain number (about 1.5 Sun's mass) is unable to equalize its own gravitation with thermonuclear energy radiated from its center. And so it collapses.
But after all I thing Golem is full of sh**, because it doesn't prove the uselessnes of phisics if one finds a singularity here or there. What's the big deal?