Reflections
She made the top-ten list, but who is she?
If you were to pick the ten greatest mathematician, alive or dead, who would you pick? How many would be alive? How many would be women?
Think about it and then have a look at Alex Bellos’ selection here.
Update:
A BBC documentary on Georg Cantor, Ludwig Boltzmann, Kurt Gödel and Alan Turing.
May 23rd, 2010 at 2:50 am
One of my favorites in that list is Cantor. To save you a click, here’s the excerpt about him:
“Of all the great mathematicians, Cantor most perfectly fulfils the (Hollywood) stereotype that a genius for maths and mental illness are somehow inextricable. Cantor’s most brilliant insight was to develop a way to talk about mathematical infinity. His set theory lead to the counter-intuitive discovery that some infinities were larger than others. The result was mind-blowing. Unfortunately he suffered mental breakdowns and was frequently hospitalised. He also became fixated on proving that the works of Shakespeare were in fact written by Francis Bacon.”
While I admit it is counterintuitive that some infinities are larger than others, the fact that some get completely bent out of shape over it is astounding. {1, 2, 3, 4, 5, …, ∞) is clearly smaller than {2, 4, 6, 8, 10, …, ∞).
May 23rd, 2010 at 12:16 pm
Mike, you’re not claiming that the first infinity is half the size of the second one, are you? Or is it the other way around?
May 23rd, 2010 at 2:04 pm
Cantor said that if there is a 1-1 correspondence between two sets then they have the same cardinality, or size if you like. From there follows that some proper subsets are as big as the original set, like the set of even numbers and the set of natural numbers.
I don’t have a problem with that. A definition is made and one has to pay the consequences.
What I would like to know is if other definitions of cardinality has been proposed and if not, why not.