Computers have always been envisioned as levers for the mind. The fact that mathematicians of all people aren't taking full advantage of that principle utterly boggles my mind too.
> Let us call a set "abnormal" if it is a member of itself, and "normal" otherwise.
> Now we consider the set of all normal sets, R. Determining whether R is normal or abnormal is impossible: If R were a normal set, it would be contained in the set of normal sets (itself), and therefore be abnormal; and if R were abnormal, it would not be contained in the set of all normal sets (itself), and therefore be normal. This leads to the conclusion that R is neither normal nor abnormal: Russell's paradox.
Russel's paradox "broke" set theory. In the century since he discovered it, category theory was introduced as a mathematical way to capture groupings in a way that set theory failed to do.
I don't see how computers can assist in this kind of mathematical research. I do believe there's lots of research of this kind too, pushing the limits of our current mathematical structures.
How long can you mock your older brother in front of your hip young friends before he decides to ignore you and go play with his own friends somewhere else?
I thought the consensus was that it really depends on the type of problems one is trying to solve, and that most programmers can in fact get away with knowing little math.
Levers. No one said the pulley (or CAD) rendered the architect defunct, and no one is saying computers should do the same for mathematicians. We're just trying to understand this resistance to using tools to help do heavy lifting, the “human-centric bigotry” as the article puts it. Reading some of the responses here, it's probably being overstated, but even so.
And ignore you and go play somewhere else? A good number of the most influential computer scientists have actually been psychologists, not mathematicians, so the older brother needs to get the fuck over himself if that's his attitude!
I'd like to hear who you consider influential computer scientists coming from psychology. The ones I hold dear are mostly settlers from math.
If the younger brother were as wise as he thinks he is, he wouldn't need to get so worked up as to substitute profanity for an articulate argument.
Edit: As for psychologists, you're seriously telling me you never heard of Licklider? That's... astounding.
Consider programming. You don't need anything more than punch-cards to program. You don't need anything more than assembler. But higher-level languages can be useful, because they can make the task easier, give you greater leverage.