The mathematician's lament

Page 2 of 2 -- IDEAS: They were great friends, but it seems an odd pairing. There is Einstein, the icon, and Gödel, the virtual unknown. What drew them together?

ADVERTISEMENT

GOLDSTEIN: On a psychological level, this was a friendship that baffled people.... But for me, it doesn't seem so mysterious. Both men were very much at odds with the intellectual climate, even of their peers. Both men saw their work in this light of objectivity.

IDEAS: How has Gödel's theorem been misinterpreted over the years?

GOLDSTEIN: It's taken to show that math has no foundations, that math is uncertain. So just as relativity was misinterpreted - as meaning everything is just relative to points of view, that we create the truth, that it's all at heart human - [Gödel's theorems] were interpreted that way as well.

I just feel such sympathy [for Gödel]. He was somebody who hated to argue face-to-face, and he was in a [discussion] group, the Vienna Circle, which was completely at odds with everything he thought and he just sat there and he listened and meanwhile he's brewing this theorem that was going to just devastate their point of view, but he never says anything. He just stays mum. He wanted his math to do all his talking for him. And then he produced this theorem that did what he wanted - miraculously, amazingly - and everyone misinterpreted it.

IDEAS: How did his math shape his life?

GOLDSTEIN: [Gödel showed that] one of the things you can't prove is that the world you're working with is consistent - that it won't lead to a contradiction. And this is interesting because it has a very sad, poignant parallel with the man himself. Gödel did suffer from mental illness. He did have these paranoid delusions. He believed that he had enemies, that there were plots out for him, that truth would be suppressed. He really thought there was something malicious going on. The parallel I'm trying to draw is if your whole thought system is infected by persecution, how do you get outside the system to show that the system isn't leading you to untruths or, even worse, to self-destructive madness? He eventually ... starved himself to death because he thought he was being poisoned. It's an extraordinarily stunning though tragic parallel with his second Incompleteness theorem.... When you're mad, you can't get out of your system.

IDEAS: What does Gödel's theorem mean for the person on the street?

GOLDSTEIN: I think all of us want to know what kind of a world we live in, we want to know what is the ontological furniture - what exists, what's the furniture of the world? There's the existence of God, this sort of abstract entity - do objective moral values exist? And does math also present us with something other than things we can reach out and touch? Is math itself somehow descriptive of a reality other than what we can see and feel? I think the man on the street worries about what exists. God, moral values, and what else?

Carolyn Y. Johnson is a Globe staff writer. Email cjohnson@globe.com.