Uncommon Descent Serving The Intelligent Design Community

God’s perfect proofs? Are there such things?

arroba Email

From Erica Klarreich at Quanta:

In January, Ziegler traveled to San Diego for the Joint Mathematics Meetings, where he received (on his and Aigner’s behalf) the 2018 Steele Prize for Mathematical Exposition. “The density of elegant ideas per page [in the book] is extraordinarily high,” the prize citation reads.

The 2014 book is Proofs from the Book (that is, a book of God’s alleged proofs, the most beautiful ones). Here’s the interview with Günter Ziegler (his co-author of Martin Aigner) at Quanta, with a sort of assist from Paul Erdős (1913-1996)

Quanta: You’ve said that you and Martin Aigner have a similar sense of which proofs are worthy of inclusion in THE BOOK. What goes into your aesthetic?

Ziegler: We’ve always shied away from trying to define what is a perfect proof. And I think that’s not only shyness, but actually, there is no definition and no uniform criterion. Of course, there are all these components of a beautiful proof. It can’t be too long; it has to be clear; there has to be a special idea; it might connect things that usually one wouldn’t think of as having any connection.

For some theorems, there are different perfect proofs for different types of readers. I mean, what is a proof? A proof, in the end, is something that convinces the reader of things being true. And whether the proof is understandable and beautiful depends not only on the proof but also on the reader: What do you know? What do you like? What do you find obvious?More.

This all seems so modern instead of post-modern (po-mo). The assumption is that there is a rational series of steps in thought that should convince any reasonable person but to the po-mo, that is just imperialism.

Has the time for books like this passed? Will it decline to a much smaller share of the previous academic market?

See also: New Scientist coins a new term: Uglyverse Of course, a universe in which we have not found a multiverse must be ugly to New Scientist readers. For others, beauty remains a possibility, best explained by apparent fine-tuning of our universe, which has always been the real problem for them.

"Erdos referred to God as the Supreme Fascist." Apparently the ironclad Godwin's law did not make it into Erdos's initial proofs.
Godwin's Law http://i0.kym-cdn.com/photos/images/newsfeed/000/923/260/c00.png
:) Note: Perhaps the authors need to think a bit more deeply about the exact nature of the field (mathematics) that they claim to be experts in?
An Interview with David Berlinski - Jonathan Witt Berlinski: There is no argument against religion that is not also an argument against mathematics. Mathematicians are capable of grasping a world of objects that lies beyond space and time…. Interviewer:… Come again(?) … Berlinski: No need to come again: I got to where I was going the first time. The number four, after all, did not come into existence at a particular time, and it is not going to go out of existence at another time. It is neither here nor there. Nonetheless we are in some sense able to grasp the number by a faculty of our minds. Mathematical intuition is utterly mysterious. So for that matter is the fact that mathematical objects such as a Lie Group or a differentiable manifold have the power to interact with elementary particles or accelerating forces. But these are precisely the claims that theologians have always made as well – that human beings are capable by an exercise of their devotional abilities to come to some understanding of the deity; and the deity, although beyond space and time, is capable of interacting with material objects. http://tofspot.blogspot.com/2013/10/found-upon-web-and-reprinted-here.html "Nothing in evolution can account for the soul of man. The difference between man and the other animals is unbridgeable. Mathematics is alone sufficient to prove in man the possession of a faculty unexistent in other creatures. Then you have music and the artistic faculty. No, the soul was a separate creation." Alfred Russell Wallace, New Thoughts on Evolution, 1910 "Why should a limited and finite organ such as the human brain have the power to see into the heart of matter or mathematics? These are subjects that have nothing to do with the Darwinian business of scrabbling up the greasy pole of life. It is as if the liver, in addition to producing bile, were to demonstrate a unexpected ability to play the violin. This is a question that Darwinian biology has not yet answered." - David Berlinski - The Devil's Deusion - page 16
The idea of The Book came from Paul Erdos, and I think is something of a mathematical meme. Erdos referred to God as the Supreme Fascist. He had an odd sense of humour. Bob O'H

Leave a Reply