Doron Zeilberger on experimental math

[gusl]

I love Zeilberger's style. From What Is Experimental Mathematics?:

Let me try and explain to you, by example, what is experimental math. It is really an attitude
and way of thinking, or rather not thinking. Mathematicians traditionally love to solve problems
by thinking. Myself, I hate to think. I love to meta-think, try to do things, whenever possible,
by brute force, and of course, let the computer do the hard work.

...

Zeilberger-style Experimental Mathematics

Traditionally there was a dichotomy between the context of discovery, that nowadays is mostly
done by computers, and the context of verification that is still mostly carried out by humans.
In my style of experimental math, the computer does everything, the guessing and the (rigorous!)
proving, if possible completely seamlessly without any human intervention. Feel free to browse my
website for many examples.

Comments

[gaspaheangea.livejournal.com]

Have you read A=B? Or at least glanced through it? Also, there are two books by the Borwein brothers about experimental mathematics that I want.

[easwaran.livejournal.com]

That's a very odd way for him to put things - I would have thought the context of discovery is where computers are still quite bad. They're useful at coming up with lots of interesting little facts, but not very good at formulating the conjectures and picking out the useful theorems.

[gustavolacerda.livejournal.com]

He's right that most verification is still carried out by humans. This is because most proofs today are written informally. However, saying that discovery is mostly done by computers is probably not true of mathematics today.

I like people with a radical rhetorical style because they are good at breaking unquestioned common wisdom (or at least, transforming it into questioned common wisdom).

Zeilberger is attacking stereotypes like: "computers are only good at doing routine calculations", "computers can't be creative", etc. which are only true of computers lacking the representations necessary for the broader reasoning used in discovery tasks. It's not the computer that's failing to be creative: it's the users who are failing to program it creatively.