The Mathematical Opinions of Dr. Doron Zeilberger(math.rutgers.edu)
math.rutgers.edu
The Mathematical Opinions of Dr. Doron Zeilberger
http://www.math.rutgers.edu/~zeilberg/OPINIONS.html
2 comments
As I'm not versed in math, I wonder, are his opinions valid?
I am versed in mathematics, and I am finding these opinions, as they are no doubt intended to be, bloody infuriating. There are truths, no doubt, but I think these are doing far more harm than good.
I'd like to see a computer proof of the emergence of the giant component in a random graph process. I'd like to see a computer proof that the TSP is equivalent to 3-coloring a graph. I'd like to see a computer proof of the Banach-Tarski paradox.
No doubt many experiments would be shown and then the conclusions drawn without actual proof. There is a place for experiment to create and guide intuition, and a place for computer assistance in complex manipulations, but to pretend that mathematicians are "clinging to pencil and paper" instead of simply learning to use computers is laughable.
If only he weren't so eloquent and persuasive I'd be less angry.
It is also true that many things are currently done badly by people who could do better if they were trained in skills they currently lack. There is an application of sharpening the saw, but his implications of incompetence are unfounded and distasteful.
I'd like to see a computer proof of the emergence of the giant component in a random graph process. I'd like to see a computer proof that the TSP is equivalent to 3-coloring a graph. I'd like to see a computer proof of the Banach-Tarski paradox.
No doubt many experiments would be shown and then the conclusions drawn without actual proof. There is a place for experiment to create and guide intuition, and a place for computer assistance in complex manipulations, but to pretend that mathematicians are "clinging to pencil and paper" instead of simply learning to use computers is laughable.
If only he weren't so eloquent and persuasive I'd be less angry.
It is also true that many things are currently done badly by people who could do better if they were trained in skills they currently lack. There is an application of sharpening the saw, but his implications of incompetence are unfounded and distasteful.
I'd like to see a computer proof of the emergence of the giant component in a random graph process.
Maybe this will help: http://arxiv.org/abs/0808.1549
Maybe this will help: http://arxiv.org/abs/0808.1549
OK, I've spent literally two minutes as I'm in the middle of something urgent, and I'll come back to it later, but my impression is that while the result is interesting, and the authors may have used computer experiments to gain intuition about what was happening, it's not a computer proof. It's a tradtional proof of something that's relevant to computers.
If I'm wrong please provide a better summary so I can read it with your insights to guide me.
If I'm wrong please provide a better summary so I can read it with your insights to guide me.
I would like to see a human proof of the Four Color Theorem ;-)
Computers are better than humans at many tasks. Zeilberger has a lot of valid points, IMHO. However, he could be less opinionated and more tactful. Creating flame wars just for kicks is definitely not the best / wisest way of presenting one's point of view.
Computers are better than humans at many tasks. Zeilberger has a lot of valid points, IMHO. However, he could be less opinionated and more tactful. Creating flame wars just for kicks is definitely not the best / wisest way of presenting one's point of view.
The current best proof of the 4CT is a human proof, it's just that there are a lot of cases to check. It's largely just the same as the 5CT, but with more examples to run through. Using the computer is faster and avoids errors of tiredness and boredom. However, in contrast to the way it's always presented, the basic proof is simple and generated by humans in a way that computers can't yet do.
It's like using advanced techniques to prove that all even numbers from 10^100 onwards are the sum of two primes, then using computers to check everything up to 10^100, and thus claiming a proof of the Goldbach conjecture. The difficult bit was creating the proof. The easy bit was getting the computer to check that the cases worked.
It's not a proof by computer, despite what you've heard.
It's like using advanced techniques to prove that all even numbers from 10^100 onwards are the sum of two primes, then using computers to check everything up to 10^100, and thus claiming a proof of the Goldbach conjecture. The difficult bit was creating the proof. The easy bit was getting the computer to check that the cases worked.
It's not a proof by computer, despite what you've heard.
this one is particularly true: http://www.math.rutgers.edu/~zeilberg/Opinion78.html
I read a paper by him on ultrafinitism^^ a few years ago and was intrigued and entertained.
^ http://en.wikipedia.org/wiki/Doron_Zeilberger
^^ http://www.math.rutgers.edu/~zeilberg/mamarim/mamarimPDF/rea...