Feedback on Doron Zeilberger's Opinion 72 and the Author's Response

Quite a few reactions appeared in Suresh's Geomblog weblog . I will only respond to those by Jeff Erickson and David Eppstein.

Feedback by Jeff Erickson and Zeilberger's response

>By the end of the first paragraph, I guessed correctly that Zielberger is reacting to one of his own papers getting rejected.
Liar! I am sure that you only realized it towards the end, when I explicitly mentioned this fact as an example of human narrow-mindedness.

>As a sanity check, I looked at the paper, and I can see exactly why it was rejected.
And since when are you an expert on Enumerative Combinatorics? You give away your ignorance by not even spelling Zeilberger correctly. Anyone who knows modern enumerative combinatorics would know how to spell Zeilberger correctly.

>Never mind that he's "merely" implementing known enumeration techniques.
the "merely" should indeed be in quotes, Implementation is the message, this implementation has not been done before (if it did, please supply a reference or website), and besides if you read it carefully there is implicitly lots of new math there, but it is understated. If a great expert like Mireille Bousquet-Melou missed it, I don't expect you to get the subtlety.

>Never mind the snarky remarks about his program producing "infinitely many...PhD theses"
OK, it was poetic license, since I don't believe in infinity anyway, I meant "many"

>and other researchers being "extremely lucky",
This is not an insult to Kasteleyn, I am sure that he would agree too.

>No, the answer is right on the first page, where he writes " I had to spend a few
>weeks writing such a program myself." A few WEEKS?! So he
>*admits* that the paper describes trivial work! And then he has the gall to complain when his paper is rejected?
Who said that spending a few weeks on a project makes it trivial?

>In any case, his basic point is absolutely wrong. The point of mathematics is not to explain things to computers.
>(That's not even the point of computer science!) The point of mathematics (and computer science) is to
>extend the boundaries of HUMAN understanding.
It is Your basic point that is absolutely wrong! The point of mathematics and computer science is to advance our knowledge (by humans but especially by computers). At this time, we still need humans as coaches, so human understanding is a useful tool for making us humans better coaches, so that we can teach computers to acquire new knowledge, eventually much more efficiently than we can ever hope to do it ourselves.

>Computer-generated proofs are certainly a useful tool in that pursuit
It is not a tool it is the goal (that will lead us to to the ultimate goal of furthering our knowledge). I don't like the word "understanding" it is too human-centric.

>It it is patently ridiculous to assume (as Zielberger advocates)
>that they are the only such tool, even within the realm of mathematics
This proves that the first "Zielberger" was not a typo and that you don't know how to spell Zeilberger, and hence shows that you are a complete ignoramus in Enumeration and Experimental Mathematics, and hence your are definitely not qualified to put down my beautiful paper.

Feedback by David Eppstein and Zeilberger's response

>I think Z's point is that strong AI will eventually make such advances in mathematics that any human progress we might make will be rendered trivial.
"Strong AI" is only one approach, there are many ways to further our mathematical knowledge than try to emulate human intelligence.

>But what I fail to see is how programming efforts that will similarly be rendered trivial are any
>more of an advance than the human proofs he derides.
Of course eventually they won't be needed either, but we still have between fifty and a hundred years where at least some programming must be done by humans, and then it is a much more efficient use of humans' time to teach computers how to prove rather than try to prove things by ourselves.

>If he wants to advance the cause of strong AI, he should work on automated reasoning more generally,
As I said above, strong AI is only one approach that had very limited success because it tried to do too much too soon, and also slavishly tried to adapt human ways of thinking.

>not ad hoc programs for specialized combinatorial enumeration problems.
We have to start modestly, if you try to do too much too soon you won't get very far.

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