Doron Zeilberger

Yeah, but this is so boring and oh-so-run-of-the-mill. (If the mafiosi could read the following paper before rushing to click down-vote, then I'd be much obliged. http://www.math.rutgers.edu/~zeilberg/mamarimY/DM85.pdf)

This reminds me of http://www.math.rutgers.edu/~zeilberg/Opinion71.html, where a number of prominent mathematicians and computer scientists are traced to an Israeli mathematical magazine for young people. These are certainly not kids who had no calculation skills. They wrestled with difficult problems and developed great problem-solving skills that have served them in their careers. Incidentally, Zeilberger is definitely an advocate of more computer use in math, but not in the same way. See almost any of his Opinions: http://www.math.rutgers.edu/~zeilberg/OPINIONS.html

Thankyou for writing this. As a humble seer trying to find his way in this world of bean-counters, I really appreciate it. Doron Zeilberger has written about this aswell: """ The usual names are "theory-builders" vs. "problem-solvers", but these two protoypes of mathematicians also appear under various other appellations. Some other names are strategists vs. tacticians, "monkeys that climb up the tree" vs. "monkeys that climb down", globalists vs. localists, and folowing א ח ד ה ע ם, I once called them prophets vs. priests. """ [1] > something to help fund the Seers, à la startup incubator The problem with this is that the Seers tend to sound like crazy people (and alot of them probably are just nuts). Especially to a craftperson, they really struggle to follow the seer. John Baez is a good example of someone who can balance the Seer with the craft, but i've noticed he will team up with someone who is more seer than he is to get those really good ideas. [1] http://www.math.rutgers.edu/~zeilberg/Opinion95.html

Don’t forget Alan Smithee, a pseudonym used when a director wants to disclaim credit for a film: https://en.wikipedia.org/wiki/Alan_Smithee Doron Zeilberger, a mathematician, coauthors papers with his computer, which he refers to by the name Shalosh Ekhad: http://www.math.rutgers.edu/~zeilberg/ekhad.html https://en.wikipedia.org/wiki/Doron_Zeilberger

I would pay to see Motl and Doron Zeilberger in a cage match about discrete math: http://www.math.rutgers.edu/~zeilberg/

If you're still having trouble accessing it, here are direct links to the mirrors: http://www.math.upenn.edu/~wilf/AeqB.pdf http://www.math.rutgers.edu/~zeilberg/AeqB.pdf http://www.fmf.uni-lj.si/aeqb/AeqB.pdf The license agreement is (copied and pasted from the download page): Copyright 1996 by A K Peters, Ltd. Reproduction of the downloaded version is permitted for any valid educational purpose of an institution of learning, in which case only the reasonable costs of reproduction may be charged. Reproduction for profit or for any commercial purposes is strictly prohibited.

It reminded me of what Dr. Doron Zeilberger has been repeating ad-nauseam ( eg: http://www.math.rutgers.edu/~zeilberg/Opinion36.html ) Ultimately automated theorem provers are going to rule. Dr.Z actually takes the very radical stand of calling all paper-pencil math proofs of Paul Erdos trivial, whereas "Theorems that only computers can prove...are not quite as trivial". The fact that we have to reach out to a computer to assist in solving min-sudoko is unfortunate but at the same time, inevitable. Dr. Z mentions Four Color Theorem, Kepler's Conjecture, and Conway's Lost Cosmological Theorem as other theorems only computers can solve.

This is an interesting "book" that reduces geometry to automated symbol pushing. http://www.math.rutgers.edu/~zeilberg/GT.html

The actual report and reply is here: http://www.math.rutgers.edu/~zeilberg/RefTipesh.html

His "opinions" page, http://www.math.rutgers.edu/~zeilberg/OPINIONS.html , is full of interesting reading.

His "Opinion 37: Guess What? Programming is Even More Fun Than Proving, and, More Importantly It Gives As Much, If Not More, Insight and Understanding" is also very interesting: http://www.math.rutgers.edu/~zeilberg/Opinion37.html Fun fact: Doron is known for crediting his computer "Shalosh B. Ekhad" as a co-author.

I found the responses linked in the article interesting as well: http://www.math.rutgers.edu/~zeilberg/fb36.html

The fabled mathematician Shalosh B. Ekhad may have something to say about that. http://www.math.rutgers.edu/~zeilberg/pj.html

As another scientist I have to strongly second this. Some things might take real work on your part to understand though. Even within different fields of mathematics there are difficulties in understanding (complaint about this: http://www.math.rutgers.edu/~zeilberg/Opinion104.html).

Yes, he is quite the character and a legitimate mathmetician^. I also looked into him and questioned his validity after first reading his opinions. 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/real.pdf

this one is particularly true: http://www.math.rutgers.edu/~zeilberg/Opinion78.html

Quick note: many of you are saying that this guy is totally out of touch with how math works, and that formal derivation of proofs is just fantasy. It's true that that's an extreme view, but it is in fact one that is held by some top mathematicians, even if a small minority. There are people who have built up research programs out of trying to make it a reality. See, for instance, Doron Zeilberger, who apparently describes himself as an "ultrafinitist": http://en.wikipedia.org/wiki/Doron_Zeilberger http://www.math.rutgers.edu/~zeilberg/OPINIONS.html I'm not saying I agree with that, just that it's not lunacy. Carry on.

Correction, tons of physicists use real values (or complex real values) in their calculations. That doesn't imply that the corresponding values in the world are irrational, transcendental, infinitely-precise, etc. There are a few ways we can avoid the reals in physics. Abstractly, there are results such as Skolem's "paradox" ( https://en.wikipedia.org/wiki/Skolem%27s_paradox ) which tell us that theories involving uncountable sets (such as the reals) can be satisfied by countable models. More concretely, physicists never manipulate real numbers directly; only symbols which may represent real numbers. Such symbolic manipulation could, in principle, be performed by a turing machine, and hence any value obtained from such theories (e.g. experimental predictions) must be in the set of computable numbers. Hence the reals are just an 'implementation detail' of any theory, and their purported presence cannot have any influence on the theory's predictions. As I said previously, I have nothing against the reals as a useful mathematical tool; I just disagree with the name, and claims that they are physically real. Others go further though, arguing that discrete mathematics is more general and useful than continuous, e.g. http://www.math.rutgers.edu/~zeilberg/OPINIONS.html

SAT is the boolean satisfiability problem, a simple NP-complete problem often used to prove the other problems are NP-complete. An instance of SAT is a boolean formula, and the answer to it is yes if and only if the formula can be true for some assignment of variables. 3SAT is the same problem, only with the formula in a conjunctive normal form and each clause having exactly three variables. Also, it seems the poster is really just trying to get attention. Complexity theorists do know all that and have spent a lot of time trying to see which postulated consequences of P?=NP are necessary and which are not. (If I were to argue it is an ill-posed question, I'd go more in the direction of CO-NP (which is the set of problems for which "NO" answers have short certificates), and why this really strong emphasys on "yes" certificates for NP problems) Doron Zeilberger's take on that ( http://www.math.rutgers.edu/~zeilberg/Opinion98.html ) is a lot more interesting. And, also, the "easy" equals "polynomial time" is (a) a good heuristic, if you assume computational power increases exponentially (hence, a problem will be solvable in the foreseeable future if all it needs is polynomially more processing power for larger instances); (b) it is an easy to study class, since it is composable; (c) not the only thing complexity theorists argue about (ie, P=NP means practical bounds for some problems and collapses a lot of classes that are not trivially seen to be equal, like AM and MA)

For anyone who might be misled, here are some links that people can use to judge for themselves how "crank" someone is: Professor Norman Wildberger's homepage: http://web.maths.unsw.edu.au/~norman/ ...a paper by Wildberger tackling some of the issues in this thread: Set Theory: Should You Believe? http://web.maths.unsw.edu.au/~norman/papers/SetTheory.pdf Some interesting works by Gregory Chaitin Meta Math! The Quest for Omega https://arxiv.org/abs/math/0404335 Exploring Randomness https://www.cs.auckland.ac.nz/~chaitin/ait/ How Real are Real Numbers? https://arxiv.org/abs/math/0411418 People who are interested in ultrafinitism would also want to check out Doron Zeilberger http://www.math.rutgers.edu/~zeilberg/ and Edward Nelson https://web.math.princeton.edu/~nelson/

Grothendieck "died" in the sense meant by Paul Erdos (stopped doing new mathematical research) at a surprisingly young age, while Israel Gelfand kept going into his nineties, not "dying" (ceasing to be a mathematician) until he "left" (died in the usual sense of the term). http://www.math.rutgers.edu/~zeilberg/Opinion62.html Gelfand was a mathematician who also cared deeply about mathematics pedagogy, and his textbooks are delightful. http://www.amazon.com/Algebra-Israel-M-Gelfand/dp/0817636773 http://www.amazon.com/Functions-Graphs-Dover-Books-Mathematics/dp/0486… http://www.amazon.com/Method-Coordinates-I-M-Gelfand/dp/0817635335/ http://www.amazon.com/Trigonometry-I-M-Gelfand/dp/0817639144/ Gelfand poses delightful problems that give students a workout in arithmetic (and CAN'T be done with a calculator) and that build conceptual understanding and interest in higher mathematics.