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  • Rated by Kirro on Jul 17, 10:22pm

    I think the other commentators have said enough about the problems with this article. Here's the short of it: Should you believe set theory? Yes. Just go with the understanding that it isn't a complete theory and probably never will. In fact, all of mathematics is based on a foundation that is unprovable. But it works, so we accept certain things which we know to be true, but cannot be proven. If you need an example, 1 + 1 = 2.

  • Rated by erkaer on Feb 04 2009, 12:57pm

    At last, someone.

  • Reviewed by spoon737 on Feb 04 2009, 11:24am

    There are so many problems with this article, I'm not really sure where to start. First of all, he seems to be suggesting a more complete and logical development of mathematics in school curriculum. Guess what? We tried that already during the "New Math" era of the 1960's. Guess what else? It failed miserably. At it's outset, a rigorous and logical understanding of the foundations of math sounds great, but as he demonstrates in this article, it's far more complicated than it sounds. The problem arises in teaching students at a level that is on par with their current cognitive development. Try teaching even basic set theory to your average middle school student, you'll see what a bad idea this is. Students need to have an intuitive grasp on mathematical concepts BEFORE they can understand their more abstract definitions. The rest of his article can be summed up by saying "if it can't be given a real world representation or application, mathematicians shouldn't bother with it." Well, guess what the mathematical community thought of Riemann's famous lecture on geometry in higher dimensions? They thought it was far too abstract to be of any real use. Then, a few decades later, Einstein comes along and uses this theory as a framework for his own theory of general relativity. Woops, guess it wasn't so useless after all! If mathematicians limited themselves to only working with concepts that had obvious real world uses, we would be centuries behind in our understanding of math. The job of the mathematician is to gain a greater understanding of the extents of a particular theory, the applications come later. Then, toward the very end, he challenges us to find one real world example where infinite sets are useful. Given that this guy is a career mathematician, I assume he isn't stupid enough to reject the usefulness of calculus. And yet, calculus hinges on the existence of infinite sets. Riemann integration is only possible because you can infinitely partition an interval. Otherwise, you're just estimating, and would good is that if you can be precise?

  • Rated by polveroj on Aug 16 2006, 4:40am

    An illogical rant by someone who can't understand mathematics and thinks nobody else (especially not mathematicians) do either. The author seems to think that abandoning a logical foundation to mathematics would be a good idea and that mathematicians should abandon all theoretical work that does not directly correspond to countable numbers of atoms in the real world. He repeatedly fails to see uses for and denounces as nonsensical areas of mathematics vital to computer science. I'd love to ask what he thinks about Chaitin's Constant: an irrational, non-computable number that provably (even to him, I think) contains an infinite amount of information.

  • Rated by Monkey-Pilot on Aug 10 2006, 5:02pm

    I stopped reading when he said that numbers too big to represent in this universe should not be representable in maths, unfortunately that was right at the end.

  • Rated by Codebender on Aug 07 2006, 10:38am

    "Let me remind you that mathematical theories are not in the habit of collapsing. We do not routinely say, 'Did you hear that Pseudo-convex cohomology theory collapsed last week? What a shame! Such nice people too.'"

  • Rated by DRMacIver on Aug 07 2006, 8:36am

    An incoherent rant about foundations by someone who has very little understanding of the mathematical or philosophical underpinnings of such. Yes, mathematics can be confusing. Yes, logicians and set theorists sometimes place too much emphasis on their platonism. Yes, infinite sets can be counterinutive. Is this a problem? Possibly. There are good arguments in favour of finitism. None of which are present in this rant. In attempting to convince us that these subjects don't make sense, all he actually proves is that he does not understand them. Update: I've just realised that this was written by the idiot who did "rational trigonometry". If I'd realised that before I wrote the above then I wouldn't have bothered, considering it to be self evident.