Previous post: What is combinatorics and what this blog is about according to Igor Pak.
There is a new thread of comments to the post "What is mathematics?" started by Sandro Magi. The post is dated April 3; this thread started on May 31. The thread is concerned with only one claim in that post: proofs are not needed at all for applications of mathematics.
Unfortunately, the very first phrase of Sandro Magi set the tone for the rest of the discussion: "This is blatantly false". I do not like to discuss things in such a manner: with a total lack of cooperation. The combinatorialists at Gowers's blog are much more friendly even after a direct attack on their field. But, I believe that the reason is not any kind of malice of either party. This dialog is a good illustration of the near impossiblity of people thinking linearly and verbally to understand people thinking visually. In this case the dialog of a mathematician (every mathematician thinks at least partially visually) and a software engineer turned out to be impossible. I encountered the same sort of difficulties while discussing essentially any other subject, from the movies to the current affairs. I see also this lack of understanding of visual and "the big picture" issues in the design and functionality of almost all the software.
Still, it seems to me that there are some important ideas in that discussion. Of course, it would be better to give a coherent exposition. But an attempt to write it would take a lot of time, and who knows when it would be ready.
If somebody wants to comment on any issue there, I suggest to post comments here; this will result in a more clear structure of comments. As an additional benefit for the next 30 days the comments here are not moderated; they are moderated at that post. This rule is subject to change without notice. :-) I would like to ask Sandro Magi to continue our discussion in comments to "What is mathematics?" and not here (of course, he is under not obligation to continue); then the whole discussion will be at the same place.
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Tuesday, June 11, 2013
Saturday, June 1, 2013
What is combinatorics and what this blog is about according to Igor Pak
Previous post: About Timothy Gowers.
I came across the post “What is Combinatorics?” by Igor Pak. His intention seems to be refuting what is, in his opinion, a basic fault of my notes, namely, the lack of understanding of what is combinatorics.
Unfortunately, he did not show me anything. I come across his post while searching other things by Google. May be he is afraid that giving me a link in a comment will engage him in conversation? I would be glad to discuss these issues with him, but if he is not inclined, how can I insist? My intention was to write a comment in his blog, but for this one needs to be registered at WordPress.com. Google is more generous, as is T. Gowers, who allows non-WordPress comments in his blog.
Indeed, I don't know much about “traditional sensitivities” of combinatorics. A Google search resulted in links to his post and to numerous papers about “noise sensitivity”.
Beyond this, he is fighting windmills. I agree with most of what he wrote. Gian-Carlo Rota is my hero also. But I devoted a lot of time and space to explaining what I mean by "combinatorial" mathematics, and even stated that I use this term only because it is used by Gowers (and all my writings on this topics have a root in his ones), and I wasn't able to find quickly a good replacement (any suggestions?). See, for example, the beginning of the post “The conceptual mathematics vs. the classical (combinatorial) one” , as also other posts and my comments in Gowers's blog. In particular, I said that there is no real division between Gowers's “second culture” and “first culture”, and therefore there is no real division between combbinatorics and non-combinatorics.
So, for this blog the working definition of combinatorics is “branches of mathematics described in two essays by T. Gowers as belonging to the second culture and opposed in spirit to the Grothendieck's mathematics”.
I don't like much boxing of all theorems or papers into various classes, be they invented by AMS, NSF, or other “authorities”. I cannot say what is my branch of mathematics. Administrators usually assign to me the field my Ph.D. thesis belongs to, but I did not worked in it since then. I believe that the usual division of mathematics into Analysis, Algebra, Combinatorics, Geometry, etc. is hopelessly outdated.
Next post: New comments to the post "What is mathematics?"
I came across the post “What is Combinatorics?” by Igor Pak. His intention seems to be refuting what is, in his opinion, a basic fault of my notes, namely, the lack of understanding of what is combinatorics.
“While myself uninterested in engaging in conversation, I figured that there got to be some old “war-time” replies which I can show to the Owl blogger. As I see it, only the lack of knowledge can explain these nearsighted generalizations the blogger is showing. And in the age of Google Scholar, there really is no excuse for not knowing the history of the subject, and its traditional sensitivities.”
Unfortunately, he did not show me anything. I come across his post while searching other things by Google. May be he is afraid that giving me a link in a comment will engage him in conversation? I would be glad to discuss these issues with him, but if he is not inclined, how can I insist? My intention was to write a comment in his blog, but for this one needs to be registered at WordPress.com. Google is more generous, as is T. Gowers, who allows non-WordPress comments in his blog.
Indeed, I don't know much about “traditional sensitivities” of combinatorics. A Google search resulted in links to his post and to numerous papers about “noise sensitivity”.
Beyond this, he is fighting windmills. I agree with most of what he wrote. Gian-Carlo Rota is my hero also. But I devoted a lot of time and space to explaining what I mean by "combinatorial" mathematics, and even stated that I use this term only because it is used by Gowers (and all my writings on this topics have a root in his ones), and I wasn't able to find quickly a good replacement (any suggestions?). See, for example, the beginning of the post “The conceptual mathematics vs. the classical (combinatorial) one” , as also other posts and my comments in Gowers's blog. In particular, I said that there is no real division between Gowers's “second culture” and “first culture”, and therefore there is no real division between combbinatorics and non-combinatorics.
So, for this blog the working definition of combinatorics is “branches of mathematics described in two essays by T. Gowers as belonging to the second culture and opposed in spirit to the Grothendieck's mathematics”.
I don't like much boxing of all theorems or papers into various classes, be they invented by AMS, NSF, or other “authorities”. I cannot say what is my branch of mathematics. Administrators usually assign to me the field my Ph.D. thesis belongs to, but I did not worked in it since then. I believe that the usual division of mathematics into Analysis, Algebra, Combinatorics, Geometry, etc. is hopelessly outdated.
Next post: New comments to the post "What is mathematics?"
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