Search All of the Math Forum:
Views expressed in these public forums are not endorsed by
NCTM or The Math Forum.


GS Chandy
Posts:
7,950
From:
Hyderabad, Mumbai/Bangalore, India
Registered:
9/29/05


Re: Learning new concepts Vs. Creating new concepts (math/other disciplines)
Posted:
May 29, 2014 8:31 PM


Robert Hansen (RH) posted May 26, 2014 1:30 PM (http://mathforum.org/kb/message.jspa?messageID=94724650)  GSC's remarks interspersed: > > Tao, Poincare, Newton, all mathematicians. Are you > making my own point? > No. You're making mine. > > Poincare isn?t talking about the art, he is, more or > less, talking about the role of intuition in > mathematics. > And Robert Hansen has managed to separate out "the art of mathematics" from "the intuition of mathematics"? (Remarkable, indeed... and my hearty congratulations!)
As Joe N. observed: You're a funny guy.
I'll go even further: You're a very, VERY funny guy indeed, in regard to your observations about math and, for that matter, about cognition (below). > >Some of us who study cognition, with the > help of numerous other since Poincare, have come a > long way since Poincare. > I guess the following is part of RH's 'study of cognition' as applied to math: > >(Robert Hansen): "Even though knowledge is there on the surface, the >creative mathematician is > studying the art behind it". > >"Real mathematicians are in it for the art of >mathematics, not the knowledge of mathematics". > And when Robert Hansen plasters all the walls of the halls and corridors of the offices where he works, he is doing that in pursuit of "the art of mathematics" no doubt? > > (Robert Hansen): With regards to mathematics... > > Intuition is that which we feel to be true, > viscerally, rather than reasonably. While some of our > most basic axioms, if not in fact all of them, are > visceral, those intuitions alone do not make > mathematics. It falls on the mathematician to find > the logical connections between these intuitions. The > art of finding those connections is the art of > mathematics. > WOW!
The Revelations according to Robert Hansen!
"Intuition is that which we feel to be true, viscerally, rather than reasonably".
Most profound indeed, and we should all take note. Here's even more and better!: > > (RH): "It falls on the mathematician to find > the logical connections between these intuitions. The > art of finding those connections is the art of > mathematics. > > The Collatz conjecture appears to be > true, viscerally, so why not simply accept it as true > and move on? Because the art of mathematics is not > concerned with simply knowing what is true and what > is false. It is concerned with connecting what is > true and what is false with everything else that is > true and false. > Now THAT is truly special and deserves to be inscribed in Letters Of Gold. So let's do it: > >(RH): "The art of mathematics is not concerned with >simply knowing what is true and what is false. It is >concerned with connecting what is true and what is false >with everything else that is true and false". > GOT IT!!! It's The Gospel According To Robert Hansen! > > (RH): I?ll mention this to Poincare when I see him.:) > I'm SURE you will. And doubtless he'll respond with a hearty roar of laughter. For you're a very, VERY funny guy indeed!
(But I seem to have read, somewhere, that Poincare wasn't much given to hearty bursts of laughter... Perhaps he might only have smiled dubiously?) > > I posted a very simple question that neither you nor > Joe seem willing to answer. When a musician creates a > song, do you credit the musician or the song? > TOUGH QUESTION! We shall have to depend on Robert Hansen to give us The Answer!
Anyway, whenever I'm seeking to get a good laugh, I'd look for stuff under the "The Wit and Wisdom of GW Bush on practically any subject (or Robert Hansen on mathematics)".
If anyone is interested in going a bit deeper than RH, he/she may like to seek some knowledge (or the 'art of knowledge', or something, as RH would probably have it), there is plenty available, and a few of those links I've pointed to in my earlier posts. I admit that I do owe Robert Hansen a huge debt of gratitude, for it was his exegeses that stimulated these specific explorations that have led to a potentially most fruitful area for study.
There IS a fair bit available about "creativity in math" (and in other fields), though much of it is not adequately 'organised' by any means. Just search for "creativity in math", and you'll find plenty).
The source of ideas (of any kind) in the human mind is still, largely, a mystery. We do know that ideas are 'associated' in various ways with electrochemical impulses that flood the brain, but not much else. Just what is 'creativity' in general (or in math, for that matter) is still a mystery to science  though of course Robert Hansen claims to have unraveled it all. > > I have never had a problem gaining access to "math > club". I have posted enough unique solutions and > derivations here to make that point. I don?t see > anything in what you are writing that reflects what > goes on in "math club". > So what did Henri Poincare and others in this "math club" that you frequent have to say about your "unique solutions and derivations that you've been posting here"? As far as I'm concerned:
You have indeed provided a good many laughs. For which I for one surely owe you my heartfelt thanks in this desolate world. > > As always, you seem to be > talking about somewhere you haven't been. This was > puzzling me because I wondered why not talk about > somewhere you have been, rather than somewhere you > haven't, let alone with someone who has. And then I > realized, the reason you do this so often is that you > have never been anywhere. > > Bob Hansen > Admittedly, I haven't created any profound new concepts in math  nor have you, for that matter, notwithstanding your claim above, to the effect that you "have posted enough unique solutions and derivations here".
Though it seems to have escaped your profound attention, I have indeed systematically been and have systematically explored 'systems and how we common people may cope with them'.
And all you've ever had to say about that (along with 'Genius' Haim) is the unabashed lie:
"OPMS is just listmaking and nothing else!"
And you followed that up with the suggestion that I (GSC) needs to study some (American) English poetry in order to understand the profundity of Robert Hansen! So do keep telling us, Mr Hansen, about these wonderful places you have been (or where you are coming from), such as, for instance: > >(Robert Hansen): "Even though knowledge is there on the >surface, the creative mathematician is studying the art > behind it". > >"Real mathematicians are in it for the art of >mathematics, not the knowledge of mathematics". > >"A mathematician seeks truth in logic and the real >numbers and in doing so, increases our understanding of >both." > The depth! The veritable profundity!
But I seem to notice that 'complex numbers', 'transcendental numbers', 'patterns' and the like seem to have escaped Mr Hansen's 'expert' attention thus far.
GSC ("Still Shoving! NOT PUSHING!! Not GOADING!!!")



