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Courant is kinda saying the opposite here, by de-emphasising the need for purely abstract formalisms, or by saying that they have to go hand-in-hand with applic
by jordigh 14y ago
Courant is kinda saying the opposite here, by de-emphasising the need for purely abstract formalisms, or by saying that they have to go hand-in-hand with applications, or are worthless without applications. As a numerical analyst, he of course thinks "applications" of mathematics are tantamount to its existence.
The thesis in the linked article is that we need to emphasise the importance of purely abstract formalisms, not only in the context of possible applications.
- stiff 14y agoWhat I meant is that he described the same problem in a more complete way, not that he just said the same thing more nicely. There are infinitely many formal systems and after all we choose only some particular ones, what guides this choice? Isn't the existence of models in the real world one of the most important factors in choosing which formalism is valuable to develop? Courant how I understand him is saying that the tension between the two approaches is vital to the development of mathematics. There is also a nice lecture [1] from Vladimir Arnold, who was very much on the side of intuition, where he raises an interesting point that is related: in todays mathematics all the praise goes to the people who prove theorems, where perhaps the person who first _stated_ an theorem that is interesting and relevant deserves at least as much credit. [1] http://www.msri.org/web/msri/online-videos/-/video/showVideo/2714 http://www.msri.org/web/msri/online-videos/-/video/showVideo...