Apart from the useful introductory comments by Scott Barry Kaufman and the excerpt itself, the 'multi-part' thread, "Scientific American - Excerpt from 'The Philosophy of Creativity'" (starting May 17, 2014 6:22 PM, http://mathforum.org/kb/thread.jspa?threadID=2632746) has drawn a number of insightful and insightless inputs on the nature of (mathematical and other) creativity.
Robert Hansen has sought (May 19, 2014 9:04 AM, http://mathforum.org/kb/message.jspa?messageID=9467689) to draw a distinction (insofar as I've been able to understand his message) between what he terms as 'the knowledge of math' and the 'creative art of math' (words/ ideas to this effect): > > (RH): I disagree even with the implication that studying > math can create mathematical creativity. I agree that > creativity does not happen in a vacuum and it is > inevitably connected to the current state, but Saxon > had it wrong. Creativity isn?t tied to the current > state of knowledge, it is tied to the current state > of the art. Most people get educated because they > like the feeling of having things explained to them > and knowing. I get that. Most if not all college > classes feed this. But the creative mathematician, > which in my mind is the only actual mathematician, is > after the state of the art. Even though knowledge is > there on the surface, the creative mathematician is > studying the art behind it. I took analysis my first > year of college and I was quite disappointed by > knowledge centric view of mathematics in college. The > class was complete but delivered the material as if > it was just knowledge. Maybe if I was a math major > instead of a physics major I would have had a key to > the ?real? math classes. But I was a physics major and > they delivered physics as if it was just knowledge as > well. The only place that felt right was hanging out > in the math department itself. Which is confusing, > because there was a lot of mathematical energy in > algebra and high school, and I thought this would > only increase in college. It didn?t increase, it > disappeared entirely, except for the math department. > And this was 30 years ago. Is there even anything > left in the math department? > I profoundly disagree with Mr Hansen (assuming always that I've understood him correctly, which he claims I have not as he says I've not read enough [American] English poetry to understand him properly!)
I believe, to the contrary, that there is considerable *real creativity* involved in the 'learning of math' (at any level) - from the most elementary to the most advanced (i.e., in the 'acquisition of knowledge' of math).
At, say, the graduate school level (in math), I know for sure that there is considerable creativity involved in the 'construction of suitable instances, examples and counterexamples' to enable understanding of new concepts and the like. No theorem is ever *effectively* understood unless the learner constructs a sizable number of instances, examples, counterexample.
On the one hand: i) Something new has to be 'grasped';
On the other: ii) Something new has to be 'created'.
There probably is a sizable difference in the 'kind of creativity' involved in 'creating new concepts in math' from the 'kind of creativity' needed to learn a new concept in math.
The differences in scale and 'kind' are whole orders apart, I agree. But I claim that both 'i' and 'ii' above are aspects of the same 'mental phenomenon': the 'creator' is not a whole breed apart from the 'learner' (which is what I understand Mr Hansen wants to claim).
I have never created 'a new concept in math'.
However, I have indeed created 'a new concept' in systems science: the 'One Page Management System' (OPMS).
I needed to learn plenty in systems science (i.e., acquire a whole bunch of knowledge) in order to create that concept in systems science. I claim there is plenty of 'creativity' in both learning (any new concept) and in 'creating' (any new idea/product). I know that one instance does not prove the case. However, it is better than nothing.
Can Mr Hansen point to anything (concept or product) he has ever created (in math, or in any other field) - apart from, of course, those fabulous 30-foot PERT Charts that he plastered over all the walls and corridors of the offices he worked in? We're eagerly waiting to hear from Mr Hansen.
Googling for "the difference between learning and creating" didn't give me much that is useful (despite millions of links!)
I did, however, find a document "High Achiever, Gifted Learner, Creative Thinker" by Bertie Kingore http://www.bertiekingore.com/high-gt-create.htm that contains a pretty useful table showing characteristics of each kind of personality in the above title. (I do plan to continue searching, as I believe there is much I can use to help developing documentation for the 'One Page Management System' [OPMS]).
I claim that the distinctions that Robert Hansen has sought to draw between "knowledge" and "art" are rather less than insightful.
I also believe that there is rather less than meets the eye to Robert Hansen's 'insights'.