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We should not forget that as academics we are in the business, not only of formulating new ideas, but of communicating ideas, both old and new. The challenge of communicating ideas long known to us, to our pupils and our peers, is the challenge of making ideas new. It is not enough even to simply bridge from what they know to what we know. We must be entertained by the subject matter to make it entertaining, and know what is confusing to know what should be emphasized.
The idea of 4 dimensional space, to give an example, is one that baffles and fascinates many outside of math, as well it should. Unfortunately, we have answers to the question "what is 4 dimensional space?", which never require any thought on our part. It is the space of 4 ordered real numbers, after all. The best teachers are those who can remain in awe of ideas which earned our awe the first time through, while knowing the pathways in and out of and around those ideas.
I love teaching most of all because I love finding ideas impressive again.
I am putting together a series of animations entitled "In Light of Leibniz," beginning with calculus, though later works in the series will branch far and wide, into other disciplines. I'm interested in working with other artists and academics to communicate compelling stories and profound ideas in novel ways.
It will be important in my career to work with other academics who are similarly in awe of ideas in their respective fields and desiring to share those ideas, in exchange, and to collaborate when it can be done. I will be looking for a university where multidisciplinary collaboration is encouraged if not expected.