Mathematics grips the world through differential equations.

Andrew Gleason, that wonderful member of our mathematics community, who taught at Harvard for so many years and led the successful calculus reform effort there said, "Mathematics grips the world through differential equations."

Dan Flath of Macalester College shared that in his rich differential equation course page. Dan said of the quote from Gleason, "He said it to me face to face.  It was one of my greatest mathematical pleasures to get to know him through my work as coauthor of a calculus textbook (with Deb Hughes-Hallett and many others)."

Gleason and his career may not be well-known to some (how can that be?), but you can read all about his career and contributions in the November 2009 issue of  Notices of the AMS. We could not do justice to his brilliant career here, nor would we try, nor could enough appositives be rendered to give the reader insight into what Gleason was and offered us as fellow mathematicians.

Just consider the quote, "Mathematics grips the world through differential equations." I have come to believe it more and more over the years, but I was not able to articulate it in such fine grain and concise form. I appreciate Dan Flath's saving it for us all.

Dan points out in his course page the significance of F = ma and how a is the second derivative with respect to time of position. So when we are describing force (and the universe runs on force!) we are using differential equations, especially when one thinks of Newton's Second Law of Motion which says that the mass times the acceleration on a body is the sum of the external forces applied to that body. Thus differential equations describe the world and, indeed, have a firm grip on what goes on in the world.

Thank you Andy and thank you Dan.


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