On Saturday morning in Madison at Mathfest, I attended a fantastic talk by Robert Ghrist, titled “Putting Topology to Work”. He has apparently given versions of this lecture in several other locations, including the Young Mathematicians’ Conference at Ohio State; from their site at http://www.ymc.osu.edu/2011/speaker1.php, you can watch a video of the talk. Highly recommended.
The version of the talk that he gave at Mathfest had a different ending. After sharing a bunch of really cool, cutting edge applications of algebraic topology, Robert said a question had plaguing him: “How do we bring these ideas to the people who can and need to use them?” It seemed like he first had in mind engineers, but also undergrads, who both (in his opinion) should learn to think topologically, early and often. He spoke about how when linear algebra was first introduced as a discipline, people derided it as abstract, arcane, and useless. Some of the biggest early critics (physicists), are now the biggest end users of the subject. And now we teach linear algebra to freshmen and sophomores (and sometimes even HS students).
Robert made the argument that he thinks algebraic topology will be a similar discipline; and stated that one of his goals is that within the next decade or two, students will have the opportunity to start thinking topologically much earlier in their education. He has a plan for how he will try to impact that change through an effort to bring algebraic topology to the masses (ok, the really bright masses, but more masses than just math grad students).
To that end, he closed his talk by discussing his plans to start teaching calculus “the right way” (by which, he clarified, he meant “the topological way”) so as to start to engender sophisticated and topological thinking in his students. He is teaching a Coursera class this fall (I think he said 26000 students (!!) are already enrolled — you can learn more at https://www.coursera.org/course/calcsing) and he is going to put some of his new ideas to work. He has a very brief, very unusual, but very entertaining calculus book (FLCT – fun little calculus text) that you can find online at his website (and the book is very free!) at http://www.math.upenn.edu/~ghrist/FLCT/index.html.
There are a whole bunch of game-changers here. Like other Coursera courses, the “masses” can study, for free, under the tutelage of a spectacular professor from one of the world’s top universities; calculus is being taught with way different goals and perspective, goals that are relevant for the 21st century and far afield from the relatively traditional calculus goals that most schools abide by; and Prof. Ghrist is making his written resources available free of charge. Traditional universities and traditional textbook companies are both going to have to wrap their minds around this new reality if they wish to survive.
He closed his talk with a statement to the following effect (I’m paraphrasing, as I didn’t record it): “The limiting resource should not be access, but rather time and talent.” I like that a lot.