{"id":64,"date":"2020-01-03T21:08:51","date_gmt":"2020-01-03T21:08:51","guid":{"rendered":"http:\/\/blogs.ams.org\/livingproof\/?p=64"},"modified":"2020-01-03T21:08:51","modified_gmt":"2020-01-03T21:08:51","slug":"follow-your-heart-by-jeff-weeks","status":"publish","type":"post","link":"https:\/\/blogs.ams.org\/livingproof\/2020\/01\/03\/follow-your-heart-by-jeff-weeks\/","title":{"rendered":"Follow Your Heart, by Jeff Weeks"},"content":{"rendered":"
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Throughout my seven years as a math grad student, there was a constant struggle for attention between \u201cwhat I was supposed to be working on\u201d and \u201cwhat my heart was into.\u201d\u00a0This theme played out in different ways over those seven years.<\/p>\n

When I first arrived in Princeton in 1978, I discovered that I was the only one in my entering class who hadn\u2019t already taken graduate-level courses as an undergrad.\u00a0Worse still, the Math Department, catering to its typical clientele, offered no introductory graduate courses.\u00a0None at all.\u00a0Our mandate was to learn\u2014or, for my classmates, review\u2014the basic stuff on our own, and then dive into the research-level courses that the various professors offered.<\/p>\n

I was adrift.\u00a0What should I have been doing?\u00a0Studying even harder about Noetherian rings, the Radon-Nikodym theorem, etc. etc., all at a level of abstraction that I found neither useful nor interesting.\u00a0 What was my heart into?\u00a0Learning some concrete geometry and topology, along with some general relativity.\u00a0You can guess what I spent most of my time doing.<\/p>\n

As you might imagine, my qualifying exams did not go well.\u00a0On my first attempt, they let me off the hook on the basic topics with a humiliating but welcome remark that \u201cyou can learn this stuff when you teach it.\u201d\u00a0But for the advanced topics, they wanted me to try again the next year.\u00a0They weren’t impressed then either, but they decided that I should start working on a thesis anyhow.<\/p>\n

By then, I\u2019d signed on with Bill Thurston as my advisor.\u00a0I don\u2019t remember what problems I was supposed to be working on, but I made no progress with them.\u00a0What was my heart into?\u00a0By that time, my fellow grad students, colored chalk in hand, had introduced me to the beautiful world of low-dimensional topology, and I\u2019d fallen in love with it.\u00a0I\u2019d also noticed that all books on the subject involved a lot of graduate-level algebra and analysis that really wasn\u2019t needed to understand and appreciate the core concepts of geometric topology.\u00a0So, I decided to ignore my thesis problems and instead took it upon myself to write the \u201cmissing book,\u201d something that would welcome everyone\u2014from high school students on up\u2014into the magic world of multi-connected spaces.<\/p>\n

That project took several years, with the book, The Shape of Space<\/em>, finally completed in my fifth year as a grad student.\u00a0My grad student stipend ended that year, so during what would have been my sixth year, I taught at Stockton State College and saved up enough money to return to Princeton and write a thesis in the seventh year.\u00a0I don\u2019t remember what I was supposed to be working on, but while Bill Thurston was away for the winter holidays, I decided to grant myself an indulgence to investigate some especially simple 3-manifolds and write a little computer program to find hyperbolic structures for some of them.\u00a0I was lucky enough to stumble onto the smallest closed hyperbolic 3-manifold.\u00a0During my first meeting with Bill after the holidays, I figured I\u2019d briefly mention this little discovery.\u00a0Bill responded with some ideas for how I might move forward with these investigations and how I might extend my little computer program.\u00a0He said not a word about my old boring thesis topic, so by the time the hour was over, it was clear I had his blessing to do a thesis with my software for putting hyperbolic structures on 3-manifolds.\u00a0\u201cWhat my heart was into\u201d had finally become \u201cwhat I was supposed to be doing\u201d!<\/p>\n

Throughout six-and-a-half of my seven grad school years, I\u2019d always felt that I would have been better off with a different advisor at a different school, with a firmer hand to guide me.\u00a0But in retrospect, Thurston\u2019s approach was exactly the right one:\u00a0he let me find my own path.\u00a0By the end of those seven years, I had some research software (SnapPea) and a book (The Shape of Space<\/em>).\u00a0In my heart, the book was my true dissertation. Even though it did nothing to satisfy Princeton\u2019s Ph.D. requirements, it set the tone for my whole professional life, both in content (geometry, topology, cosmology) and style (exposition for the general public).<\/p>\n

As for my advice to current students, I dearly wish I could say \u201cfollow your heart\u201d and leave it at that.\u00a0 But, of course, it\u2019s not quite that simple. One needs a paying job.\u00a0So, my advice is: follow your heart, and find a way to turn your passion into your livelihood. I wish you good courage and the best of luck.<\/p>\n

\"\"<\/p>\n

Jeff Weeks is a free-lance geometer, topologist and occasional cosmologist.\u00a0 His favorite successful projects are the third edition of his book The Shape of Space and the Geometry Games software.\u00a0 His favorite unsuccessful project was collaborating with cosmologists to deduce the topology of the universe from the cosmic microwave background.\u00a0 Support over the years has come from the National Science Foundation, a MacArthur Fellowship, lectures, and occasional work for science museums.\u00a0 In his spare time, he enjoys biking (spring, summer, autumn) and cross-country skiing (winter) with his wife, and learning foreign languages.<\/em><\/p>\n

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Throughout my seven years as a math grad student, there was a constant struggle for attention between \u201cwhat I was supposed to be working on\u201d and \u201cwhat my heart was into.\u201d\u00a0This theme played out in different ways over those seven … Continue reading →<\/span><\/a><\/p>\n

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