From the archives

Our consultants review some old writings.

Recently our astronomer pulled out some volumes of class notes from graduate school.  The immediate motivation comes from our tutoring consultant, who is pondering a workshop on note-taking for his students.  We admit that none of us was a particularly attentive note-taker in High School, where our tutor’s students are found.  However, the astronomer’s grad school notes are an example of what high-quality notes can be.

We should explain.  His course at Cambridge, Part III of the Mathematical Tripos, consisted of a series of lectures by professors.  There was no set textbook, though a selection of them was available in the common room.  Each professor followed his own syllabus, remarking now and then that “there is a good treatment of this in Rindler” or “Landau and Lifshitz show this in detail, but it’s too long and dense.”  There were no weekly quizzes or mid-term tests.  The grade for each course was based on a two- or three-hour exam in June.  So our astronomer could very well have to write a long mathematical essay on material he’d last seen in person six months before.  Good notes were essential for survival.  He scribbled down everything he could in class, then rewrote each days’ work in full sentences and with all the mathematical details filled in; at the end he provided a table of contents and a cross-reference to sample problems.

As he progressed, as a student and then as a recent postdoc, he attended workshops and conferences, and added his notes from these to the existing volumes.  They were not so complete and organized, but benefited from habits developed during the Tripos.

Going back to these works, he was struck both by their breadth and depth.  There are subjects he hasn’t worked in or even thought about since studenthood.  And most of them go into much more detail than he’s dealt with since (with a few exceptions where he’s done original research).  So we can ask: what good did all this careful learning do?  As far as anything our astronomer has actually done in the field, much of this looks like wasted time.

We can’t use the idea we had for primary and secondary schoolwork, that the exercise of the brain as such is the point.  He would certainly have gotten plenty of exercise even in a more restrictive program.  And there are those scientists who have specialized early and gone far.

But we can point out that no one can really predict how a scientist’s career will go.  Even if he or she appears to have a fixed direction and program through grad school, many things can cause a change: developments in another field or one’s own, or perhaps finding that a great question has been answered or rendered irrelevant.  More positively, an idea from a workshop on something else can often fertilize one’s own work.  A note from some long-ago lecture can indeed lead to a new line of thought.

We’re planning to go back through our grad school notes.  It’s not a matter of nostalgia as much as stimulation for the future.