In my science bookstore business one of my principle interests is antique manuscript notebooks in the sciences. It is a pleasure to see someone working through a problem, or finding what the writer thought to be the most interesting point in a lecture on a particular subject, and to read the occasional doodles and see the timely gloss every now and then. I’ve had notebooks from an advanced and very careful student for a course given by the great Robert Bunsen that was filled with hundreds of pages of what the master was trying to communicate to his pupils.
There’s also a series of notebooks from the spectacular period of Cornell physics history (1948-1949), including 6 notebooks of classes with Richard Feynman, including several hundred pages from his 1948/9 course in advanced quantum mechanics, which included (a very early) use of the Feynman diagrams. The thing that makes these observant, advanced notes taken during Feynman’s classes have more than a pedagogical interest (which is substantial and enough on its own)—they have a capacity to show the logic behind the man’s thinking and how he presented his ideas over a period of some months. Also, and curiously, notebooks like these seem to have not survived.
Then there’s the notebooks taken by the team of Charlotte and Fritz John when they were pursing doctoral degrees at Goettingen (1929-1933), until forced to leave with the enforcement of the Nazi laws against non-Aryans. Goettingen happened (and happens) to be the seat of a long, great mathematical heritage, home of Felix Klein, Emmy Noether, David Hilbert and Bernhard Riemann (among many others). The notebooks—some two linear feet of them—represented four years of advanced interactions with some of the finest mathematical minds in Germany. I was told by Mrs. John that they were required to take such full notes—but let me tell you, these notebooks were typed transcriptions of the daily handwritten notes, compiled over the course of a class, and then bound. They are beautiful, and go far beyond my concept of “required”. Mrs. John told me the story of the class notes that she and Dr. John took while taking a course with the great Hermann Weyl (who had taken his doctorate under the iconic David Hilbert, and who was also forced to flee Goettingen because his wife was Jewish): everyone of course was required to take extensive notes during the day and work on them during the night, turning them in the following day for appraisal. She told me that she still vividly remember placing their notes on a long wooden table at the front of the class, and then picking that set of note up the next day. After a month of this, she, said, they became convinced that Weyl was not looking at the notes at all, as everything seemed always to be in the spot that they left it in. One week they decided to see if the notes were being moved, and placed a hair carefully on the interior page, reasoning that if the notes were reviewed, the hair would be gone. For a week, the hairs stayed in place. “And so, what did that mean to you?”
Mrs. John replied that it really didn’t mean anything, and that they continued to do the notes as they would, and leave them on the long wooden table. They never slacked off (which I can fully imagine). She said that they did it for themselves, of course, but also they did it for Dr. Weyl, fully expecting that the day that they missed handing in their notes would be the day that they were looked for by Dr. Weyl. Plus they were studying with a famous and fabulous thinker, and did not want to disappoint themselves or their instructor.
I do enjoy the historic or significant material like this, but I also quite the naïve, homegrown, elementary manuscript attempts by children at doing math or understanding physics. Cipher books have always been a little hard to find in my field, wit many of them (I think) winding up in the genealogy area), and they just don’t seem to be very much on the findable side of things anymore.
The example I’ve reproduced here are from an anonymous (but dated 1818) work on different elementary areas of mathematics. What makes this special to me is the precision of the penmanship and the extreme effort that is being used for a simple display of division. It would certainly convey the message if the author had used two five-figure numbers to display division rather than these enormous, never-to-be-encountered numbers.
Surely there were pages and pages of scrap used to get to this point as the operator machined his numbers down, showing us the result rather than the real process. But what is left to us in this effort is a thing of considerable beauty—the found art of practicing elementary math.