# A kind of "Zettelkasten" for mathematics

edited June 2021

Not strictly a Zettelkasten, but almost. I was ready "How to write mathematics" by P. R. Halmos. and on page 134, he discusses how he organizes a book or long article:

At one stage of writing a 300-page book I had 1000 sheets of paper, each with a mathematical statement on it, a theorem, a lemma, or even a minor comment, complete with proof. The sheets were numbered, any which way. My job was to indicate on each sheet the numbers of the sheets whose statement must logically come before, and then to arrange the sheets in linear order so that no sheet comes after one on which it's mentioned.

Emphasis mine.

It is of course not quite a Zettelkasten, since the numbers are only used to describe predecessors, but I think it is still interesting to look at these examples of almost-Zettelkasten. I think it gives credibility to the Zettelkasten technique that it is not really something entirely new, but that the elements can be recognized elsewhere.

• The study of some of the early predecessors to the zettelkasten method does reveal insight. Like your example, mathematicians have been dancing around the ZM without ever putting it all together for some time. In this example, similar tools for thought, to those that help link ideas/zettel together, are described by Poincaré.

Is this a description of how notes relate to each other in a zettelkasten? A zettelkasten, this is not but it describes a tool that can be appropreated for use.

...what is mathematical creation? It does not consist in making new combinations with mathematical entities already known. Any one could do that, but the combinations so made would be infinite in number and most of them absolutely without interest. To create consists precisely in not making useless combinations and in making those which are useful and which are only a small minority. Invention is discernment, choice.

How to make this choice I have before explained; the mathematical facts worthy of being studied are those which, by their analogy with other facts, are capable of leading us to the knowledge of a mathematical law just as experimental facts lead us to the knowledge of a physical law. They are those which reveal to us unsuspected kinship between other facts, long known, but wrongly believed to be strangers to one another. ...The sterile combinations do not even present themselves to the mind of the inventor. Never in the field of his consciousness do combinations appear that are not really useful, except some that he rejects but which have to some extent the characteristics of useful combinations.* (p. 325)

The Monist, Volume 20. Mathematical Creation by Henri Poincaré (written in 1908) https://archive.org/details/jstor-27900262

Will Simpson
My zettelkasten is for my ideas, not the ideas of others. I will try to remember this. I must keep doing my best even though I'm a failure. My peak cognition is behind me. One day soon, I will read my last book, write my last note, eat my last meal, and kiss my sweetie for the last time.
kestrelcreek.com

• @henrikenggaard said:
I think it gives credibility to the Zettelkasten technique that it is not really something entirely new, but that the elements can be recognized elsewhere.

Here is an older example of a zettelkasten: https://blog.sub.uni-hamburg.de/?p=8736 (the material is in German).
The author Joachim Jungius (1587-1657) is not well known, but he was held in very high esteem by Leibniz. (I take my information from the Wikipedia.)

I first heard about Jungius in the "Taking Note"blog written by Manfred Kuehn. The blog was a treasure trove of facts about zettelkästen, note taking, writing habits, software etc. It does no longer exist, which to me is a real loss.

What I find puzzling: With pioneers such as Jungius, and later proponents like Luhmann, why did zettelkasten practices not become much more prominent and widespread?

• edited June 2021

the Zettelkasten didn't make it into my education system and public internet access started in the early 90s. IMO, It's only a matter of time when a popularity is going to discuss his/her Zettelkasten with us on Zettelkasten.de

Post edited by zk_1000 on

my first Zettel uid: 202008120915