# Using a zettelkasten in mathematics research

@bradfordfournier wrote here:

Any shared experiences re mathematics research in your zettelkasten would be great.

I think this deserves a discussion of its own, with a more telling title than the one where it came up.

@bradfordfournier - I hope you are OK with this.

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## Comments

Of course. Thanks.

Side note on quickly getting some latex into your editor / zk :

One external piece of software / app that I've found incredibly helpful is the iOS app "Snip" which takes a picture of some mathematics and converts via ocr, to latex in multiple formats. It's excellent with hand-written OCR as well.

Attached is the image taken of a simple bit of math and the app interface which provides the result.

The result provides multiple formats as well as the confidence in the OCR. It can handle much more complex images including category theory etc. Very helpful for quickly getting some math into your preferred editor / zk software.

My current ideas on paper-ZK-based problem solving is outlined here, and the crucial question to me seems that of problem solving tools: Which tools are the most useful, given one's mathematical domain of work, knowledge, skills and expertise?

(In a way, I suspect the tool collection could be a kind of plug-in - you could have tool collections for maths, for physics, for philosophy etc., with a certain overlap in general methods and any amount of diversity in specific methods.)

Having a tool collection that can be adapted with ease and that co-evolves with its user seems of paramount importance.

The math tool collection from George Polya's "How to Solve It" is perhaps the most famous in mathematics, but personally, I never found it very helpful with its four stages of

1) Understanding

2) Making a Plan

3) Carrying Out the Plan

4) Looking Back,

and its heavy reliance on using "related problems" one had solved earlier.

I found the methods developed by Mason / Burton / Stacey in "Thinking Mathematically" and by Spyros Kalomitsines in "How to Solve Problems: New Methods and Ideas" much more accessible. Kalomitsines in particular gives a number of examples that show the interplay between thinking tools and "writing for insights" in the process.

In my years of study and at my university, there was practically no instruction about the methodology of problem solving, and although I had a number of friends that were

reallygood at maths, there was little informal talk about methods.Even in retrospect, I cannot describe the reasons for this.

I think that even a very small community of ZK users communicating about their experiences could profit considerably. Given an explicit framework of concepts on how to write work notes, how to organize notes, how to use tools would enable them to progress decently - by discussing questions like

how do you deal with confusion,

what do you try when you are stuck,

how do you generate new approaches,

how do you organize your tree of solution trials" etc.

Here's a passage from a 1984 interview with Michael Atiyah:

The essay examines differences between "problem solvers" and "theory builders".

I'm mentioning it here because Atiyah's approach seems to correspond to straightforward zettelkasten work.

About his own work habits, Atiyah said:

Not exactly the principal witness for my "write for insights" mantra, as it seems.

@thomasteepe

Great quotes. And while he may not be the poster boy for "write for insights" he is the poster boy for "walk for insights". I still think putting the two together is a dynamite combination.

Here's advice by Terence Tao on "Write down what you've done".

On his page "What's new" he has subsections on "Career Advice" and "On Writing".

There is no explicit connection to zettelkasten work, but tons of good advice on doing and on writing maths that can be used in any form of organizing knowledge.

One of the most relevant discussion on mathoverflow.net (a question and answer site for professional research mathematicians) seems to be "How do you keep your research notes organised?"

The discussion was closed 9 years ago, with the following howler of an argument:

There are 16 answers, mentioning paper notebooks, TeX files, wikis, photos of handwritten notes in Evernote, etc. I'm pretty sure that many of the commenters back then would agree today that a zettelkasten, digital or perhaps paper-based or hybrid, would provide a compelling basis for their work.

@GeoEng51

At this very moment, I'm looking for information about how mathematicians organise their work.

Here's something from an interview with Andrew Wiles.