I love the picture of their notes! [1] It hints of iteration and exploration (multiple drawings of flower-petal-looking graphs), corrections (scribbled over sym

I love the picture of their notes! [1] It hints of iteration and exploration (multiple drawings of flower-petal-looking graphs), corrections (scribbled over symbols), refinement ("Phase J" appears in multiple places), and, above all, collaboration (different colors!). A great representation of the process of mathematical discovery. It's so different from the austere presentation of a polished LaTeX paper. A completed proof leaves out so much of the exploration process -- the doodling, hopeful symbol-pushing, flawed intermediate conjectures and conclusions -- and just leaves an artificially linear representation of how to approach the problem. It's easy to feel despair when a textbook or paper presents something so succinctly, as if it's the most obvious thing in the world, but there was a lot of stumbling around in darkness (the dark background of the note-taking software!) before the elegant formulation was finally illuminated. Graph problems and combinatoric problems are especially fun to puzzle out in a notebook as it's especially easy to come up with examples, though it does get difficult to play around with larger graphs. Recently I tried to find an algorithm for generating round-robin tournament pairings, and ended up filling pages of notes with tables and dissections of complete graphs. It's a fun challenge, and accessible even to someone without a theoretical math background. I eventually found a horrendously complicated solution, one I was proud of, even after reading a supremely simple construction on Wikipedia. [1] https://d2r55xnwy6nx47.cloudfront.net/uploads/2021/04/Zoom-Sketch_v2.jpg https://d2r55xnwy6nx47.cloudfront.net/uploads/2021/04/Zoom-S...