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\documentclass{article}
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\usepackage{hyperref}
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\title{Collaborative Calculation in Your Web Browser}
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\author{William Stein}
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\begin{document}
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\maketitle
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I greatly appreciate the opportunity to write about online resources for
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mathematics in this theme of the Early Career Section, since such resources are
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something that I have long enjoyed sharing with the community. I first started
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creating websites for number theorists in the late 1990s when I was a graduate
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student at UC Berkeley. I started by creating tables of modular forms, inspired
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by a question from Ken Ribet, then encouraged by other people who told me that
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my data inspired their research (e.g., \cite{emerton}). I later became involved
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with the $L$-functions and Modular Forms Database (LMFDB) project \cite{lmfdb}, which organized dozens of mathematicians to
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make amazing tables of number theoretic data.
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I also created interactive online calculators, in which you could input the
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parameters of some mathematical object (e.g., an elliptic curve) into a web
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page, and the web server would compute and display extensive information. Later,
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when teaching undergraduate number theory courses at Harvard, I made similar
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online calculators that enabled my students to run calculations using PARI and
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Magma (see \cite{magma}), so that they could explore nontrivial
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computations in algebraic number theory. I wanted something similar to Magma
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that was free and open source, so I started the Python-based software SageMath
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in 2004 (see \cite{sage}).
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SageMath was difficult to install and only had a command line interface, so I
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started working to make it possible to use in a web browser. At University of
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Washington (UW) in 2006, some students and I undertook the creation of a
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web-based interactive notebook interface called the Sage Notebook, which was
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inspired by Mathematica's desktop notebook. The Sage Notebook was the first
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serious web-based computational notebook, and it was challenging for us to
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implement because of the primitive Javascript and HTML technology of the day,
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and the dangers arising from running arbitrary user code on my server. I hosted
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the notebook publicly for anybody to use starting in 2007, and my students and
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others frequently used it in courses, summer student research programs, and
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SageMath development workshops. A few years later the IPython project created a
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new notebook called Jupyter that looked and felt similar, but with a more
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modern underlying architecture that was built to work with a wide range of
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programming environments. The arrival of the Jupyter notebook was fantastic
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news, because by that time the Sage Notebook's design began to feel antiquated;
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moreover, Jupyter benefited from a multimillion dollar grant that resulted in
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substantial open source software development and publicity.
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To address more general needs related to my teaching, I started dreaming about
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creating another web application called CoCalc in 2012 (see \cite{cocalc}).
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CoCalc is an abbreviation for ``Collaborative Calculation", and I hoped it could
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provide a unified home for everything I was using for my teaching and research.
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My favorite undergraduate course to teach at UW was called ``Mathematical
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Computation"; it covered \LaTeX{}, R, Python, and computational statistics,
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abstract algebra, graph theory, symbolic calculus and cryptography using SageMath, and
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today it would significantly overlap with an introductory data science course. I
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wanted a web application that would be ideal for hosting this course.
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Prior to launching CoCalc in 2013, I taught Mathematical Computation many times
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using the Sage Notebook. However, the Sage Notebook did not adequately support
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important topics that I wanted to teach, including ``How to create \LaTeX{}
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documents'', ``How to use a Linux terminal'', and ``How to develop code in files
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instead of a notebook''. Furthermore, it did not possess the crucial ability to
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do simultaneous multiuser editing, which is a key feature of popular web
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applications today. Over the years I noticed two things about my students: (1)
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they appreciated working collaboratively with others, especially on final
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projects, and (2) they wanted to work collaboratively with themselves via a
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``time machine", in the sense that they wanted easy access to exactly what they
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were doing 15 minutes ago before they messed everything up. Having mulled over
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these issues, I decided I wanted to create a single web application that would
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support collaborative editing of Jupyter notebooks and \LaTeX{} documents,
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multiuser Linux terminals, integrated chat, and a detailed browsable time
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travel history of editing documents. The first release incorporated some of
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these things, but with stripped down functionality, and it was hosted on a
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single desktop in my office.
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That being said, I made CoCalc public and free just like the Sage Notebook, and
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a few other professors were interested in trying it out. Several students in my
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course were skilled at programming and began helping with its development.
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However, the instructors who first tried the application reported being annoyed
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with the tedium involved with uploading and downloading assignments. To combat
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this, we implemented a basic course management system, which automated
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distribution and collection of assignments.
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With this course management system in place, we received much more usage.
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Initially, I bought a few dozen servers using a grant, and hosted them in data
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centers on the UW campus. As usage grew, I received free credits on Google
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Cloud, and moved hosting to Google, which made dynamic scaling in response to
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variations in load much more efficient. We ended up facing a number of
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challenges due to the nature of our users, who were mainly people in courses
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making heavy use of Python and R. In one course, the students would regularly
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create massive plots, so we had to come up with better ways of dealing with huge
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output, especially in the context of simultaneous multiuser editing. Over a
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period of several years, we reimplemented the Jupyter stack for our purposes,
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while attempting to preserve the functionality, look and feel of the official
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Jupyter notebook.
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We also found that instructors needed access to a broad software stack, and we
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accumulated hundreds of gigabytes of installed software, along with automated
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scripts to install and test it. It was a major technical challenge for us to
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make this software quickly available for use across the cluster, periodically upgrade it
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with automated testing, and provide stable images over time. Along the way, some
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of our solutions to these problems failed at scale, which resulted in lost
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data, difficult weeks of hard work and many sleepless nights. Fortunately, we
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eventually engineered robust solutions to these problems, which have been
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working for several years.
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In 2019, I officially resigned my Full Professor position at UW to work full
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time on CoCalc as a business. Today this business is reasonably stable, with a
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manageable number of issues, and enough paying customers so that our team can
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proactively improve CoCalc, rather than reacting to crises. The company's daily
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operations are funded entirely by customers. Much of our current development
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effort on CoCalc is driven by the following question, which can be asked about
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every relevant piece of software: ``What would $X$ look like if one were to
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focus hard for 10 years on perfecting it?" This principle guides our development
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efforts, and we strive to make CoCalc faster to load and navigate, and to
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improve its efficiency, stability, and usability. As an example, we are currently working to provide beginner friendly graphical user interfaces for editing
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Jupyter notebooks and other documents. Most CoCalc users are beginners at
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scientific computation, so a graphical editor, with an easily browsable
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libraries of code snippets, makes CoCalc significantly more accessible to them.
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During the last 20 years, over one thousand people have contributed to the
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online tools I have described here.  Today these tools are relatively mature and
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powerful. I hope you find them as useful as I do, and that maybe you will help
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improve them over the coming decade.
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\begin{thebibliography}{2}
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  \bibitem{cocalc} \url{https://cocalc.com}
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  \bibitem{emerton} \url{https://link.springer.com/article/10.1007/s00208-003-0449-2}
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  \bibitem{lmfdb} \url{https://www.lmfdb.org/}
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  \bibitem{magma} \url{http://magma.maths.usyd.edu.au/calc/}
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  \bibitem{sage} \url{https://sagemath.org}
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\end{thebibliography}
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\end{document}
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