I worked with Desmos over several months, advising on a variety of projects. Their main goals at the time were increasing adoption of their online graphing calculator and improving the usability of said calculator on a variety of platforms.
One of the key problems facing a graphing calculator is getting buy in from students and teachers. There is an element on mandated adoption due to high school math classes and requirements, but the market had been dominated by Texas Instruments for quite some time. Desmos had to prove that they were better to use and to teach with.
We looked a lot at social sharing platforms and how they were getting users to stay and use the sites. While this may, at the surface, appear to not have a lot in common with a graphing calculator, it actually resonated deeply with the team. Whenever the Desmos team saw a particularly interesting graph created on their platform, they would print it out and add it to the wall.
We took that idea and placed in on the site itself. The uniqueness of their platform also allowed users to copy the graph and expand on it in their own way, utilizing the equations and thoughts of the people before them.
The art is inspiring to a lot of students, who end up using the calculator in their free time, and to teachers, who can direct creative assignments that nonetheless encourage the use of complex math and interactions.
Graphing calculators are inherently complex. Abstracting away too much makes the calculator useless to those who need it most. The balancing act here is doing as much for the user as you can, but leaving the detailed options and abilities available, and easy to find.
I worked a lot with the team to manage screen real estate. There were times that the graph needed to be viewed alone and visually manipulated and other times where functions needed to be added or tweaked.
The team has now moved far beyond from when I was there, as they've brought in more actions for the users and abstracted away some of the choices, but the main elements of screen usage have remained the same. The graph itself is always there as the primary element, with panels and modules available to manipulate it. This keeps the focus on the graph for not only the users, but it helps keep the team homed in on what is most important.