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Frankly I think the name Jupytercloud is much, much better than sagemathcloud. The reason is that anything containing the word 'math' instantly kills 99.9% of your targetgroup. I have been a mathematician for half of my professional life and I share a a love for all things mathematics, but in the second half of my professional life I have learned (the hard way) that 99.9% of people instantly shut off as soon as math is brought up. Sadly this is even true for most engineers and scientists. Anything called mathcloud is instant negative marketing, especially as doing a google search quickly turns up, talk about L-functions, number theory and commutative algebra. All of these capabilities you are rightly proud of, but which for most anybody outside of academic math departments it is a clear sign that sage/sagemathcloud is "not for me". This includes mathematics teachers, who, however, seem to like geogebra, a system with much more limited capabilities, but sufficient for elementary algebra, plotting functions and elementary geometry. One of its strength is that it can used in a (chrome) browser.

On the other hand there is a much larger group (if only non-math students) for which a "google docs/github" for shared, zero-install, browser based python/R/Ruby programming, data-analysis, plotting, statistics, technical-scientific writing /Numpy numerical and yes, Sage symbolic computation environment is a great proposition. Of course this is exactly what SageMathcloud is offering. However, if I may exaggerate a bit, SageMathcloud is now positioned as a cloud system to support mathematicians that can also do things like plotting and statistics, because it is really handy for doing statistics of the zero's of the zeta function. Completely understandable from where you come from, but a marketing disaster. A name like Jupyther cloud that reflects such a "neutral" programming/technical/statistical/data position would be a great boon.

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