When I finished my high-school education in 1980, I studied mathematics because I have a deep love for its depth and generality. A few years later, I was dazzled to learn about the new interactions between theoretical physics and many areas in pure mathematics. This effort brought clarity and new results to both areas, and was initiated by great thinkers such as Atiyah, Donaldson, Manin and Witten. I believe one particularly beautiful paper showing how far reaching these interactions are is that of Graeme Segal entitled Space and Spaces.

Since I moved into computer science and its applications to scientific computing, I have never encountered the wealth of different, deep relations with mathematics that I have seen in physics. To gain deeper and more influential connections between the extremely complex problems in applied computing and areas in mathematics, do we already have the right foundations and is complexity making their application very difficult? Or are we lacking abstractions, and will these - as they did in connection with physics - perhaps take centuries to mature?

Machine learning similarly does not yet have rich connections with mathematics, but this area seems to be evolving much faster, perhaps due to a focus that is narrower than computing in general.