Like public-key cryptography, deep learning was ahead of its time when first studied, but, thanks to the pioneering efforts of its founders, it was ready to be used when the technology caught up.
Mathematical developments take a long time to mature, so it is essential that applied mathematical research be done ahead of the time of its application, that is, at a time when it is basic research. Maybe quantum computing will be the next example to teach this lesson.
By the way, this summer the Simons Institute will host a program on the foundations of deep learning, co-organized by Samy Bengio, Aleks Madry, Elchanan Mossel and Matus Telgarsky.
Sometimes, it is not just the practical applications of a mathematical advance that take time to develop: the same can be true even for its theoretical applications! Which brings me to the next announcement of this post, namely that the call for nominations for the FOCS test of time award is out. Nominations are due in about four weeks.