The 50's to the 80's saw tremendous growth of applied math, driven mainly by PDEs and numerical algorithms. The integration of the two produced the "Courant School", which has had a far-reaching impact on applied math and beyond, particularly in the area of fluid mechanics.

Since the 90's, the Courant school has faced some serious challenges. On one hand, a lot of the basic problems in numerical analysis and PDEs were already solved, the ones left proved to be truly difficult. On the other hand, efforts to move beyond fluid mechanics have not reproduced the kind of success that applied math had in fluid mechanics. In fact, during this period of time, applied math benefited more from the growth of signal processing, such as wavelets, image processing  and compressed sensing.

Machine learning has come to the rescue for the Courant school, and it also provides the platform for the natural integration between the first principle-driven PDE school and the data-driven  harmonic analysis/statistics school. The integration of these two schools of thoughts will give rise to unprecedented power for solving the problems we have faced in applied math and computational science. At the same time, it also provides the final missing component for applied math to become a mature scientific discipline with a unified scope and curriculum that will boost our ability to attract and educate young talents.