It is well-known that mathematics are everywhere nowadays, from the design and improvement of most things that we use every day to the ubiquitous algorithms that govern our lives more and more. After a brief discussion of the nature of maths today, we wish to recall some historical facts that go back to the dawn of mathematics and that emphasize the fast growing role of mathematics with the use of computers and machine learning (AI). We shall describe how real world problems are being tacked with the help of mathematical models and equations that are often partial differential equations. And we wish to emphasize how the study of applications goes hand in hand with the development of maths. We will do so by discussing, without mathematical details, examples using Mean Field Games theory or random matrices.