In these troubled times, when countless clouds are gathering over our heads, heralding destructive storms, it is urgent to praise mathematics, that difficult science, the most abstract of all, the furthest removed from the realities of the world.
This science is both particularly admired and increasingly neglected. In France in particular, it is both highly prized, as our country boasts a large number of Field medallists – the discipline’s equivalent of the Nobel Prize; and discredited, as it is less and less taught in the final year of secondary school, drying up the training streams not only for the mathematicians of the future, but also for physicists, chemists, biologists, computer scientists and engineers, who cannot do without this basic language for all their disciplines. Two examples, among others, of this French discredit: the reduction of mathematics teaching hours in high school; and, as we celebrate the 400th anniversary of Blaise Pascal’s birth, few people take this opportunity to note that he was the inventor of the first calculating machine and of the calculus of probabilities, that he came very close to the infinitesimal calculus and the integral calculus, that he made decisive advances in hydrodynamics and hydrostatics, and that geometry owes him major advances, in particular from his work on circle conchoid.
Having practised it extensively from my earliest youth, and continuing to keep abreast of its advances as much as possible, I can testify that it has provided me with some of my greatest intellectual joys. The infinite universe opened up by each of its various dimensions (arithmetic, geometry, algebra, analysis, probability), linking forms and objects for uses that are at first very prosaic (counting, measuring, evaluating), then much more abstract, moving away from any utilitarian use (such as the theory of distributions, vector theories, chaos theory, spectral theory, algebraic topology and many others), to find itself, very often, the only language capable of explaining the strangest, least intuitive (and most poetic, too) properties of nature, and more generally of the cosmos.
As if the universe, and all its creatures, had been conceived by mathematicians. And (even stranger), as if the human brain had been designed to conceive these theories, to deduce hidden laws from the rest of the universe.
It is much more than a science: it is a language, a universe, into which, once you’ve entered, you’re overwhelmed by the sheer scope of what you discover. It is also the gateway to the analysis of our world’s problems and solutions. Humanity has used it to build architectural, scientific, industrial, digital and biological marvels, as well as warlike monstrosities. Because, as with everything man discovers, nothing is good or bad; it all depends on how he uses it. And it is through mathematics and the sciences derived from it that we will find the essential solutions to the problems of the future. Nowadays, Artificial Intelligence, which is a new avatar of mathematics, will never replace the immensity of the universe opened up by its multifaceted science.
Finally, mathematics teaches us to reason rigorously, to make hypotheses, to draw conclusions from them, to use previous conclusions to go further, to distinguish between what is necessary and what is sufficient, to admit that what is true can be different from what is obvious or intuitive.
No one will be able to live freely in tomorrow’s world without mastering mathematics, to ensure that we make the best use of it.
Admittedly, it is not an easily accessible universe. One have to make a bit of an effort. Sometimes a lot. But no one is excluded. There’s no such thing as “math bulge”. It is all about hard work, learning to open that door and marvelling all that lies behind it. There are also marvellous teachers and increasingly well-tried methods, using text, images and even video games.
So, when we discuss sobriety, we must remember that nothing would be more awkward than a sobriety of the mind. Stop wasting fossil fuels, yes. Stop consuming artificial sugars, stop buying fast-fashion clothes, of course.
But never be sober in the acquisition of knowledge, in the practice of art, in conversation, in debate. Never stop learning, and learning mathematics first.
j@attali.com