Stobaeus recounts, in his book Florilegium, an anecdote that took place with Euclid on the first day of class. The Greek mathematician had just finished explaining the first theorem when a student interrupted him, asking: “What benefit will I get from this?” Euclid called for a slave and ordered: “Give him a coin, since he needs to profit from what he learns.”

To learn to appreciate mathematics, as Abraham Flexner would say, we must abolish the word utility and thus free the human spirit. Learning and doing mathematics, first and foremost, is a personal experience. Mathematics connects two faculties: intuition and reason. It is an intimate, silent yet vibrant dialogue between immediacy and reflection. Every small step we take is guided by intuition, but it is not a firm step until reason validates it.

David Bessis, in his book Mathematica: Une aventure au cœur de nous-mêmes, presents an interesting example related to this idea. We draw a circle on a sheet of paper and ask ourselves: at most, how many points will a straight line crossing the page intersect the circle? Intuition gives us an immediate answer: a single straight line will intersect the circle at most at two points. This intuitive solution is as certain as it is simple to reach. However, if we want to prove it formally, we’ll need the equation of the line, the equation of the circle, and we’ll have to solve a system to find the points of intersection. The algebraic solution gives us three possibilities: the line intersects the circle at two points, at no point, or at a single point (a tangent line). Thus, the reasoned answer confirms our initial intuition: at most, the line intersects the circle at two points. To validate this, we’ve used mathematical language. Moreover, in every step (formulating the proof, setting up the system, solving it, etc.) no matter how small each step may be, we constantly rely on intuition.

These continuous validations lead to an improvement in our mathematical intuition, which we can clearly observe evolving over time. In this sense—and also in other, more mundane ways that we won’t delve into now—mathematics invites us, above all, to experience its practice as a journey of personal growth.

Everything discussed so far is independent of the specific mathematics syllabus you may be working on. It applies equally to the most basic exercises in primary school and to the more complex topics in Algebra or Calculus at university level. Every course is a new opportunity to discover and deepen this understanding. The course in Statistics and Mathematical Analysis is one such opportunity. The Mathematical Analysis part is an extension of differential calculus to functions of more than one variable. In the second semester, we will focus on Probability and Statistics, which will likely be new to everyone.

If you’ve made it this far and are still unsure of what benefit you might gain from all this, let me add that this course also lays the mathematical foundations for many subjects you’ll encounter later on, such as: Signals and Transmission Systems, Knowledge-Based Systems, Electromagnetic Propagation, Acoustic Engineering, Audio and Speech Processing, Digital Signal Processing, Data Mining, Physical Simulation, Communications in Hostile Environments, Data Network Interconnection, Robotics, Optical Communications, Digital Image Processing, and more.

However, as mentioned earlier, we invite you to free yourselves from the need to find a practical use for mathematics, so that you can instead focus on the discipline itself, which is, in truth, a way of focusing on yourselves.