Today, mathematics is the focus of attention in education and research, in technological innovation and in international economic competition. More and more studies and comparisons are revealing the penalties inflicted on societies where the handling of knowledge, reasoning and information associated with mathematical knowledge is weakening. And in societies overexposed to algorithmic tools and productions, numeracy is becoming a major civic issue. And yet, in France, the gap is widening between the still high value of our mathematical research and the training of students, which is losing effectiveness and equity. Elsewhere, great nations are reacting effectively to educate their youth and attract talent. To understand this trend, we need to explore the inner workings of this prestigious, demanding and intimidating science.