Maths and medicine

The art of healing is not an exact science: an identical treatment, curative or preventive, applied to several groups of sick or healthy individuals, often yields paradoxical results, given the astonishing variety of living things. Whether it is to compare the effects of different drugs or placebos, to determine an ideal body mass index or to quantify the reliability of a screening test, the use of statistical and probabilistic reasoning proves indispensable in medicine.

External transmission of microbes or viruses as well as internal propagation of malignant cells follows algorithms whose modeling is governed by a branch of mathematics: that of dynamic systems. Associated with probability theory, the models thus constructed make it possible not only to predict the evolution of diseases, but also to make decisions, both in terms of individual therapy choices and in terms of public policy, for example regarding isolation or vaccination.

Behind new medical techniques, mathematics hide more than ever. The development of imaging, whose most well-known tools are the scanner or the MRI, has revolutionized practices. Many branches of mathematics were called upon to develop these new technologies: geometry, Fourier analysis, the Radon transform and, more recently, wavelet theory. Furthermore, more and more individuals are testing, via their smartphone, various indicators such as their heart rate, their blood pressure or their weight. This may be useful, but not without risk…