Mathematics at Work

Abstract

In this chapter, we take a look at how the mathematical method works in modern science. In Newton’s work only such mechanical categories as space, time and motion (and the same for optical phenomena) were mathematized, but soon various qualities began to surrender to mathematics: colors, sounds, heat. All these qualities were reduced to mechanical quantities; in the case of heat with the help of statistical methods. It seemed that the whole universe was but a big, pointless mechanical construct. But soon the revolt began in the heart of physics itself. The discovery of electromagnetic theory in the second half of the 19th century triggered revolutionary changes at the very foundations of physics. In the first decades of the 20th century a new physics begun to emerge, and it was by no means “mechanistically dull.” If poets could follow its mathematical language, they would be delighted with its abstract fantasy, enormously surpassing any human imagination: light bending around celestial bodies, clocks accelerating and slowing down, space-times changing their geometries depending on the motion of masses, and the entirely new quantum worlds in which the material substances of elementary particles dissolve into probability waves. Even chaotic phenomena, which hitherto seemed to be reserved only for untamed contemplation, have now surrendered to the overwhelming mathematics. The miracles of mathematics were not exhausted in creating general relativity, quantum physics and chaos theory. Its power is still at work. It drives us to the final goal, the full unification of physics and the ultimate understanding of the world. And the inevitable question: does the mathematical method of investigating the world have any limits? We can only suspect that if such limits do exist, it is the mathematical method itself that would be powerful enough to discover them. And this indeed seems to be the case.