ON THE PERCEPTION OF SCIENCE IN MODERN TIMES - MATHEMATICS AND THE VIEW OF THE WORLD IN EARLY MODERN TIMES - The Remarkable Role of Evolution in the Making of Mathematics - Mathematics and the Real World

Mathematics and the Real World: The Remarkable Role of Evolution in the Making of Mathematics (2014)

CHAPTER III. MATHEMATICS AND THE VIEW OF THE WORLD IN EARLY MODERN TIMES

23. ON THE PERCEPTION OF SCIENCE IN MODERN TIMES

Following the huge strides taken in the development and progress in understanding the world, a modern philosophical approach took shape with regard to how science operates and how nature is understood. We will summarize that philosophy very briefly. First, mathematics occupied its rightful position in the center of the stage. No scientific finding was considered understandable unless it was supported by mathematics that described it both qualitatively and quantitatively. Second, the requirement that mathematical principles explaining the findings must reflect some sort of purpose was abandoned. The very fact that a law of nature can be described by a simple and elegant mathematical description constitutes a purpose. The description can be in the form of an equation that nature “solves,” or in the form of a “purpose,” for example, to minimize a certain quantity, such as minimizing the time a process takes or minimizing effort. Newton's contribution showed that a special, new mathematics can be developed that is appropriate for the description and analysis of natural phenomena that can be measured, and he thus cleared the path for the search of new mathematical systems to describe the laws of nature.

The empirical approach developed by Galileo Galilei in Italy and Francis Bacon in England (according to which the mathematical developments must be initiated based on experiments) has been adopted, but the predictions provided by mathematics would not be acceptable unless backed up by the results of experiments. In all aspects of the essence of mathematics and the link between mathematics and nature, despite the fact that the Aristotelian search for a purpose as the basis for all natural phenomena was abandoned, the new philosophy adopted Aristotle's formalistic attitude to mathematics (see section 11). The philosophy that developed in the early modern age still holds today, with certain refinements that we will discuss in the next chapter.