07/11/2018

Mathematics, the science that knows nothing of observation.

Reproduction of Marcelo Viana's column in Folha de S.Paulo.

The philosopher Auguste Comte (1798-1857), founder of Positivism, believed that science is the "investigation of reality." And he placed mathematics at the top: "It is through the study of mathematics, and only through this means, that one can form a correct and profound idea of what is meant by science."

This viewpoint, which makes the mathematical method the model and objective of all scientific investigation, is received in different ways. Mathematicians tend to repeat it whenever possible; colleagues from other fields are less enthusiastic.

One of the fiercest critics was the biologist Thomas H. Huxley (1825-1895), a self-taught man and formidable debater. Having embraced Charles Darwin's (1809-1882) ideas on evolution, he defended them with such vigor and passion that he became known as "Darwin's bulldog".

The two naturalists also had in common the fact that they knew almost nothing about mathematics. While Darwin lamented his ignorance, Huxley was irritated by it.

In an article in the Fortnightly Reviews magazine, Huxley presented a caricatured view: "The mathematician begins with some statements so obvious that they are called self-evident, and the rest of the work consists of subtle deductions from them." And he ridiculed Comte: "Does this mean that the only study that can give 'a correct and thorough idea of what is meant by science' is precisely this one (mathematics) which knows nothing about observation, experimentation, induction or causality?"

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