structural:reformatting
Mathematization

Scientific knowledge, according to the Aristotelians, was concerned with establishing true and necessary causes of things. To the extent that medieval natural philosophers used mathematical problems, they limited social studies to theoretical analyses of local speed and other aspects of life. The actual measurement of a physical quantity, and the comparison of that measurement to a value computed on the basis of theory, was largely limited to the mathematical disciplines of astronomy and optics in Europe.

In the 16th and 17th centuries, European scientists began increasingly applying quantitative measurements to the measurement of physical phenomena on the Earth. Galileo maintained strongly that mathematics provided a kind of necessary certainty that could be compared to God's: "...with regard to those few which the human intellect does understand, I believe its knowledge equals the Divine in objective certainty..."

Galileo anticipates the concept of a systematic mathematical interpretation of the world in his book Il Saggiatore:

Philosophy is written in this grand book—I mean the universe—which stands continually open to our gaze, but it cannot be understood unless one first learns to comprehend the language and interpret the characters in which it is written. It is written in the language of mathematics, and its characters are triangles, circles, and other geometrical figures, without which it is humanly impossible to understand a single word of it; without these, one is wandering around in a dark labyrinth.

In 1591 François Viète published In Artem Analyticem Isagoge, which gave the first symbolic notation of parameters in algebra. Newton's development of infinitesimal calculus opened up new applications of the methods of mathematics to science. Newton taught that scientific theory should be coupled with rigorous experimentation, which became the keystone of modern science.