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Linné on line arrow Mathematics in Linnaeus’ time arrow The infinitely small

The infinitely small

Illustration from Euler's Introductio in analysin infinitorum
Image taken from Euler's Introductio in analysin infinitorum (1748).

In the late 1600s a revolution took place in mathematics. Scholars had long attempted to understand the relationships between numbers and geometric objects like lines, plane figures, and bodies. It should be possible to measure lengths, areas, and volumes. But there always has to be a unit to measure with. Sometimes this is not possible. It is said that one of Pythagoras' students who discovered in the 5th century B.C. that the length of a diagonal in a square is not measurable was drowned in the sea. Such a horrifying discovery could not be allowed to be passed on.

Kvadrat med sidan a och diagonalen a roten ur 2
An irrational number, like √2 cannot be ”measured” with a unit.

It was difficult to understand infinity, or rather the infinitely small. It was possible to divide a length a finite number of times, any number of times, but not an infinite number of times, making it infinitely small. Newton and Leibniz succeeded in constructing theories for the infinitely small, the so-called infinitesimal.

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