Original version of This story Appears in Quanta Magazine.
Calculus is a powerful mathematics tool. However, for hundreds of years since its invention in the 17th century, it stood on a volatile foundation. Its core concepts were rooted in intuition and informal arguments rather than accurate formal definitions.
In response, two ideas emerged accordingly Michael Baraniea historian of mathematics and science at the University of Edinburgh. French mathematicians were generally large content to continue. They were interested in applying computation to physics problems. For example, they used it to calculate the trajectory of a planet, and studied the behavior of currents. But by the 19th century, German mathematicians were beginning to demolish things. They set out to find counter exampurs that undermine long-standing assumptions, and eventually used those counterstoscrops to place calculus on a more stable and durable scaffold .
One of these mathematicians was Carl Wires Truss. Although he showed early aptitude for mathematics, his father turned to his attention to joining Prussian civil servants and pressured him to study finances and management. Woehr’s Truss, tired of his college coursework, is said to have spent most of his time drinking and fencing. In the late 1830s, after failing to earn his degree, he became a secondary school teacher, giving him all his lessons, from mathematics and physics to defensive and gymnastics.
WeierStrass did not begin his career as a professional mathematician until he was 40 years old.
The pillar of calculus
In 1872, WeierStrass published a feature that threatens everything that mathematicians think they have understood about calculus. He encountered indifference, anger and fear, especially from the mathematical giants of the French Faculty of Thought. Henri Poincaré has accused the Wire’s Truss of functioning as “anger towards common sense.” Charles Hermite called it “a lamentable evil.”
To understand why WeierStrass’ results have become so unsettling, we first help us understand two of the most basic concepts in calculus: continuity and discriminatory.
That’s exactly what continuous functions hear. This function has no gaps or jumps. You can trace paths from any point in such a function to other paths without lifting the pencil.
Calculus is to determine how quickly such a continuous function changes. It works roughly by approximating a particular function with a straight, non-vertical line.
Illustration: Mark Belan/Quanta Magazine
