Original version With This story appeared in How much warehouse.
The bill is a powerful mathematical tool. But for hundreds of years after his invention in the 17th century he stood at a shaky foundation. His basic concepts were rooted in intuition and informal arguments, not precise formal definitions.
According to two thinking schools, they appeared in response Michael BaranyHistorian of mathematics and science at the University of Edinburgh. French mathematicians were essentially content. They were more worried about using a differential account to problems in physics – using, for example, plaet trajectories or to test electrical currents. But in the nineteenth century German mathematicians began to break. They decided to find counter -arms that would undermine long assumptions, and eventually used these counter -examples to put the bill to a more stable and hard-wearing foundation.
Karl Weierstrass was one of these mathematicians. Although he showed early mathematics skills, his father forced him to study public finances and administration, having regard to joining the Prussian civil service. It is said that he spent most of his time on university courses drinking and fence; At the end of the 1830s, after he did not get a diploma, he became a high school teacher, giving lessons from everything from mathematics and physics to writing and gymnastics.
Weierstrass did not start his career as a professional mathematics until he was almost 40 years venerable. But he would change the field by introducing a mathematical monster.
Differential account pillars
In 1872, Weierstrass published a function that threatened everything that mathematicians thought they understood a differential account. He met with indifference, anger and fear, especially from the mathematical giants of the French school of thinking. Henri Poincaré condemned the function of Weierstrass as “indignation against common sense.” Charles Hermite called it “regretted evil.”
To understand why the WEPIERSTRASS result was so disturbing, it helps first understand the two most basic concepts of differential account: continuity and difference.
The continuous function is exactly as it sounds – a function that has no gaps or jumps. You can trace the path from any point to such a function to any other without lifting a pencil.
The bill is largely to determine how quickly such continuous functions change. It works, loosely, bringing a given function with plain, haphazard lines.
Illustration: Mark Belan/Quanta magazine