Original version of This story appeared in How many magazines.
Calculus is a powerful mathematical tool. But hundreds of years after his invention in the 17th century, he stood on a trembling foundation. Its fundamental concepts are rooted in intuition and informal arguments, not precise formal definitions.
Two thoughts of thoughts appeared in response, according to Michael Baranyhistorian of mathematics and science at the University of Edinburgh. French mathematicians were largely to continue. They were more involved in applying the calculations to the problems in physics – using it to calculate the planet path, for example, or to study the behavior of electrical currents. But by the 19th century, German mathematicians began to overthrow things. They intended to find a counter-recreation that would undermine long-term assumptions, and eventually used these counter-recreationals to put an account on a more stable and durable basis.
One of these mathematicians was Karl Weierstrass. Although he showed an early ability for mathematics, his father pressed him to study public finances and administration, with the aim of joining the Prussian civil service. Bored with his university courses, Weierstress is said to have spent most of his time drinking fences; In the late 1830s, after not being able to acquire a diploma, he became a high school teacher, giving lessons in everything, from mathematics and physics to Penman and gymnastics.
Weierstress did not start his career as a professional mathematician until he was almost 40. But he would continue to transform the field by introducing a mathematical monster.
Calculation columns
In 1872, Weierstress published a function that threatened everything that mathematicians thought they understood about calculating. He met indifference, anger and fear, especially from the mathematical giants of the French school of thought. Henri Poincaré condemned Weierstrass’s function as “anger against common sense.” Charles Hermite called it “bereaved crimes.”
In order to understand why the result of Weierstrassa was so nervous, it helps to first understand the two most basic concepts in calculating: continuity and diversity.
A continuous function is exactly the way it sounds – a function that has no emptiness or jumps. You can follow the path from any point in such a function to any other without lifting the pen.
The calculation is largely in determining how quickly such continuous functions change. It acts, gently speaking, approaching a particular function with flat, non -vertical lines.
Illustration: Magazine Mark Belan/Quanto