Believing that mathematics should be based on clear, simple, and solid evidence, he refrained from publishing his works until he met these conditions. Therefore, he is known for his meticulous approach to his work.
Karl Weierstrass is known as the father of modern analysis. He designed tests for the convergence of series and contributed to the theory of periodic functions, functions of real variables, elliptic functions, Abelian functions, convergent infinite products, and calculus of variations. He also developed the theory of bilinear and quadratic forms.
Believing that mathematics should be based on clear, simple, and solid evidence, he refrained from publishing his works until he met these conditions. Therefore, he is known for his meticulous approach to his work. Many of his contemporaries admired Karl's unity of thought. He is considered the most important German mathematician of the nineteenth century, after Gauss and Riemann.
Karl Theodor Wilhelm Weierstrass (31 October 1815 – 19 February 1897) was a German mathematician often cited as the "father of modern analysis". Despite leaving university without a degree, he studied mathematics and trained as a school teacher, eventually teaching mathematics, physics, botany and gymnastics. He later received an honorary doctorate and became professor of mathematics in Berlin.
He was born on 31 October 1815 in Ostenfelde, Westphalia (now Germany). His father, Wilhelm Weierstrass, is a well-educated person with extensive knowledge of the arts and sciences. Karl is the eldest of four children. When his mother dies, his father remarries. While attending Catholic High School, he works part-time with an accountant to contribute to the family budget. In the same period, he learned mathematics quite successfully and gave mathematics lessons to his brother.
When he finished high school in 1834, his father made him enroll at the University of Bonn. However, due to internal conflict, he cannot concentrate on either mathematics or finance. While in college, he attended fencing classes for four years and drank heavily.
After a while, he worked on Laplace's celestial mechanics and Carl Jacobi's theory of elliptic functions on his own. In 1838, he stayed at the University of Bonn for another term. Then he quits his finance education. Contrary to his father's opinion, he decided to concentrate on mathematics.
Saddened by this situation, his father provides the necessary conditions for his son to become a secondary school mathematics teacher. Afterward, Karl enrolled at the Münster Academy in 1839. The reason why he joined this academy with great enthusiasm is that the German mathematician Gudermann (1798 - 1852), who studied elliptic functions, was teaching at the same academy.
Teaching Life of Karl Weierstrass
Gudermann teaches his work to Karl. While under the influence of Gudermann, he prepared three more unpublished articles in 1841 and 1842. Weierstrass taught mathematics in West Prussia (now Poland) between 1842 and 1848; He also teaches physics, botany, geography, history, German, calligraphy, and even gymnastics. He had severe headache attacks for about 12 years from 1850, and this had a negative effect on his work.
With the article he wrote, Königsberg University awarded him an honorary doctorate degree on March 31, 1854. He takes a year off from the teaching profession in order to concentrate on his mathematics studies. In fact, he made this decision, never to return.
Karl's mathematical achievements attract the attention of students from many parts of the world. His lectures include the applications of the Fourier series to physics and mathematics, the theory of integrals, analytic functions, the application of elliptic functions to geometry and mechanics problems, and Abelian functions.
In December 1861, his health deteriorated considerably. He starts teaching again a year later. But it can never fully recover. While giving a lecture, a student writes on the board and he has to sit in a chair and lecture. His students include many famous mathematicians such as Sofia Kovalevskaya, Cantor (German Mathematician, 1845 – 1918), and Hensel (German Mathematician, 1861 – 1941). He published his works in two volumes in 1894 and 1895. All his works were published in a single volume in 1902, 1903, 1915, 1927, and 1967 after his death.
Sadly, he spent the last three years in a wheelchair before his death. He died in 1897 due to pneumonia he had suffered.
Weierstrass is a well-liked teacher by his students. He is interested in and supports their problems in both their academic and daily lives. Together with Kummer (German Mathematician, 1810 – 1893), he organized the first mathematics seminar in Germany.
His article “Zur Theorie der Abelschen Functionen – About the Theory of Abelian Functions” was published in 1854. This article not only gives a preliminary study of the inverses of hyperelliptic integrals developed by Karl but also gives preliminary definitions of methods representing commutative functions of continuously converging power series. In 1856, he improved his article, "Theorie der Abelschen Functionen - Theory of Abelian Functions", in which he presented preliminary definitions of inverses of hyperelliptic integrals.