In this essay we will discuss the significant impact of Karl Theodor Wilhelm Weierstrass on mathematics.
Karl Theodor Wilhelm Weierstrass was born October 31, 1815 in the small German town Ostenfeld, in Westphalia. His father, Wilhelm Weierstrass, was an officer, the secretary of the mayor. In those days it was a very prestigious position.
Charles was 11 years old when his mother died, Theodore Fonderforst. In his family, he was a senior, still had a brother, Peter, and two sisters, Clara and Eliza. Wilhelm Weierstrass was an educated man. It is known that in his youth he worked as a teacher, but as the salary of a teacher in Germany was very low, he decided to change his profession and became a clerk. The house Weierstrass reigned intellectual atmosphere, studied foreign languages sounded English and German, French and Latin.
Karl Weierstrass finished lower school and high school in Munster in Paderborn. During his studies at the gymnasium Paderborn fascinated the boy, studying languages. Gymnasium on the plaque is still his name was listed as one of the best students in the history of this institution.
He insisted on legal education, and Carl arrives at the Law Faculty of the University of Bonn, with his head dipped in student life. Of course, the first lecture, but there is still a feast and jousts that even though they were banned, but often occurred at clarifying the relationship between the student unions, of which there were a great many. Younger brother Charles, Peter Weierstrass recalls that Carl was a skilled swordsman, liked to fight duels and always won.
Eventually mathematics was dearer law, Karl Weierstrass stopped attending lectures and began teaching himself he studied mathematics. He laments that his father spent a lot of money for his education, which remained in vain. And in 1838, 23 -year-old Carl returns home after spending at Bonn University for four years, but has not received a certificate of graduation from the university.
What to do? Start all over again, but on another faculty? This is four years. Besides the family budget could not bear such expenses. Six months of reflection were the heaviest for Charles. Finally he decided: go to Munster and there to pass the exam for the title of master. Carl went to Munster, where a course of lectures on mathematics and beloved, most importantly, brilliantly passed the exam. Now he is - a graduate school teacher.
In the small town of Deutsch-Krone, north of Poznan, he began working as an assistant teacher. It is worth mentioning that in Munster Carl passed the exam facultae docendi, entitling lectures. Position regular teacher, he gets some time, making it more stable position, he gets a raise.
It is difficult to imagine how in such a wilderness as the Deutsch-Krone, but still working in the Catholic preschools, Karl managed to conduct scientific work. There was a library, the load reached 30 hours a week, moreover, Weierstrass led many more subjects: mathematics, physics, botany, geography, history, German language, calligraphy and gymnastics. In order to teach gymnastics, he even finished special courses.
For six years he worked in the Weierstrass Deutsch-Krone. He was a very good teacher. The secret to its success? The answer, of course, the identity of the Weierstrass addition, the teacher should have a good liberal arts education. Recall that the 15 -year-old Weierstrass perfectly proficient in humanities in Paderborn gymnasium.
So, six years of successful work as a teacher left behind, and 33 -year-old moved to Brownsburg Weierstrass, where he became a teacher in a Catholic school. It took another eight years. For scientific work conditions were better, was a scientific library. And the young mathematician with his head dipped into science. Once in high school a scandal has happened. Students sit in the classroom, waiting for the teacher, Karl Weierstrass, and he still was not. Headmaster very well disposed to Weierstrass, knew of his scientific work and strongly encouraged his pursuits. He went to the apartment and found the Weierstrass interesting picture: a young teacher sitting at his desk doing. He did not notice that it was morning already and I had to go to school.
Early mathematical work appeared in the weeklies Weierstrass preschools in Deutsch-Krone and gymnasium in Braunsberg. It was the turn and mathematical journal Crelle. The first article appeared Weierstrass in 1853, after which he immediately became known in the mathematical world, and the article was one of the best. A year later Weierstrass Konigsberg University awarded a PhD without protection - honoris causa.
But hard work at night is not wasted, his health deteriorated, there were headaches. Doctors diagnosed exhaustion. But work differently, he could not, the scientist did not spare himself.
Through publications Karl Weierstrass name becomes known, and was offered a professorship at the Industrial Institute in Berlin. July 16, 1856 Order of the Minister of Trade Weierstrass claim professor in the Department of Pure Mathematics, and after four months he became extraordinary professor at the University of Berlin. Just a week later Weierstrass elected to the Berlin Academy of Sciences. In 1861 he becomes an academician of the Bavarian Academy of Sciences.
Teaching activities in the Industrial Institute and the University absorbs it completely, it's sixteen hours a day. Scientist again not enough time, since the rest are engaged in scientific work. He did not rest. And during a lecture at the University of Weierstrass felt ill, he became dizzy. After this incident, he could not stand at the blackboard, he had to sit and dictate, and students were recorded. Nevertheless, all noted that the logic of presentation, fundamental, conciseness and clarity of lectures Weierstrass - are masterpieces.
He was entrusted to deliver a speech at the Academy of Sciences on the occasion of the birthday of Leibniz. New academic applause greeted say about the famous foursome mathematicians Kronecker, Kummer, Borchardt and Weierstrass. Among mathematicians Weierstrass greatly respected, loved him for his kindness, openness and responsiveness. Gradually he gets " unprecedented authority" in the academic world, in the words F.Kleyna. Lectures Weierstrass walk on her hands, he has a lot of ideas, he loves and knows how to put the challenge to young scientists, he - "generator of mathematical ideas."
His research focuses on mathematical analysis, the theory of functions, he gave a rigorous proof of the basic properties of continuous functions on an interval, also showed his talent in differential geometry and linear algebra.
Arriving in Berlin from Brownsburg, Weierstrass, who was already forty-one years, became Berliner until the end of his life, having lived here for forty years. He was unmarried, as well as his brother, Peter Weierstrass.
Famous student of mathematics was Sophia Kovalevskaya. She came from Russia to Berlin, when she was twenty, and Weierstrass - 55 years. Later they began to "you", closer, their linked scientific work and gentle human friendship. Sonia - so called her Weierstrass in his numerous letters of friendship.
A characteristic feature of the scientist as a great mathematician - is some slowness in publishing their findings results. He adhered to the system approach: first, they put forward the general idea, and then perform mathematical research. Everything must be done strictly and elegantly, and finally beautiful. And as for beauty could approach infinite, then Weierstrass lingered, polished, worked. " In the methods of Mr. Weierstrass was unusual clarity and rigor flavor " - wrote Zh.Molk Sofya Kovalevskaya.
Meanwhile, scientists continue to study science, but with less intensity, as feeling unwell, lecturing him hard. Not enough money for rest, treatment and long trips abroad. There were other troubles. Worsened relations with other famous mathematician Leopold Kronecker friend who was unusually touchy and irascible.
In 1875, Karl Weierstrass awarded one of the highest distinctions - "For merits in the field of science and the arts." To this class belongs pleasant events and celebrating the seventieth anniversary of Weierstrass. It went very heartily, had a lot of congratulations and articles, it was an international event. After celebrating the anniversary with Weierstrass sisters and adopted son Ferenhenom went to Switzerland for treatment.
After a wonderful holiday on Lake Geneva, in an atmosphere of pure, ringing air, he felt better. However, a year later he again begin to chase the disease. Absolutely refused feet, he veins, swollen legs. Weierstrass sick, but come to him colleagues, friends, students, young scientists. He is affable with all lights kindness. Now another mathematician and rector of the university, and this work is time-consuming. Many organizational affairs, you need to control all student organizations, to preside in the Senate, which controls the entire life of the university.
Weierstrass works at home, to care for it sister Clara and Eliza, who never married and devoted his life to the care of his older brother. Past three years, Karl Weierstrass moves around the apartment just in a chair on wheels.
80th anniversary of the great mathematician hardly mentioned, the doctor is not allowed to talk to him more than two hours. Among the friends was Johannes Knoblauch. It instructs him Karl Weierstrass custody of adopted son and the publication of his works.
In January 1897 a scientist with the flu and after complications leading to pneumonia, died February 19, 1897.
Edition of the works of the great mathematician was completed 30 years later, came seven volumes. In the first three - Weierstrass work in others - treatment of his lectures, clear, logical and perfect, they are the real pedagogical masterpieces. Scientists XX century tried to look into the creative laboratory of the great master. Some moments of creativity Karl Weierstrass not unraveled until now: it working just a teacher in the province, became a great scholar as he could get on their own mathematical education at the highest level, why so late - between thirty and forty years - creative flowering occurred away from research centers, in small provincial towns.
O'Connor, John J.; Robertson, Edmund F., "Karl Weierstrass", MacTutor History of Mathematics archive, University of St Andrews.
Grabiner, Judith V. (March 1983), "Who Gave You the Epsilon? Cauchy and the Origins of Rigorous Calculus", The American Mathematical Monthly 90 (3): 185–194, doi:10.2307/2975545, JSTOR 2975545
Biermann: Karl Weierstraß. Ausgewählte Aspekte seiner Biographie. Journal reine angew. Mathematik 1966.