Karl theodur wilhelm weierstrass biography

Then, copy and paste the text into your bibliography or works cited list. Because each style has its own formatting nuances that evolve over time and not all information is available for every reference entry or article, Encyclopedia. Karl Theodor Wilhelm Weierstrass gale. Learn more about citation styles Citation styles Encyclopedia. More From encyclopedia.

Karl Richard Lepsius. Karl Pearson. Karl Marx University. Karl Martin Leonhard Albrecht Kossel. Karl Kani Infinity, Inc. Karl Guthe Jansky. Karl Gustav Jacob Jacobi. Karl Georg Christian von Staudt. Karl Friedrich Wilhelm Ludwig. Karl Friedrich von Gaertner. Weierstrass did not receive the appointment at Breslau. According to Hilbert, he had realized one of the greatest achievements of analysis, the solution of the Jacobian inversion problem for hyperelliptic integrals.

There was talk if appointment to a post in Austria, but before formal discussions could take place Weierstrass accepted on 14 June an appointment as professor at the Industry Institute in Berlin, a forerunner of the Technische Hochschule. While he did not have to return to the Gymnasium in Braunsberg, his hopes for appointment to the University of Berlin had not been realized.

In Septemberwhile attending a conference of natural scientists in Vienna, Weierstrass was offered a special professorship at any Austrian university of his choice. He was still undecided a month later, when he was invited to the University of Berlin as associate professor. He accepted. On 19 November he became a member of the Berlin Academy.

It was not until July that he was able to leave the Industry Institute and assume a chair at the university. Having spent the most productive years of his life teaching elementary classes, far from the centers of scientific activity, Weierstrass had found time for his own research only at the expense of his health. Heavy demands were again made on him at Berlin, and on 16 December he suffered a complete collapse; he did not return to scientific work until the winter semester of Henceforth he always lectured while seated, consigning the related work at the blackboard to an advanced student.

Nevertheless, he became a recognized master, primarily through his lectures. It was only gradually that Weierstrass acquired the masterly skill in lecturing extolled by his later students. Initially his lectures were seldom clear, orderly, or understandable. His ideas simply streamed forth. Yet his reputation for lecturing on new theories attracted students from around the world, and eventually some students attended his classes.

Since no one else offered the same subject matter, graduate students as well as university lecturers were attracted to Berlin. Moreover, he was generous in suggesting topics for dissertations and continuing investigations.

Karl theodur wilhelm weierstrass biography

But the lack of rigor that he detected in all available works on the subject, as well as the fruitlessness of his own efforts to surmount this deficiency, frustrated him to the degree that he decided not to present this course again. His position concerning the applications of his research was clarified in his inaugural speech at the Berlin Academy on 9 Julyin which he stated that mathematics occupies an especially high place because only through its aid can a truly satisfying karl theodur wilhelm weierstrass biography of natural phenomena be obtained.

To some degree his outlook approached that of Gauss, who believed that mathematics should be the friend of practice, but never its slave. These lectures were given only out of a sense of obligation, however—not from any interest in the subject; for Weierstrass considered geometric demonstrations to be in very poor taste. If, as has been alleged, he sometimes permitted himself to clarify a point by using a diagram, it was carefully erased.

In addition to lecturing, Weierstrass introduced the first seminar devoted exclusively to mathematics in Germany, a joint undertaking with Kummer at the University of Berlin in Here again he developed many fruitful concepts that were frequently used by his students as subjects for papers. Auditors or participants in the seminar included Paul Bachmann.

Hermann Amandus Schwarz, and Otto Stolz. The philosopher Edmund Husserl —insofar as he was a mathematician—was also a student of Weierstrass. Weierstrass was not without his detractors: Felix Kleinfor instance, remarked that he and Lie had merely fought for their own points of view in the seminars. Doubts were not permitted to arise, and checking was hardly possible since Weierstrass cited very few other sources and arranged his methodical structure so that he was obliged to refer only to himself.

Schwarz 3 October :. It is self-evident that any and all paths must be open to a researcher during the actual course of his investigations; what is at issue here is merely the question of a systematic theoretical foundation. Although Weierstrass enjoyed considerable authority at Berlin, he occasionally encountered substantial resistance from his colleagues; and such criticism hurt him deeply.

Determined to prevent such a catastrophe, he resolved to remain in Berlin after all. They had a fruitful intellectual, and kindly personal relationship that "far transcended the usual teacher-student relationship". He mentored her for four years, and regarded her as his best student, helping to secure her a doctorate from Heidelberg University without the need for an oral thesis defense.

From until her death inKovalevskaya corresponded with Weierstrass. Upon learning of her death, he burned her letters. About of his letters to her have been preserved. Weierstrass was immobile for the last three years of his life, and died in Berlin from pneumonia on the 19th of February, Weierstrass was interested in the soundness of calculus, and at the time there were somewhat ambiguous definitions of the foundations of calculus so that important theorems could not be proven with sufficient rigour.

Although Bolzano had developed a reasonably rigorous definition of a limit as early as and possibly even earlier his work remained unknown to most of the mathematical community until years later, and many mathematicians had only vague definitions of limits and continuity of functions. The basic idea behind Delta-epsilon proofs is, arguably, first found in the works of Cauchy in the s.

Notably, in his Cours d'analyse, Cauchy argued that the pointwise limit of pointwise continuous functions was itself pointwise continuous, a statement that is false in general. The correct statement is rather that the uniform limit of continuous functions is continuous also, the uniform limit of uniformly continuous functions is uniformly continuous.

This required the concept of uniform convergencewhich was first observed by Weierstrass's advisor, Christoph Gudermannin an paper, where Gudermann noted the phenomenon but did not define it or elaborate on it. Weierstrass saw the importance of the concept, and both formalized it and applied it widely throughout the foundations of calculus.

He also proved the Bolzano—Weierstrass theorem and used it to study the properties of continuous functions on closed and bounded intervals. Weierstrass also made advances in the field of calculus of variations. Using the apparatus of analysis that he helped to develop, Weierstrass was able to give a complete reformulation of the theory that paved the way for the modern study of the calculus of variations.

Among several axioms, Weierstrass established a necessary condition for the existence of strong extrema of variational problems. He also helped devise the Weierstrass—Erdmann conditionwhich gives sufficient conditions for an extremal to have a corner along a given extremum and allows one to find a minimizing curve for a given integral. In later life Weierstrass described the "unending dreariness and boredom" of these miserable years in which [ 1 ] From around Weierstrass began to suffer from attacks of dizziness which were very severe and which ended after about an hour in violent sickness.

Frequent attacks over a period of about 12 years made it difficult for him to work and it is thought that these problems may well have been caused by the mental conflicts he had suffered as a student, together with the stress of applying himself to mathematics in every free minute of his time while undertaking the demanding teaching job. It is not surprising that when Weierstrass published papers on abelian functions in the Braunsberg school prospectus they went unnoticed by mathematicians.

This paper did not give the full theory of inversion of hyperelliptic integrals that Weierstrass had developed but rather gave a preliminary description of his methods involving representing abelian functions as constantly converging power series. With this paper Weierstrass burst from obscurity. In Weierstrass applied for the chair at the University of Breslau left vacant when Kummer moved to Berlin.

Kummerhowever, tried to influence things so that Weierstrass would go to Berlin, not Breslau, so Weierstrass was not appointed. A letter from Dirichlet to the Prussian Minister of Culture written in strongly supported Weierstrass being given a university appointment. Details are given in [ 10 ]. After being promoted to senior lecturer at Braunsberg, Weierstrass obtained a year's leave of absence to devote himself to advanced mathematical study.

He had already decided, however, that he would never return to school teaching. There was a move from a number of universities to offer him a chair. While universities in Austria were discussing the prospect, an offer of a chair came from the Industry Institute in Berlin later the Technische Hochschule. Although he would have prefered to go to the University of Berlin, Weierstrass certainly did not want to return to the Collegium Hoseanum in Braunsberg so he accepted the karl theodur wilhelm weierstrass biography from the Institute on 14 June Offers continued to be made to Weierstrass so that when he attended a conference in Vienna in September he was offered a chair at any Austrian university of his choice.

Before he had decided what to do about this offer, the University of Berlin offered him a professorship in October. This was the job he had long wanted and he accepted quickly, although having accepted the offer from the Industry Institute earlier in the year he was not able to formally occupy the University of Berlin chair for some years. Weierstrass's successful lectures in mathematics attracted students from all over the world.

We described above the health problems that Weierstrass suffered from onwards. Although he had achieved the positions that he had dreamed of, his health gave out in December when he collapsed completely. It took him about a year to recover sufficiently to lecture again and he was never to regain his health completely. From this time on he lectured sitting down while a student wrote on the blackboard for him.

The attacks that he had suffered from stopped and were replaced by chest problems. In his lectures he proved that the complex numbers are the only commutative algebraic extension of the real numbers. Gauss had promised a proof of this in but had failed to give one. In his emphasis on rigour led him to discover a function that, although continuous, had no derivative at any point.