Karl Weierstraß (1815-1897) was a German-born mathematician, father of complex analysis, and one of the founders of modern function theory. He is known for giving the first formal definition of the continuity of a function and for proving the Bolzano-Weierstrass theorem and the Weierstrass theorem.
Considered one of the most influential mathematicians of the 19th century, he taught and inspired some of the most talented mathematicians in Europe and made important contributions in elliptic functions, abelian functions, infinite convergent products, and the calculus of variations, among other areas.
Karl Weierstraß Source: Conrad Fehr (painter)
Biography
Karl Weierstraß was born on October 31, 1815 in the city of Ostenfelde, in Prussia (now part of Germany). His parents were Wilhelm Weierstraß and Theodora Vonderforst, who had three other children after Karl.
At birth, his father was secretary to the mayor of Ostenfelde and later became a tax inspector. This position made them travel very frequently, so Karl also had to move from one school to another as the family was transferred to Prussia.
In 1827 his mother, Theodora, died and a year later his father remarried. Despite having to work part-time as an accountant to help with family finances, Weierstraß achieved a level of mathematical proficiency far beyond expectations. He even taught one of his brothers.
However, Weierstraß's father diverted him from that initial inclination by wanting him to study finance, accounting and law. This is how at the age of 19 he sent him to the University of Bonn as he had planned.
Karl was internally struggling and did not attend classes or pay any attention to his career for 4 years, during which he indulged in drinking and returned home without a degree. At that time he devoted himself to studying mathematics on his own.
Dark years
It was in 1839 when, persuaded by a friend of his father's, he decided to enter the Theological and Philosophical Academy in Münster to become a secondary school teacher. There he studied under the influence of Cristof Gudermann, a professor of mathematics, particularly interested in the theory of elliptic functions.
Three years later, in 1842, he graduated as a teacher and began his 14-year career as a mathematics teacher. He obtained a position at the Pro-Gymnasium at Deutsche Krone (1842-1848) and at the Collegium Hoseanum in Braunsberg (1848-1856). At the same time, he worked incessantly in analysis and research, publishing some articles on elliptic and complex functions.
Weierstraß in later years described this stage of his life as one of "endless sadness and boredom," since he had neither a colleague for mathematical discussions nor access to an area library. Also, he couldn't afford to exchange scientific letters.
Life in the academy
Unexpectedly in 1854 Weierstraß's memoirs on the theory of abelian functions were published in Crelle's Journal, which attracted the attention of the University of Königsberg which went so far as to award him an honorary doctorate.
In the following years, European universities tried to attract Weierstraß to join its faculty, but in 1856 he chose to be a professor at the University of Berlin. This position was actually able to take over in 1864 because he had previously made commitments to the Berlin Institute of Industry.
The German mathematician managed to develop a great series of lectures: "Introduction to the theory of analytical functions", "Theory of elliptic functions", "Application of elliptic functions to problems of geometry and mechanics", "Theory of abelian functions", «Application of abelian functions to the solution of selected geometric problems» and «Calculus of variations».
He even gave one on "Synthetic Geometry," thus fulfilling a promise he made to the Swiss geometer, Jakob Steiner, before his death.
In 1861 he presented the first seminar dedicated exclusively to mathematics in Germany, in collaboration with Ernst Kummer. It was in that same year that he suffered a severe collapse, but it was not the first time that it happened as he had been experiencing serious health problems for more than a decade.
This time it took him almost a year to recover and from then on he sat down to give his lectures, while a student wrote on the blackboard for him.
During this phase as a university professor he influenced several students and future mathematicians such as Georg Cantor, Ferdinand Frobenius, Felix Klein, Hermann Schwarz, Gösta Mittag -Leffler, Sophus Lie and Sonya Kovalevskaya. An estimated 250 students attended his lectures.
Death
On February 19, 1897, in the city of Berlin, one of the founders of the modern theory of functions, Karl Weierstraß, died at the age of 81. The cause of his death was pneumonia, although he had lost the ability to move three years earlier.
Weierstraß published very little during his career, many of his findings were announced at his lectures. The first two volumes of his collected works were published before his death, and another five were published posthumously.
Contributions to science
Weierstraß provided a formal definition of continuity of a function. Source: Qualc1
Among the achievements of this German mathematician is his definitions of continuity, limit and derivative of a function, which are still used today. These constructs allowed him to tackle a set of theorems that had not been rigorously proved, such as the mean value theorem, the Bolzano-Weierstrass theorem, and the Heine-Borel theorem.
He is also notable for his contributions to the theory of periodic functions, functions of real variables, elliptic functions, abelian functions, convergent infinite products and the calculus of variations. He also devised tests for series convergence and advanced the theory of bilinear and quadratic forms.
Weierstraß is known as "the father of complex analysis" because he conceived and largely carried out a program known as the arithmeticization of analysis, which was based on a rigorous development of the real number system.
Today, complex analysis has many applications in engineering, in analytical number theory or the study of the properties of numbers and in string theory, a hypothesis about conformal-invariant quantum fields.
References
- American Psychiatric Association (2013). Diagnostic and Statistical Manual of Mental Disorders, Fifth Edition (DSM-V).
- Simpson, SA; Wilson, MP; Nordstrom, K (2016). Psychiatric Emergencies for Clinicians: Emergency Department Management of Alcohol Withdrawal. The Journal of emergency medicine.
- Walker, Valentina (2015). Alcohol Withdrawal: Symptoms, Treatment and Alcohol Detox Duration. Recovered from webmd.com.
- MedlinePlus (2017). Neonatal abstinence syndrome. Recovered from medlineplus.gov.
- PubMed Health. Neonatal Abstinence Syndrome. Recovered from ncbi.nlm.nih.gov.
- E Appiani, R Ossola, DE Latch, PR Erickson (2017). Aqueous singlet oxygen reaction kinetics of furfuryl alcohol. Recovered from pubs.rsc.org.
- SP Kurtz, ME Buttram, HL Surratt (2017). Benzodiazepine dependence among young adult participants in the club scene who use drugs. Journal of psychoactive drugs.