Karl Weierstrass facts for kids
Quick facts for kids
Karl Weierstrass
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| Karl Weierstraß | |
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| Born | 31 October 1815 Ennigerloh, Kingdom of Prussia
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| Died | 19 February 1897 (aged 81) |
| Nationality | German |
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| Scientific career | |
| Fields | Mathematics |
| Institutions | Gewerbeinstitut, Friedrich Wilhelm University |
| Academic advisors | Christoph Gudermann |
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Karl Theodor Wilhelm Weierstrass (German: Weierstraß; 31 October 1815 – 19 February 1897) was a German mathematician. He is often called the "father of modern analysis". Analysis is a branch of mathematics that deals with limits, continuity, and derivatives.
Even though he left university without a degree, Karl Weierstrass studied mathematics and became a school teacher. He taught math, physics, botany, and even gymnastics. Later, he earned an honorary doctorate and became a professor of mathematics in Berlin. He helped make the definitions of mathematical ideas like "continuity" much clearer. He also proved important theorems, like the intermediate value theorem.
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Biography
Karl Weierstrass was born into a Catholic family in Ostenfelde, a village near Ennigerloh, in Germany. His father, Wilhelm Weierstrass, was a government official. His mother was Theodora Vonderforst.
Karl became interested in mathematics when he was a student at the Theodorianum school in Paderborn. After school, he went to the University of Bonn. His father wanted him to study law, economics, and finance to prepare for a government job. But Karl really wanted to study mathematics. He spent most of his time studying math on his own, and because of this, he left the university without a degree.
He then went to the Münster Academy, which was known for its math programs. His father helped him get into a teacher training school in Münster. Karl later became a certified teacher there. During this time, he learned about elliptic functions from his teacher, Christoph Gudermann.
From 1843, he taught in a town called Wałcz (then Deutsch Krone) and later at the Lyceum Hosianum in Braunsberg starting in 1848. Besides math, he also taught physics, botany, and gymnastics.
After 1850, Karl Weierstrass was sick for a long time. But he still managed to publish important math papers that made him famous. The University of Königsberg gave him an honorary doctor's degree on 31 March 1854. In 1856, he became a professor at the Gewerbeinstitut in Berlin. This institute later became part of the Technical University of Berlin. In 1864, he became a professor at the Friedrich-Wilhelms-Universität Berlin, which is now the Humboldt Universität zu Berlin.
In 1870, when he was 55, Weierstrass met Sofia Kovalevsky. He tutored her privately because she couldn't get into the university. They had a very productive working relationship. Weierstrass was not able to move much during the last three years of his life. He died in Berlin in 1897 from pneumonia.
Making Math More Accurate
Weierstrass was very interested in making sure that calculus was built on strong, clear rules. At the time, some definitions in calculus were a bit unclear. This made it hard to prove important math ideas with enough certainty.
Earlier, a mathematician named Bernard Bolzano had created a very clear definition of a limit in 1817. But most mathematicians didn't know about his work until much later. Many mathematicians had only vague ideas about limits and how functions were continuous.
The basic idea for proving limits (called Delta-epsilon proofs) first appeared in the work of Augustin-Louis Cauchy in the 1820s. However, Cauchy didn't clearly separate continuity from "uniform continuity" (a special kind of continuity) over a range of numbers. For example, Cauchy once said that if you add up many continuous functions, the result is always continuous. This is not always true. It's only true if the functions come together in a "uniform" way.
Weierstrass's teacher, Christoph Gudermann, first noticed this idea of "uniform convergence" in 1838. But he didn't fully explain it. Weierstrass saw how important this idea was. He made it a clear definition and used it widely to improve the foundations of calculus.
Weierstrass gave a clear definition of what it means for a function to be continuous. In simple words, a function is continuous at a point if, as you get very close to that point, the function's value also gets very close to the value at that point. He used this definition to prove the intermediate value theorem. He also proved the Bolzano–Weierstrass theorem and used it to study how continuous functions behave over certain ranges.
Solving Tricky Math Problems
Weierstrass also made big steps forward in a field called calculus of variations. This area of math deals with finding the best way to do something, like finding the shortest path between two points. Using the new, clearer math tools he helped create, Weierstrass completely remade this theory. This new way of thinking helped modern mathematicians study the calculus of variations much better.
Other Important Math Ideas
Many other important ideas in mathematics are named after Karl Weierstrass. Here are a few:
- Stone–Weierstrass theorem
- Casorati–Weierstrass theorem
- Weierstrass elliptic function
- Weierstrass function
- Weierstrass M-test
- Weierstrass preparation theorem
- Lindemann–Weierstrass theorem
- Weierstrass factorization theorem
- Weierstrass–Enneper parameterization
Students
Weierstrass taught many students who became famous mathematicians themselves, including:
Awards and Recognition
The lunar crater Weierstrass and the asteroid 14100 Weierstrass are named after him. There is also the Weierstrass Institute for Applied Analysis and Stochastics in Berlin, a research center for math.
His Writings
Here are some of the important books and papers Karl Weierstrass wrote:
- Zur Theorie der Abelschen Funktionen (1854)
- Theorie der Abelschen Funktionen (1856)
- Abhandlungen-1, Math. Werke. Bd. 1. Berlin, 1894
- Abhandlungen-2, Math. Werke. Bd. 2. Berlin, 1895
- Abhandlungen-3, Math. Werke. Bd. 3. Berlin, 1903
- Vorl. ueber die Theorie der Abelschen Transcendenten, Math. Werke. Bd. 4. Berlin, 1902
- Vorl. ueber Variationsrechnung, Math. Werke. Bd. 7. Leipzig, 1927
See Also
In Spanish: Karl Weierstraß para niños
- List of things named after Karl Weierstrass
