Max Dehn facts for kids
Quick facts for kids
Max Dehn
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| Born | November 13, 1878 |
| Died | June 27, 1952 (aged 73) |
| Nationality | American |
| Alma mater | University of Göttingen |
| Known for | Dehn invariant Dehn's algorithm Dehn surgery Dehn's lemma Dehn twist Dehn function Dehn plane Dehn's rigidity theorem Dehn-Sommerville equations Dehn-Nielsen theorem |
| Scientific career | |
| Fields | Mathematics |
| Institutions | University of Münster Goethe University Frankfurt Black Mountain College |
| Doctoral advisor | David Hilbert |
| Doctoral students | Ott-Heinrich Keller Wilhelm Magnus Ruth Moufang |
Max Wilhelm Dehn (born November 13, 1878 – died June 27, 1952) was a German mathematician. He is famous for his important work in geometry, topology, and geometric group theory. These are all branches of mathematics. Dehn started his career in Germany. But he had to leave his job in 1935. He then fled Germany in 1939 and moved to the United States.
Dehn was a student of a very famous mathematician, David Hilbert. In 1900, Dehn solved one of Hilbert's big math problems. It was called Hilbert's third problem. This made him the first person to solve one of Hilbert's 23 famous problems. Max Dehn also taught many students who became great mathematicians themselves. He even mentored artists, showing how math connects to art.
Contents
Max Dehn's Life and Work
Max Dehn was born into a Jewish family in Hamburg, which was part of the German Empire at the time.
Early Studies and Discoveries
In 1899, he studied the basics of geometry with David Hilbert at the University of Göttingen. He proved a theorem about Jordan curves for shapes with straight sides. In 1900, he wrote his main paper about a geometry rule called the Legendre angle sum theorem. He created special shapes called Dehn planes. These shapes showed that the rule didn't always work in certain types of geometry.
From 1900 to 1911, Dehn worked as a researcher at the University of Münster. In 1900, he solved Hilbert's third problem. He did this by inventing something called the Dehn invariant. This was the very first time one of Hilbert's challenging math problems was solved.
Exploring Topology and Groups
Later, Dehn became very interested in topology and combinatorial group theory. Topology is about shapes and spaces. Group theory studies how things can be combined. In 1907, he wrote the first book on the basics of combinatorial topology with Poul Heegaard. It was known as analysis situs back then. Also in 1907, he described how to build a new type of homology sphere.
In 1908, Dehn thought he had proved the Poincaré conjecture. This was another very famous math problem. But another mathematician, Tietze, found a mistake in his proof.
In 1910, Dehn published a paper about three-dimensional topology. In this paper, he introduced Dehn surgery. He used it to create more homology spheres. He also mentioned Dehn's lemma. However, a mistake was found in his proof by Hellmuth Kneser in 1929. The correct proof was finally given in 1957 by Christos Papakyriakopoulos. In 1911, Dehn also asked a famous question called the word problem for groups.
Later Discoveries and Family Life
Max Dehn married Antonie Landau on August 23, 1912. In the same year, Dehn invented what is now called Dehn's algorithm. He used it to solve problems related to groups. The idea of a Dehn function is also named after him. This function helps measure how complex certain math problems are.
In 1914, he proved that the left and right trefoil knots are different. In the early 1920s, Dehn introduced a result known as the Dehn-Nielsen theorem. Its proof was published in 1927 by Jakob Nielsen.
Teaching and Moving to America
In 1922, Dehn took over from Ludwig Bieberbach at the Goethe University Frankfurt. He stayed there until he was forced to retire in 1935. During this time, he led a special class about old math books. Many smart mathematicians, like Carl Ludwig Siegel and André Weil, attended this class. Weil thought Dehn's class was his most important contribution to mathematics.
Dehn stayed in Germany until January 1939. Then he fled to Copenhagen, Denmark. From there, he went to Trondheim, Norway, and worked at the Norwegian Institute of Technology. In October 1940, he left Norway for America. He traveled a very long way through Siberia and Japan because crossing the Atlantic Ocean was too dangerous during the war.
In America, Dehn first worked at Idaho Southern University. This school is now called Idaho State University. In 1942, he got a job at the Illinois Institute of Technology. In 1943, he moved to St. John's College in Maryland. Finally, in 1945, he moved to an unusual arts college called Black Mountain College. He was the only mathematician there.
He passed away in Black Mountain, North Carolina in 1952.
Time at Black Mountain College
In March 1944, Max Dehn was asked to give two talks at Black Mountain College. He decided to talk about the history and ideas behind mathematics. He felt that a very advanced math lecture would not be right for the audience. Instead, he gave talks like "Common roots of mathematics and ornamentics." He also spoke about "Some moments in the development of mathematical ideas."
Soon after, the college offered him a full-time job. After agreeing on a salary, Dehn and his wife moved into housing provided by the school. He started teaching in January 1945.
Teaching Style and Influence
At Black Mountain College, Dehn taught many subjects. These included Mathematics, Philosophy, Greek, and Italian. In his class called "Geometry for Artists," Dehn taught students about basic geometry. They learned about points, lines, planes, and solids. He also taught about cones and how they can be cut into circles, ellipses, parabolas, and hyperbolas. Students also studied spheres and regular polyhedrons. His classes focused on how different shapes relate to each other. This idea is very useful in art.
Dehn loved the forested mountains around Black Mountain. He often held his classes outdoors in the woods. He would give lectures during hikes. His talks often went off-topic. He would discuss philosophy, art, and nature, and how they connected to mathematics. He and his wife were active in the college community. They often ate meals in the dining room. They also had long breakfasts with the famous inventor Buckminster Fuller and his wife.
In the summer of 1952, Dehn was made a Professor Emeritus. This meant he could stay on campus and continue to advise students. Sadly, he died of a blood clot shortly after. He passed away after seeing several dogwood trees removed from the campus. He is buried in the woods on the campus grounds.
See also
In Spanish: Max Dehn para niños Many math ideas are named after Max Dehn. Some of them include:
- Dehn's rigidity theorem
- Dehn invariant
- Dehn's algorithm
- Dehn's lemma
- Dehn plane
- Dehn surgery
- Dehn twist
