**Lefschetz** was the main source of the algebraic aspects of topology.

- Since Lefschetz was educated in France from a young age, French was his first language.
- Fully understanding this, in November 1905 at the age of 21, Lefschetz went to the United States.
- As one might imagine this accident had a major mental impact on Lefschetz in addition to the physical disability he suffered.
- While on the graduate program at Clark, Lefschetz met one of the mathematics students Alice Berg Hayes.
- Lefschetz received his Ph.D. in mathematics in 1911 with a thesis on algebraic geometry entitled On the existence of loci with given singularities.
- That same year, 1911, Lefschetz was appointed an instructor in mathematics at the University of Nebraska in Lincoln, then, two years later, he was appointed to the University of Kansas in Lawrence.
- Poincaré had studied curves on a surface but Lefschetz pushed the ideas into much more general settings by building a theory of subvarieties of an algebraic variety.
- On Alexander's recommendation, in 1924 Lefschetz went to Princeton as a visiting professor for a year.
- But Lefschetz had overcome far more formidable obstacles in his life than a bunch of prissy Wasp snobs.
- Lefschetz worked on results which provided a deep generalisation of Émile Picard's theorems in function theory to several complex variables.
- Lefschetz was able to go further than Émile Picard and incorporate Poincaré's ideas.
- The word 'topology' comes from the title of a monograph written by Lefschetz in 1930.
- Lefschetz had two artificial hands over which he always wore a shiny black glove.
- For Lefschetz, independent thinking and originality were what mattered in mathematical research.
- Even if there is little truth in a joke which circulated about Lefschetz, namely that he never wrote a correct proof or stated an incorrect theorem, there is an underlying truth in it reflecting on his style of mathematics.
- In this somewhat indirect manner, Lefschetz profoundly affected the development of mathematics in the United States.
- Lefschetz was a strong supporter of the American Mathematical Society serving as its President from 1935 to 1936.
- In 1944 these two influences inspired Lefschetz to return to his interest in engineering but now he had deep mathematical skills which he could bring to bear on the problems.
- Although initially his work was rather concrete, over the years it became more abstract as Lefschetz developed it further.
- Lefschetz had many students working in this area and, between 1950 and 1960, a series of important publications Contributions to the theory of nonlinear oscillations appeared in the Annals of Mathematics Studies, published by Princeton University Press.
- From this work by Lefschetz's school, came the two important concepts of structural stability and genericity.
- Lefschetz did remarkable work even well into his 80's.
- During the 1920s and 1930s Lefschetz was able to indulge his love of travel with many trips to European countries.
- This was one of many honours which were awarded to Lefschetz.

Born 3 September 1884, Moscow, Russia. Died 5 October 1972, Princeton, New Jersey, USA.

View full biography at MacTutor

Origin Russia, Topology

**O’Connor, John J; Robertson, Edmund F**: MacTutor History of Mathematics Archive