Ernesto Cesàro

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Ernesto Cesàro

Ernesto Cesàro (born March 12, 1859 in Naples , † September 12, 1906 in Torre Annunziata ) was an Italian mathematician .

Ernesto Cesàro grew up in Torre Annunziata during difficult economic times of upheaval for the family (see Risorgimento ), where his father ran a farm. After his school education in Naples and Nola , Ernesto was sent to Liège by his father in 1873 , where his older brother Giuseppe Raimondo Pio Cesàro was a lecturer in mineralogy and crystallography at the École des mines . Since his efforts to gain admission to an Italian university were initially unsuccessful, he studied mathematics in Liège with Eugène Charles Catalan .

Cesàro returned to Torre Annunziata and married there. The death of his father in 1879 exacerbated his family's financial problems, but in the end he was able to go back to Belgium on the basis of a scholarship in 1882 and continue his studies. There he published his first treatise Sur diverses questions d'arithmétique the following year . During this time in Liège, Cesàro also visited Paris , where he attended lectures by Charles Hermite , Jean Gaston Darboux , Joseph Serret and others.

After a dispute with a professor in Liège, he returned to Italy without a degree. With the support of Luigi Cremona and Ulisse Dini , he received another scholarship that allowed him to do research at the University of Rome from 1884 . In the following two years he wrote eight papers on topics from arithmetic , function theory , probability theory and, influenced by Darboux, differential geometry . He already held a position at Terenzio Mamiani when he received his doctorate in 1887. He then accepted the offer for a teaching position in Palermo . From 1891 he held a chair for analysis in Naples, where he stayed until his death. In 1895 he was elected a corresponding member of the Accademia dei Lincei .

Cesàro died in tragic circumstances. While trying to help his 17-year-old son Manlio, who was in need , during a bathing trip in Torre Annunziata , he slipped in the bath cabin and sustained a fatal head injury.

Cesàro's main area of ​​work was differential geometry. He was also interested in number theory and improved Chebyshev's results on the prime number distribution . He also worked in mathematical physics , dealt with the theory of elasticity and contributed to the spread of Maxwell's electrodynamics .

Works

Ernesto Cesàro has written some important standard works:

  • Corso di analisi algebrica con introduzione al calcolo infinitesimale (1894) ISBN 1-4297-0100-5
  • Lezioni di geometria intrinseca (1896) ISBN 1-4297-0344-X ( also available in German under the title Lectures on Natural Geometry )
  • Elementi di calcolo infinitesimale con numerosi applicazioni geometriche (1905) ISBN 1-4297-0178-1

See also

  • Theorem of Stolz-Cesàro : A theorem about the existence of the limit of a quotient of two sequences.
  • Cesàro mean : the arithmetic mean of sequences and their convergence behavior.
  • Cesàro curve : a fractal curve.
  • Coprime : Cesàro's theorem about the probability that two randomly chosen natural numbers are coprime.

literature

Web links

personal data
SURNAME Cesàro, Ernesto
BRIEF DESCRIPTION Italian mathematician
DATE OF BIRTH March 12, 1859
PLACE OF BIRTH Naples
DATE OF DEATH September 12, 1906
Place of death Torre Annunziata