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Ulisse Dini (14 November 1845 – 28 October 1918) was an Italian
mathematician A mathematician is someone who uses an extensive knowledge of mathematics in their work, typically to solve mathematical problems. Mathematicians are concerned with numbers, data, quantity, structure, space, models, and change. History On ...
and
politician A politician is a person active in party politics, or a person holding or seeking an elected office in government. Politicians propose, support, reject and create laws that govern the land and by an extension of its people. Broadly speaking, ...
, born in
Pisa Pisa ( , or ) is a city and ''comune'' in Tuscany, central Italy, straddling the Arno just before it empties into the Ligurian Sea. It is the capital city of the Province of Pisa. Although Pisa is known worldwide for its leaning tower, the ci ...
. He is known for his contribution to
real analysis In mathematics, the branch of real analysis studies the behavior of real numbers, sequences and series of real numbers, and real functions. Some particular properties of real-valued sequences and functions that real analysis studies include conv ...
, partly collected in his book "''Fondamenti per la teorica delle funzioni di variabili reali''".


Life and academic career

Dini attended the
Scuola Normale Superiore The Scuola Normale Superiore in Pisa (commonly known in Italy as "la Normale") is a public university in Pisa and Florence, Tuscany, Italy, currently attended by about 600 undergraduate and postgraduate (PhD) students. It was founded in 181 ...
in order to become a teacher. One of his professors was Enrico Betti. In 1865, a scholarship enabled him to visit
Paris Paris () is the capital and most populous city of France, with an estimated population of 2,165,423 residents in 2019 in an area of more than 105 km² (41 sq mi), making it the 30th most densely populated city in the world in 2020. Si ...
, where he studied under
Charles Hermite Charles Hermite () FRS FRSE MIAS (24 December 1822 – 14 January 1901) was a French mathematician who did research concerning number theory, quadratic forms, invariant theory, orthogonal polynomials, elliptic functions, and algebra. ...
as well as Joseph Bertrand, and published several papers. In 1866, he was appointed to the University of Pisa, where he taught
algebra Algebra () is one of the broad areas of mathematics. Roughly speaking, algebra is the study of mathematical symbols and the rules for manipulating these symbols in formulas; it is a unifying thread of almost all of mathematics. Elementary ...
and
geodesy Geodesy ( ) is the Earth science of accurately measuring and understanding Earth's figure (geometric shape and size), orientation in space, and gravity. The field also incorporates studies of how these properties change over time and equival ...
. In 1871, he succeeded Betti as professor for
analysis Analysis ( : analyses) is the process of breaking a complex topic or substance into smaller parts in order to gain a better understanding of it. The technique has been applied in the study of mathematics and logic since before Aristotle (3 ...
and
geometry Geometry (; ) is, with arithmetic, one of the oldest branches of mathematics. It is concerned with properties of space such as the distance, shape, size, and relative position of figures. A mathematician who works in the field of geometry is c ...
. From 1888 until 1890, Dini was ''rettore'' of the Pisa University, and of the ''
Scuola Normale Superiore The Scuola Normale Superiore in Pisa (commonly known in Italy as "la Normale") is a public university in Pisa and Florence, Tuscany, Italy, currently attended by about 600 undergraduate and postgraduate (PhD) students. It was founded in 181 ...
'' from 1908 until his death in 1918. He was also active as a
politician A politician is a person active in party politics, or a person holding or seeking an elected office in government. Politicians propose, support, reject and create laws that govern the land and by an extension of its people. Broadly speaking, ...
: in 1871 he was voted into the Pisa
city council A municipal council is the legislative body of a municipality or local government area. Depending on the location and classification of the municipality it may be known as a city council, town council, town board, community council, rural coun ...
, and in 1880, he became a member of the Italian parliament.


Honors

He has been elected honorary member of
London Mathematical Society The London Mathematical Society (LMS) is one of the United Kingdom's learned societies for mathematics (the others being the Royal Statistical Society (RSS), the Institute of Mathematics and its Applications (IMA), the Edinburgh Mathematical ...
.


Work


Research activity

Dini worked in the field of mathematical analysis during a time when it was begun to be based on rigorous foundations. In addition to his books, he wrote about sixty papers. He proved the Dini criterion for the convergence of
Fourier series A Fourier series () is a summation of harmonically related sinusoidal functions, also known as components or harmonics. The result of the summation is a periodic function whose functional form is determined by the choices of cycle length (or '' ...
and investigated the
potential theory In mathematics and mathematical physics, potential theory is the study of harmonic functions. The term "potential theory" was coined in 19th-century physics when it was realized that two fundamental forces of nature known at the time, namely gra ...
and
differential geometry Differential geometry is a mathematical discipline that studies the geometry of smooth shapes and smooth spaces, otherwise known as smooth manifolds. It uses the techniques of differential calculus, integral calculus, linear algebra and mult ...
of surfaces, based on work by Eugenio Beltrami. His work on the theory of real functions was also important in the development of the concept of the measure on a set.See . The implicit function theorem is known in Italy as the Dini's theorem.


Teaching activity

One of his students was
Luigi Bianchi Luigi Bianchi (18 January 1856 – 6 June 1928) was an Italian mathematician. He was born in Parma, Emilia-Romagna, and died in Pisa. He was a leading member of the vigorous geometric school which flourished in Italy during the later years of ...
.


Books by U. Dini


Serie di Fourier e altre rappresentazioni analitiche delle funzioni di una variabile reale
(Pisa, T. Nistri, 1880)
Lezioni di analisi infinitesimale. vol. 1
(Pisa, T. Nistri, 1907–1915)
Lezioni di analisi infinitesimale.vol. 2 part 1
(Pisa, T. Nistri, 1907–1915)
Lezioni di analisi infinitesimale.vol. 2 part 2
(Pisa, T. Nistri, 1907–1915)
Fondamenti per la teorica delle funzioni di variabili reali
(Pisa, T. Nistri, 1878)


See also

* Dini criterion * Dini derivative * Dini test * Dini's theorem *
Dini's surface In geometry, Dini's surface is a surface with constant negative curvature that can be created by twisting a pseudosphere. It is named after Ulisse Dini and described by the following parametric equations: : \begin x&=a \cos u \sin v \\ y&=a \ ...
* Dini continuity * Dini–Lipschitz criterion


Notes


References

*. "''Riemann's conditions for integrability and their influence on the birth of the concept of measure''" (English translation of title) is an article on the history of measure theory, analyzing deeply and comprehensively every early contribution to the field, starting from Riemann's work and going to the works of Hermann Hankel, Gaston Darboux,
Giulio Ascoli Giulio Ascoli (20 January 1843, Trieste – 12 July 1896, Milan) was a Jewish-Italian mathematician. He was a student of the Scuola Normale di Pisa, where he graduated in 1868. In 1872 he became Professor of Algebra and Calculus of the Pol ...
,
Henry John Stephen Smith Prof Henry John Stephen Smith FRS FRSE FRAS LLD (2 November 1826 – 9 February 1883) was an Irish mathematician and amateur astronomer remembered for his work in elementary divisors, quadratic forms, and Smith–Minkowski–Siegel mass form ...
, Ulisse Dini, Vito Volterra, Paul David Gustav du Bois-Reymond and Carl Gustav Axel Harnack. *. ''Mathematics in the first half of the 20th century'' (English translation of the title) is a short survey on the development of mathematics in its various branches during the first half of the 20th century.


Further reading

*. *. *.


External links

* * {{DEFAULTSORT:Dini, Ulisse 1845 births 1918 deaths 19th-century Italian mathematicians 20th-century Italian mathematicians 20th-century Italian politicians Mathematical analysts People from Pisa University of Pisa faculty