Ulisse Dini (14 November 1845 – 28 October 1918) was an

Italia Italy ( it, Italia ), officially the Italian Republic, ) or the Republic of Italy, is a country in Southern Europe. It is located in the middle of the Mediterranean Sea, and its territory largely coincides with the homonymous geographical re ...

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, a ...

, 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 cit ...

. 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 converg ...

, 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 1810 wi ...

in order to become a teacher. One of his professors was

Enrico Betti Enrico Betti Glaoui (21 October 1823 – 11 August 1892) was an Italian mathematician, now remembered mostly for his 1871 paper on topology that led to the later naming after him of the Betti numbers. He worked also on the theory of equations, giv ...

. 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. S ...

, 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. Hermi ...

as well as

Joseph Bertrand Joseph Louis François Bertrand (; 11 March 1822 – 5 April 1900) was a French mathematician who worked in the fields of number theory, differential geometry, probability theory, economics and thermodynamics. Biography Joseph Bertrand was ...

, and published several papers. In 1866, he was appointed to the

University of Pisa The University of Pisa ( it, Università di Pisa, UniPi), officially founded in 1343, is one of the oldest universities in Europe. History The Origins The University of Pisa was officially founded in 1343, although various scholars place ...

, 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 a ...

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 equivale ...

. 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 (38 ...

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 ''

'' from 1908 until his death in 1918. He was also active as a

: 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 counc ...

, and in 1880, he became a member of the

Italian parliament The Italian Parliament ( it, Parlamento italiano) is the national parliament of the Italian Republic. It is the representative body of Italian citizens and is the successor to the Parliament of the Kingdom of Italy (1861–1943), the transitiona ...

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 S ...

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 In mathematics, Dini's criterion is a condition for the pointwise convergence of Fourier series, introduced by . Statement Dini's criterion states that if a periodic function ' has the property that (f(t)+f(-t))/t is locally integrable In mathema ...

for the

convergence Convergence may refer to: Arts and media Literature *''Convergence'' (book series), edited by Ruth Nanda Anshen *Convergence (comics), "Convergence" (comics), two separate story lines published by DC Comics: **A four-part crossover storyline that ...

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 ''p ...

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 gravi ...

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 multili ...

surface A surface, as the term is most generally used, is the outermost or uppermost layer of a physical object or space. It is the portion or region of the object that can first be perceived by an observer using the senses of sight and touch, and is ...

s, 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 Italians, Italian mathematician. He was born in Parma, Emilia-Romagna, and died in Pisa. He was a leading member of the vigorous Italian school of algebraic geometry, geometric school which fl ...

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)

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 Hermann Hankel (14 February 1839 – 29 August 1873) was a German mathematician. Having worked on mathematical analysis during his career, he is best known for introducing the Hankel transform and the Hankel matrix. Biography Hankel was born on ...

Gaston Darboux Jean-Gaston Darboux FAS MIF FRS FRSE (14 August 1842 – 23 February 1917) was a French mathematician. Life According this birth certificate he was born in Nîmes in France on 14 August 1842, at 1 am. However, probably due to the midnigh ...

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 Politecn ...

, Henry John Stephen Smith, Ulisse Dini,

Vito Volterra Vito Volterra (, ; 3 May 1860 – 11 October 1940) was an Italian mathematician and physicist, known for his contributions to mathematical biology and integral equations, being one of the founders of functional analysis. Biography Born in Anc ...

, Paul David Gustav du Bois-Reymond and

Carl Gustav Axel Harnack Carl Gustav Axel Harnack (, Dorpat (now ) – 3 April 1888, Dresden) was a Baltic German mathematician who contributed to potential theory. Harnack's inequality applied to harmonic functions. He also worked on the real algebraic geometry of pla ...

. *. ''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.

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