# Calogero Vinti

### Born: 12 July 1926 in Agrigento, Sicily, Italy

Died: 25 August 1997 in Perugia, Italy

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**Calogero Vinti**was brought up in his home town of Agrigento, close to the southern coast of Sicily. An important influence in Calogero's early education was an uncle who was a canon in the Cathedral San Gerlando in Agrigento. Calogero's education was disrupted by the events of World War II, particularly the allied invasion of Sicily in July 1943. However, once the war had ended, he was able to begin his university education at the University of Palermo. There he studied under Michele Cipolla who was a leading researcher in algebraic analysis, Benedetto Pettineo (1922-1989), a student of Cipolla's who had obtained his Laurea in 1944 and was publishing fundamental work in analysis, and Emilio Baiada (1914-1984) who had been a student of Leonida Tonelli.

In 1949 Vinti graduated from Palermo with his Laurea. His official advisor had been Pettineo but it was Baiada who was the strongest influence on him. He remained at Palermo undertaking research on partial differential equations and when Baiada returned from three years studying in the United States in 1952, the two began a close collaboration. They jointly published the 45-page paper

*Un teorema d'esistenza della soluzione per un'equazione alle derivate parziali del 1° ordine*Ⓣ in 1955 and also

*Un'applicazione della definizione di integrale per stabilire un passaggio al limite sotto il segno*Ⓣ in the same year. The first of these papers gives an existence theorem for the equation

*z*

_{x}=

*f*(

*x*,

*y*,

*z*,

*z*

_{y}) using methods which had been developed by Baiada a couple of years earlier in solving a simpler equation. The next two publications by Vinti,

*Una ripartizione del continuo ed una osservazione sulle funzioni continue rispetto ad una e non misurabili rispetto ad un'altra variabile*Ⓣ (1957) and

*L'integrale di Weierstrass*Ⓣ (1957) were single-authored but still greatly influenced by Baiada.

Vinti, who continued to work in Palermo, was very active in research over the next few years becoming a lecturer in analysis in 1960. As well as many significant papers continuing the themes of his earlier work, he did important work with Baiada on perimeters of sets. They presented some of their results on this topic in the paper

*Generalizzazione non markoviana della definizione di perimetro*Ⓣ given at the Celebrazioni Archimedee del Sec. XX in Syracuse in 1961. Baiada left Palermo and moved to Modena when he was appointed Professor of Mathematical Analysis at the University of Modena. He was keen for Vinti to join him and, in 1962, Vinti joined the faculty at the University of Modena.

He remained there until 1970 when he was named Professor of Analysis at the University of Perugia. At Perugia he gave the Department of Mathematics an international reputation with many leading researchers visiting his large research group. Among his most important publications during his years in Perugia, we mention

*On the Weierstrass integrals of the calculus of variations over BV varieties: recent results of the mathematical seminar in Perugia*(1989) and

*Problems associated with the theory of finitely additive measures: some recent results of the Scuola Matematica Perugina*(1990). He also established the Mathematical Summer Courses at Perugia, where lecturers from many countries gave courses on their speciality to the most talented young mathematicians. Let me add as a personal note that I [EFR] gave 25 lectures on Group Theory to this Summer School in 1986. The five weeks of the Summer School was an unforgettable experience, teaching enthusiastic bright students in the stunningly beautiful city of Perugia. One of the important developments that Vinti undertook at Perugia was founding the Faculty of Engineering. He was made dean of the Faculty on its foundation in 1986 and served in this capacity until 1995.

Vinti was married to Marisa who he first met when they were both students checking their examination results in Rome. Their eldest son Stefano became a lawyer and Professor in Rome while their son Gianluca became a mathematician with interests in approximation theory similar to those of his father. We have mentioned some of Vinti's research contributions, but the range of his work is best seen from the publication [1] containing a selection of his papers. The Introduction explains this broad range:-

In addition to writing papers, Vinti also wrote some textbooks on mathematical analysis. He published two volumes ofThe scientific interests of Calogero Vinti covered several areas of Mathematical Analysis, from Calculus of Variations to Differential Equations, from Approximation Theory to Real Analysis and Measure Theory. This volume collects the most important contributions in these different topics. ... Beyond the mere scientific interest and the depth of the many original results, this collection has also a strong historical value, since it demonstrates the wide variety of his interests and emphasizes mostly the evolution of his research and the connections among the different themes, that were never seen as separated topics, but were always naturally treated in an interdisciplinary fashion.

*Lezioni di Analisi matematica*Ⓣ and, with his colleague Carlo Bardaro, the book of exercises

*Complementi ed Esercizi di Analisi Matematica*Ⓣ.

Let us now quote from some of the references to get a feeling for Vinti's character. Julian Musielak writes [8]:-

Paul Butzer expresses in [5] his:-It was May1993, as I met the first time Professor Calogero Vinti, on the occasion of my first visit to the Università degli Studi di Perugia. ... Later we met many times during my consecutive visits to the Dipartimento di Matematica e Informatica of the University of Perugia, and to international conferences held in Italy. We met on the occasion of lectures, mathematical discussions, social events. I was many times a guest in his home, together with my wife Helena. There were the Professor and his wife Marisa, his son Gianluca, Professor Carlo Bardaro with his wife, my scientific collaborators, and usually some other friends. The more I knew him, the more I admired his personality. ... A professor caring for his students ... But also a man of great culture, a true son of the Italian soil, where one can find more pieces of art in a small town, than in a whole country elsewhere. A wise man, untouched by the totalitarian ideologies of the last century, friendly to the people, clear in logical thinking.

Butzer was invited by Vinti to lecture at a conference in Capri in 1990 [5]:-... deep appreciation and thanks to a man who not only influenced the science of mathematics, but whose kindness and sincerity made a tremendous impact on the people who knew him.

Vinti received many honours for his mathematical contributions. For example, his 70During my visit to Capri, I was also the thankful recipient of one of Calogero's most memorable acts of generosity to me: the unique hotel suite overlooking the beautiful Island of Capri that had been reserved for him and his spouse, Marisa.

^{th}birthday was marked by the 'Conferenze in Onore di Calogero Vinti' at the University of Perugia in September 1996. In the same year his achievements were recognised by the award of one of the most prestigious prizes in Italian universities, the Diploma di Medaglia d'Oro ai Benemeriti della Scienza, dell'Arte e della Cultura. After his death, the Italian Mathematical Union set up the "Calogero Vinti Prize" in 1998 to be awarded to a young mathematician who had made significant contributions to one of the fields in which Vinti had worked. Also in 1998, on the first anniversary of his death, the Engineering Faculty at Perugia had a memorial day on which they dedicated a plaque to his honour. This reads (in translation):-

His final paper wasCalogero Vinti, distinguished Master, Founder and first Dean of this Faculty, in memory of his fruitful work for the development of the Atheneum.

*A survey on recent results of the mathematical seminar in Perugia, inspired by the work of Professor P L Butzer*(1998). Butzer writes that this last paper [5]:-

... appeared in the Birkhauser international journal 'Results in Mathematics'; written in extreme pain, a witness to his perseverance, his passionate love for research and his willingness to continue transmitting his scientific knowledge to the end. This showed once again his great generosity, and the love which he related to his students.

**Article by:** *J J O'Connor* and *E F Robertson*

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**Mathematicians born in the same country**

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