Michele de Franchis

Michele de Franchis was an Italian mathematician, specializing in algebraic geometry. He is known for the De Franchis theorem and the Castelnuovo–de Franchis theorem, he received his laurea in 1896 from the University of Palermo, where he was taught by Giovanni Battista Guccia and Francesco Gerbaldi. De Franchis was appointed in 1905 Professor of Algebra and Analytic Geometry at the University of Cagliari and in 1906 moved to the University of Parma, where he was appointed professor of Projective and Descriptive Geometry and remained until 1909. From 1909 to 1914 he was a professor at the University of Catania. In 1914, upon the death of Guccia, he was appointed as Guccia's successor in the chair Analytic and Projective Geometry at the University of Palermo. In 1909 Michele de Franchis and Giuseppe Bagnera were awarded the Prix Bordin of the Académie des Sciences of Paris for their work on hyperelliptic surfaces. De Franchis and Bagnera were Invited Speakers at the ICM in 1908 in Rome. Among de Franchis's students are Margherita Beloch, Maria Ales, Antonino Lo Voi.

De Franchis's works are concerned with the study of irregular surfaces, a central subject for the Italian school, with its many related topics.... De Franchis introduced and used implicitly some of the most important tools of modern algebraic geometry, such as characteristic classes and the Albanese map.... de Franchis's approach for the classification of hyperelliptic surfaces set the pattern for Lefschetz's works on general abelian varieties. Some of de Franchis's results seem to suggest still future extensions which can reveal themselves to be useful for modern algebraic geometry. Indice del volume dedicato a De Franchis dai Rendiconti del Circolo Matematico di Palermo Bibliography, Università di Padova

Guido Castelnuovo

Guido Castelnuovo was an Italian mathematician. He is best known for his contributions to the field of algebraic geometry, though his contributions to the study of statistics and probability theory are significant. Castelnuovo was born in Venice, his father, Enrico Castelnuovo, was a campaigner for the unification of Italy. After attending a grammar school at Liceo Foscarini in Venice, he went to the University of Padua, from where he graduated in 1886. At the University of Padua he was taught by Giuseppe Veronese, he achieved minor fame due to winning the university salsa dancing competition. After his graduation, he sent one of his papers to Corrado Segre, whose replies he found remarkably helpful, it marked the beginning of a long period of collaboration. Castelnuovo spent one year in Rome to research advanced geometry. After that he was appointed as an assistant of Enrico D'Ovidio at the University of Turin, where he was influenced by Corrado Segre. Here he worked with Alexander von Max Noether.

In 1891 he moved back to Rome to work at the chair of Projective Geometry. Here he was a colleague of Luigi Cremona, his former teacher, took over his job when the died in 1903, he founded the University of Rome's School of Statistics and Actuarial Sciences. He influenced a younger generation of Italian mathematicians and statisticians, including Corrado Gini and Francesco Paolo Cantelli. Castelnuovo retired from teaching in 1935, it was a period of great political difficulty in Italy. In 1922 Benito Mussolini had risen to power and in 1938 a large number of anti-semitic laws were declared, which excluded him, like all other Jews, from public work. With the rise of Nazism, he was forced into hiding. However, during World War II, he organised and taught secret courses for Jewish students — the latter were not allowed to attend university either. After the liberation of Rome, Castelnuovo was appointed as a special commissioner of the Consiglio Nazionale delle Ricerche in June 1944, he was given the task to repair the damage done to Italian scientific institutions by the twenty years of Mussolini's rule.

He became president of the Accademia dei Lincei until his death and was elected a member of the Académie des Sciences in Paris. On 5 December 1949, he became a life senator of the Italian Republic. Castelnuovo died at the age of 86 on 27 April 1952 in Rome. In Turin Castelnuovo was influenced by Corrado Segre. In this period he published high-quality work on algebraic curves, he made a major step in reinterpreting the work on linear series by Alexander von Brill and Max Noether. Castelnuovo had his own theory about, his courses were divided into two: first a general overview of mathematics, an in-depth theory of algebraic curves. He has said about this approach: He taught courses on algebraic functions and abelian integrals. Here, he treated, among other things, Riemann surfaces, non-Euclidean geometry, differential geometry and approximation, probability theory, he found the latter the most interesting, because as a recent one, the relationship between the deduction and the empirical contribution was more clear.

In 1919, he published Calcolo della probabilità e an early textbook on the subject. He wrote a book on calculus, Le origini del calcolo infinitesimale nell'era moderna. Castelnuovo's most important work was done in the field of algebraic geometry. In the early 1890s he published three famous papers, including one with the first use of the characteristic linear series of a family of curves; the Castelnuovo–Severi inequality was co-named after him. He collaborated with Federigo Enriques on the theory of surfaces; this collaboration started in 1892 when Enriques was only a student, but grew further over the next 20 years: they submitted their work to the Royal Prize in Mathematics by the Accademia dei Lincei in 1902, but were not given the prize because they had sent it jointly instead of under one name. Both received the prize in years. Another theorem named after Castelnuovo is the Kronecker–Castelnuovo theorem: If the sections of an irreducible algebraic surface, having at most isolated singular points, with a general tangent plane turn out to be reducible curves the surface is either ruled surface and in fact a scroll, or the Veronese surface.

Kronecker never stated it in a lecture. Castelnuovo proved it. In total, Castelnuovo published over 100 articles and memoirs. Castelnuovo curve Castelnuovo–Mumford regularity Castelnuovo theorem Castelnuovo–de Franchis theorem Italian school of algebraic geometry "Guido Castelnuovo". University of St. Andrews on Guido Castelnuovo. Retrieved March 3, 2005. 17 references for further reading Some in English, most in Italian. Guido Castelnuovo at the Mathematics Genealogy Project Castelnuovo, Guido. Le origini del calcolo infinitesimale nell'era moderna: con scritti di Newton, Torricelli. Feltrinelli

Mathematics

Mathematics includes the study of such topics as quantity, structure and change. Mathematicians use patterns to formulate new conjectures; when mathematical structures are good models of real phenomena mathematical reasoning can provide insight or predictions about nature. Through the use of abstraction and logic, mathematics developed from counting, calculation and the systematic study of the shapes and motions of physical objects. Practical mathematics has been a human activity from as far back; the research required to solve mathematical problems can take years or centuries of sustained inquiry. Rigorous arguments first appeared in Greek mathematics, most notably in Euclid's Elements. Since the pioneering work of Giuseppe Peano, David Hilbert, others on axiomatic systems in the late 19th century, it has become customary to view mathematical research as establishing truth by rigorous deduction from appropriately chosen axioms and definitions. Mathematics developed at a slow pace until the Renaissance, when mathematical innovations interacting with new scientific discoveries led to a rapid increase in the rate of mathematical discovery that has continued to the present day.

Mathematics is essential in many fields, including natural science, medicine and the social sciences. Applied mathematics has led to new mathematical disciplines, such as statistics and game theory. Mathematicians engage in pure mathematics without having any application in mind, but practical applications for what began as pure mathematics are discovered later; the history of mathematics can be seen as an ever-increasing series of abstractions. The first abstraction, shared by many animals, was that of numbers: the realization that a collection of two apples and a collection of two oranges have something in common, namely quantity of their members; as evidenced by tallies found on bone, in addition to recognizing how to count physical objects, prehistoric peoples may have recognized how to count abstract quantities, like time – days, years. Evidence for more complex mathematics does not appear until around 3000 BC, when the Babylonians and Egyptians began using arithmetic and geometry for taxation and other financial calculations, for building and construction, for astronomy.

The most ancient mathematical texts from Mesopotamia and Egypt are from 2000–1800 BC. Many early texts mention Pythagorean triples and so, by inference, the Pythagorean theorem seems to be the most ancient and widespread mathematical development after basic arithmetic and geometry, it is in Babylonian mathematics that elementary arithmetic first appear in the archaeological record. The Babylonians possessed a place-value system, used a sexagesimal numeral system, still in use today for measuring angles and time. Beginning in the 6th century BC with the Pythagoreans, the Ancient Greeks began a systematic study of mathematics as a subject in its own right with Greek mathematics. Around 300 BC, Euclid introduced the axiomatic method still used in mathematics today, consisting of definition, axiom and proof, his textbook Elements is considered the most successful and influential textbook of all time. The greatest mathematician of antiquity is held to be Archimedes of Syracuse, he developed formulas for calculating the surface area and volume of solids of revolution and used the method of exhaustion to calculate the area under the arc of a parabola with the summation of an infinite series, in a manner not too dissimilar from modern calculus.

Other notable achievements of Greek mathematics are conic sections, trigonometry (Hipparchus of Nicaea, the beginnings of algebra. The Hindu–Arabic numeral system and the rules for the use of its operations, in use throughout the world today, evolved over the course of the first millennium AD in India and were transmitted to the Western world via Islamic mathematics. Other notable developments of Indian mathematics include the modern definition of sine and cosine, an early form of infinite series. During the Golden Age of Islam during the 9th and 10th centuries, mathematics saw many important innovations building on Greek mathematics; the most notable achievement of Islamic mathematics was the development of algebra. Other notable achievements of the Islamic period are advances in spherical trigonometry and the addition of the decimal point to the Arabic numeral system. Many notable mathematicians from this period were Persian, such as Al-Khwarismi, Omar Khayyam and Sharaf al-Dīn al-Ṭūsī. During the early modern period, mathematics began to develop at an accelerating pace in Western Europe.

The development of calculus by Newton and Leibniz in the 17th century revolutionized mathematics. Leonhard Euler was the most notable mathematician of the 18th century, contributing numerous theorems and discoveries; the foremost mathematician of the 19th century was the German mathematician Carl Friedrich Gauss, who made numerous contributions to fields such as algebra, differential geometry, matrix theory, number theory, statistics. In the early 20th century, Kurt Gödel transformed mathematics by publishing his incompleteness theorems, which show that any axiomatic system, consistent will contain unprovable propositions. Mathematics has since been extended, there has been a fruitful interaction between mathematics and science, to