mathematics

Salvatore Pincherle

Salvatore Pincherle is a mathematics topic covered in the lgStudy science library. This page brings together a partial reference excerpt, illustrations, worked examples, real-world applications and a short study plan, so you can understand Salvatore Pincherle rather than just read about it. In short: Salvatore Pincherle (March 11, 1853 – July 10, 1936) was an Italian mathematician. He contributed significantly to (and arguably helped to found) the field of functional analysis, established the Italian Mathematical Union (Italian: "Unione Matematica Italiana"), and was president of the Third International Congress of Mathematicians.

Key takeaways

Salvatore Pincherle belongs to mathematics; place it in that map before memorising details.
Learn the definition first, then one example that makes the definition concrete.
Connect Salvatore Pincherle to a quantity you can measure, compute or draw — that is where exam questions come from.
Reproduce the core statement of Salvatore Pincherle from memory before moving on to harder problems.

Reference excerpt

Salvatore Pincherle (March 11, 1853 – July 10, 1936) was an Italian mathematician. He contributed significantly to (and arguably helped to found) the field of functional analysis, established the Italian Mathematical Union (Italian: "Unione Matematica Italiana"), and was president of the Third International Congress of Mathematicians. The Pincherle derivative is named after him.

Life and Works Pincherle was born into a Jewish family in Trieste (then part of the Austrian Littoral) and spent his childhood in Marseille, France. After completing his basic schooling in Marseille, he left in 1869 to study mathematics at the University of Pisa, where he was a student under both Enrico Betti and Ulisse Dini. After he graduated in 1874, he taught at a school in Pavia until he received a scholarship in 1877. After winning the scholarship and studying abroad at the University of Berlin, Pincherle met Karl Weierstrass. Pincherle contributed to Weierstrass' theory of analytic functions, and in 1880, influenced by Weierstrass, he wrote an expository paper in the Giornale di Matematiche, which proved to be a significant paper in the field of analysis. Throughout his life, Pincherle's work greatly reflected the influence that Weierstrass had on him. He later collaborated with Vito Volterra and explored Laplace transforms and other parts of functional analysis. From 1880 until 1928, Pincherle was a Professor of Mathematics at the University of Bologna. In 1901, collaborating with Ugo Amaldi, he published his main scientific book, Le Operazioni Distributive e loro Applicazioni all'Analisi. In Bologna in 1922, he established the Italian Mathematical Union and became its first President and held the position until 1936. In 1924, he attended the Second International Congress of Mathematicians in Toronto, Ontario, Canada. Four years later, he became President of the Third International Congress and played a significant role in re-admitting German mathematicians after a ban imposed because of World War I. At this Congress, Jacques Hadamard declared in his review lecture Le développement et le rôle scientifique du Calcul fonctionnel that Pincherle was one of the most prominent founders of functional analysis. Following the Third Congress, Pincherle retired from university. In honor of the centenary of his birth, the Italian Mathematical Union edited a selection of 62 of his notes and treatises; they were published in 1954 in Rome.

References O'Connor, John J.; Robertson, Edmund F., "Salvatore Pincherle", MacTutor History of Mathematics Archive, University of St Andrews Mainardi, Francesco; Gianni Pagnini (April 2003). "Salvatore Pincherle: the pioneer of the Mellin-Barnes integrals". Journal of Computational and Applied Mathematics. 153 (1): 331–342. arXiv:math/0702520. Bibcode:2003JCoAM.153..331M. doi:10.1016/S0377-0427(02)00609-X. S2CID 14117680.

External links Salvatore Pincherle at the Mathematics Genealogy Project

Illustrations

Worked examples

Example 1 — a first encounter with Salvatore Pincherle

Start with the simplest possible case. Write down what Salvatore Pincherle claims or describes in one sentence, then invent the smallest concrete situation in which that sentence is true. In mathematics, the smallest case is usually a single object, a single equation or a single measurement. Check that every symbol or term in your sentence has a meaning in that case.

Example 2 — changing one variable

Take the situation from Example 1 and change exactly one quantity: double it, halve it, or set it to zero. Predict what should happen to Salvatore Pincherle before you calculate. Comparing your prediction with the result is the fastest way to find out whether you understand the idea or only the words.

Example 3 — an exam-style question

Typical questions about Salvatore Pincherle ask you to (a) state it precisely, (b) apply it to given data, and (c) explain a limitation. Practise writing all three answers in under five minutes; the third part is what separates a full-mark answer from an average one.

Applications of Salvatore Pincherle

In research: Salvatore Pincherle appears in mathematics research whenever the underlying quantities have to be modelled precisely. Papers usually cite it as a starting assumption and then explore where it breaks down.
In technology and industry: Engineering practice reuses Salvatore Pincherle in design rules, simulations and safety margins. Knowing the idea lets you read a specification sheet and understand why the numbers look the way they do.
In the classroom: Salvatore Pincherle is common in secondary-school and first-year university syllabi. It links to neighbouring topics 1853 births, 1936 deaths, 19th-century Italian Jews, so understanding it makes those chapters shorter.
In everyday life: Look for Salvatore Pincherle outside the textbook — in sport, cooking, traffic, electronics or the sky above you. An example you found yourself is remembered far longer than one you were given.

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How to study Salvatore Pincherle in 20 minutes

Read the reference excerpt below once, without taking notes.
Close the page and write down what Salvatore Pincherle means in your own words.
Compare your version with the excerpt and mark what you missed.
Work through the three examples above with pen and paper.
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Frequently asked questions

What is Salvatore Pincherle in simple terms?

Why does Salvatore Pincherle matter?

Because it connects several mathematics ideas at once: it gives you a definition you can apply, a quantity you can calculate, and a way to check whether a result is plausible.

How should I study Salvatore Pincherle?

Read the excerpt, restate it from memory, then work through the examples and applications listed on this page. The five-step study plan above takes about twenty minutes.

What does this page cover?

It gives you a compact reference excerpt plus original lgStudy explanations, examples, applications and study material on Salvatore Pincherle.