mathematics

Jérôme Franel

Jérôme Franel 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 Jérôme Franel rather than just read about it. In short: Jérôme Franel (1859–1939) was a Swiss mathematician who specialised in analytic number theory. He is mainly known through a 1924 paper, in which he establishes the equivalence of the Riemann hypothesis to a statement on the size of the discrepancy in the Farey sequences, and which is directly followed (in the same journal) by a development on the same subject by Edmund Landau.

Key takeaways

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

Reference excerpt

Jérôme Franel (1859–1939) was a Swiss mathematician who specialised in analytic number theory. He is mainly known through a 1924 paper, in which he establishes the equivalence of the Riemann hypothesis to a statement on the size of the discrepancy in the Farey sequences, and which is directly followed (in the same journal) by a development on the same subject by Edmund Landau. Jérôme Franel was a citizen ("bourgeois") of Provence (Vaud, Switzerland). He was born on 29 November 1859 in Travers (Neuchâtel, Suisse) and died in Zürich on 21 November 1939. George Pólya said that he was an especially attractive kind of person and a very good teacher, but that, since he spent most of his time teaching and reading French literature (for which he had a passion), he had no time left for research. After his retirement he worked on the Riemann hypothesis.

Childhood and schools Jerôme Franel spent his first years with his 12 brothers and sisters in Travers. He graduated with a sciences highschool diploma from the "Ecole industrielle" in Lausanne. He then studied at the Politechnikum in Zürich, and in Berlin where he attended courses given by Weierstrass, Kronecker and Kummer, and finally in Paris where he attended courses by Hermite. On 15 September 1883 he was awarded a science bachelor's degree ("licence") from the Paris Academy.

Career Franel taught then for two years at the "Ecole industrielle" in Lausanne. On 1 April 1886, then only 26 years old, he was appointed to the Chair of Mathematics in the French language at the Politechnikum in Zürich by the Federal Council of Switzerland. In 1896 he was a member of the organizing committee of the first International Congress of Mathematicians, which took place in Zürich in 1897. He delivered the introductory lecture to the congress, written by Henri Poincaré, but who was then unwell. In 1905 the University of Zürich awarded him an honorary doctorate, and the city of Zürich awarded him honorary citizenship ("Bourgeoisie"). Under his presidency (1905–1909) the school was entirely restructured, and it was probably through his insistence (in particular, through a 1907 speech) that the Polytechnikum finally obtained (in 1908) the right to award a doctoral degree like the university did. The first doctorates were awarded in 1909. He retired in 1929.

References and notes

Jérôme Franel's necrology, by Louis Kollros, in: Verhandlungen der Schweizerischen Naturforschenden Gesellschaft 120 (1940), 439–444. Read french document online

External links Media related to Jérôme Franel (mathematician) at Wikimedia Commons

Illustrations

Worked examples

Example 1 — a first encounter with Jérôme Franel

Start with the simplest possible case. Write down what Jérôme Franel 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 Jérôme Franel 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 Jérôme Franel 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 Jérôme Franel

In research: Jérôme Franel 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 Jérôme Franel 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: Jérôme Franel is common in secondary-school and first-year university syllabi. It links to neighbouring topics 1859 births, 1939 deaths, 19th-century Swiss mathematicians, so understanding it makes those chapters shorter.
In everyday life: Look for Jérôme Franel 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 Jérôme Franel in 20 minutes

Read the reference excerpt below once, without taking notes.
Close the page and write down what Jérôme Franel 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.
Explain Jérôme Franel out loud to somebody else — or to Teacher Smith in the lgStudy chat.

Frequently asked questions

What is Jérôme Franel in simple terms?

Why does Jérôme Franel 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 Jérôme Franel?

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 Jérôme Franel.