mathematics

Erik Ivar Fredholm

Erik Ivar Fredholm 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 Erik Ivar Fredholm rather than just read about it. In short: Erik Ivar Fredholm (7 April 1866 – 17 August 1927) was a Swedish mathematician whose work on integral equations and operator theory foreshadowed the theory of Hilbert spaces. Biography Fredholm was born in Stockholm in 1866.

Key takeaways

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

Reference excerpt

Erik Ivar Fredholm (7 April 1866 – 17 August 1927) was a Swedish mathematician whose work on integral equations and operator theory foreshadowed the theory of Hilbert spaces.

Biography Fredholm was born in Stockholm in 1866. He obtained his PhD at Uppsala University in 1898, under the supervision of Gösta Mittag-Leffler. He was docent at Stockholm University from 1898 to 1906 and professor from 1906 until his death. In 1914 he was elected a member of the Royal Swedish Academy of Sciences and in 1922 a foreign member of the Finnish Society of Sciences and Letters. Beside his academic career he was recruited to the Swedish Social Insurance Agency when it was founded in 1902. He later served as an actuary at the insurance company Skandia (1904-1927), where his Fredholm equation was used to calculate buyback-prices. From 1911, he was married to Agnes Maria Liljeblad, the secretary of Mittag-Leffler.

Mathematical work In (Fredholm 1900, 1903), Fredholm introduced and analysed a class of integral equations now called Fredholm equations. His analysis included the construction of Fredholm determinants, and the proof of the Fredholm theorems.

Honours Fredholm was a member of the Finnish Society of Sciences and Letters and of the Accademia dei Lincei; he was awarded the Poncelet Prize for 1908. The lunar crater Fredholm is named after him as is the asteroid 21659 Fredholm.

Publications Fredholm, I. (1900). "Sur une nouvelle méthode pour la résolution du problème de Dirichlet". Kong. Vetenskaps-Akademiens FBRH. Stockholm (in French): 39–46. JFM 32.0435.02. Fredholm, E.I. (1903). "Sur une classe d'équations fonctionnelles" (PDF). Acta Math. 27: 365–390. doi:10.1007/bf02421317. JFM 34.0422.02. Fredholm, I. (1955). Oeuvres complètes. Malmd: Litos Reprotryck.

Notes

References Netuka, Ivan; Veselý, Jiří (1977). "Ivar Fredholm and the origins of functional analysis". Pokroky Matematiky, Fyziky a Astronomie (in Czech). 22 (1): 10–21. hdl:10338.dmlcz/137665. MR 0532508. Zbl 0445.01009. Nörlund, N.E.; Carleman, Torsten (1928). "Nous avons le devoir douloureux d'annoncer la mort de notre collaborateur Erik Ivar Fredholm décédé à Mörby le 17 août 1927". Acta Math (in French). 51 (1): i–ii. doi:10.1007/bf02545657. MR 1555258. Zeilon, Nils (1930). "Ivar Fredholm". Acta Math (in French). 54 (1): I–XVI. doi:10.1007/bf02547515. MR 1555300. Stubhaug, Arild (2010). "The Big Poincaré Campaign". Gösta Mittag-Leffler. pp. 543–552. doi:10.1007/978-3-642-11672-8_66. ISBN 978-3-642-11671-1. Grenholm, Åke (1955). Försäkringsaktiebolaget Skandia 1855-1955. pp. 186–188.

External links O'Connor, John J.; Robertson, Edmund F., "Erik Ivar Fredholm", MacTutor History of Mathematics Archive, University of St Andrews Erik Ivar Fredholm at the Mathematics Genealogy Project Evans M. Harrell II, A Short History of Operator Theory (2004)

Illustrations

Worked examples

Example 1 — a first encounter with Erik Ivar Fredholm

Start with the simplest possible case. Write down what Erik Ivar Fredholm 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 Erik Ivar Fredholm 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 Erik Ivar Fredholm 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 Erik Ivar Fredholm

In research: Erik Ivar Fredholm 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 Erik Ivar Fredholm 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: Erik Ivar Fredholm is common in secondary-school and first-year university syllabi. It links to neighbouring topics 1866 births, 1927 deaths, 19th-century Swedish mathematicians, so understanding it makes those chapters shorter.
In everyday life: Look for Erik Ivar Fredholm 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.

Ask Teacher Smith questions about this articleOpens your AI tutor with a question about “Erik Ivar Fredholm” →

Affiliate

Preply — study more efficiently by working with a personal tutor. 50% off.

How to study Erik Ivar Fredholm in 20 minutes

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

Frequently asked questions

What is Erik Ivar Fredholm in simple terms?

Erik Ivar Fredholm (7 April 1866 – 17 August 1927) was a Swedish mathematician whose work on integral equations and operator theory foreshadowed the theory of Hilbert spaces. Biography Fredholm was born in Stockholm in 1866.

Why does Erik Ivar Fredholm 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 Erik Ivar Fredholm?

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 Erik Ivar Fredholm.