mathematics

Preda Mihăilescu

Preda Mihăilescu 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 Preda Mihăilescu rather than just read about it. In short: Preda V. Mihăilescu (Romanian pronunciation: [mihə.iˈlesku]) (born 23 May 1955) is a Romanian mathematician, best known for his proof of the Catalan's conjecture, first proposed in 1844.

Key takeaways

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

Reference excerpt

Preda V. Mihăilescu (Romanian pronunciation: [mihə.iˈlesku]) (born 23 May 1955) is a Romanian mathematician, best known for his proof of the Catalan's conjecture, first proposed in 1844.

Biography Born in Bucharest, he is the brother of Vintilă Mihăilescu. After leaving Romania in 1973, he settled in Switzerland. He studied mathematics and computer science in Zürich, receiving a PhD from ETH Zürich in 1997. His PhD thesis, titled Cyclotomy of rings and primality testing, was written under the direction of Erwin Engeler and Hendrik Lenstra. For several years, he did research at the University of Paderborn, Germany. Since 2005, he has held a professorship at the University of Göttingen.

Major research In 2002, Mihăilescu proved Catalan's conjecture. This number-theoretical conjecture, formulated by the French and Belgian mathematician Eugène Charles Catalan in 1844, had stood unresolved for 158 years. Mihăilescu's proof appeared in Crelle's Journal in 2004.

References

Sources P. J. Campbell (2002). "Science news 161". Mathematics Magazine. Vol. 75, no. 4. Ian Stewart (7 March 2013). The Great Mathematical Problems. Profile Books. p. 124. ISBN 978-1-84765-351-2. Bilu, Yuri F.; Bugeaud, Yann; Mignotte, Maurice (2014). The Problem of Catalan. Springer. OCLC 893117743. Metsänkylä, Tauno (2004). "Catalan's Conjecture: Another old Diophantine problem solved" (PDF). Bull. Amer. Math. Soc. 41: 43–57. doi:10.1090/s0273-0979-03-00993-5. MR 2015449. Mihăilescu, Preda (1997). Cyclotomy of rings and primality testing (Ph.D. thesis). ETH Zurich. Archived from the original on 4 March 2016. Mihăilescu, Preda (2004). "Primary Cyclotomic Units and a Proof of Catalan's Conjecture". Journal für die reine und angewandte Mathematik. 2004 (572): 167–195. doi:10.1515/crll.2004.048. MR 2076124. Mihăilescu, Preda (2005). Reflection, Bernoulli Numbers and the Proof of Catalan's Conjecture. European Congress of Mathematics. Stockholm, Sweden: European Mathematical Society. pp. 325–340. doi:10.4171/009-1/21. MR 2185753. Schoof, René (2008). Catalan's conjecture. Universitext. London: Springer. ISBN 978-1-84800-185-5. OCLC 656399081.

External links Preda Mihăilescu at the Mathematics Genealogy Project Web page at Göttingen Former Web page at Paderborn (no longer updated) Mihăilescu, Preda in libraries (WorldCat catalog)

Illustrations

Worked examples

Example 1 — a first encounter with Preda Mihăilescu

Start with the simplest possible case. Write down what Preda Mihăilescu 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 Preda Mihăilescu 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 Preda Mihăilescu 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 Preda Mihăilescu

In research: Preda Mihăilescu 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 Preda Mihăilescu 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: Preda Mihăilescu is common in secondary-school and first-year university syllabi. It links to neighbouring topics 1955 births, 20th-century Romanian mathematicians, 21st-century German mathematicians, so understanding it makes those chapters shorter.
In everyday life: Look for Preda Mihăilescu 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 Preda Mihăilescu in 20 minutes

Read the reference excerpt below once, without taking notes.
Close the page and write down what Preda Mihăilescu 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 Preda Mihăilescu in simple terms?

Preda V. Mihăilescu (Romanian pronunciation: [mihə.iˈlesku]) (born 23 May 1955) is a Romanian mathematician, best known for his proof of the Catalan's conjecture, first proposed in 1844.

Why does Preda Mihăilescu 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 Preda Mihăilescu?

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 Preda Mihăilescu.