mathematics

Péter Frankl

Péter Frankl 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 Péter Frankl rather than just read about it. In short: Péter Frankl (born 26 March 1953 in Kaposvár, Somogy County, Hungary) is a mathematician, street performer, columnist and educator, active in Japan. Frankl studied mathematics at Eötvös Loránd University in Budapest and submitted his PhD thesis while still an undergraduate.

Key takeaways

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

Reference excerpt

Péter Frankl (born 26 March 1953 in Kaposvár, Somogy County, Hungary) is a mathematician, street performer, columnist and educator, active in Japan. Frankl studied mathematics at Eötvös Loránd University in Budapest and submitted his PhD thesis while still an undergraduate. He holds a PhD degree from the University Paris Diderot as well. He has lived in Japan since 1988, where he is a well-known personality and often appears in the media. He keeps travelling around Japan performing (juggling and giving public lectures on various topics). Frankl won a gold medal at the International Mathematical Olympiad in 1971. He has seven joint papers with Paul Erdős, and eleven joint papers with Ronald Graham. His research is in combinatorics, especially in extremal combinatorics. He is the author of the union-closed sets conjecture.

Personality Both of his parents were survivors of concentration camps and taught him "The only things you own are in your heart and brain". So he became a mathematician. Frankl often lectures about racial discrimination.

Adolescence and abilities He could multiply two digit numbers when he was four years old. Frankl speaks 12 languages (Hungarian, English, Russian, Swedish, French, Spanish, Polish, German, Japanese, Chinese, Thai, Korean) and lectured mathematics in many countries in these languages. He has travelled to more than 100 countries.

Activities Frankl learnt juggling from Ronald Graham. He and Vojtěch Rödl solved a $1000 problem of Paul Erdős. Zsolt Baranyai helped Frankl to get a scholarship in France, where he became a CNRS research fellow. For 1984 to 1990, Frankl and Akiyama worked hard organizing a Japanese mathematical Olympiad team, and as a consequence the Japanese team is now a regular participant of the International Mathematical Olympiad. Since 1998, he is an external member of the Hungarian Academy of Sciences. He authored more than thirty books in Japanese, and with László Babai, he wrote the manuscript of a book on "Linear Algebra Methods in Combinatorics". With Norihide Tokushige he is the coauthor of the book Extremal Problems For Finite Sets (American Mathematical Society, 2018).

Frankl conjecture

For any finite union-closed family of finite sets, other than the family consisting only of the empty set, there exists an element that belongs to at least half of the sets in the family.

Illustrations

Worked examples

Example 1 — a first encounter with Péter Frankl

Start with the simplest possible case. Write down what Péter Frankl 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 Péter Frankl 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 Péter Frankl 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 Péter Frankl

In research: Péter Frankl 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 Péter Frankl 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: Péter Frankl is common in secondary-school and first-year university syllabi. It links to neighbouring topics 1953 births, 20th-century Hungarian mathematicians, 20th-century Hungarian people, so understanding it makes those chapters shorter.
In everyday life: Look for Péter Frankl 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 Péter Frankl in 20 minutes

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

Frequently asked questions

What is Péter Frankl in simple terms?

Why does Péter Frankl 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 Péter Frankl?

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 Péter Frankl.