mathematics

Gregory Freiman

Gregory Freiman 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 Gregory Freiman rather than just read about it. In short: Gregory Abelevich Freiman (Russian: Григорий Абелевич Фрейман; 3 July 1926 – 19 September 2024) was a Russian and Israeli mathematician known for his work in additive number theory, in particular, for proving Freiman's theorem. He was a professor emeritus in Tel Aviv University.

Key takeaways

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

Reference excerpt

Gregory Abelevich Freiman (Russian: Григорий Абелевич Фрейман; 3 July 1926 – 19 September 2024) was a Russian and Israeli mathematician known for his work in additive number theory, in particular, for proving Freiman's theorem. He was a professor emeritus in Tel Aviv University.

Biography Freiman was born in Kazan on 3 July 1926. He graduated from Moscow University in 1949, and obtained his Candidate of Sciences in Kazan University in 1956. From 1956 he worked in Elabuga, and in 1965 he defended his Doctor of Sciences degree under the joint supervision of Alexander Gelfond, Alexey G. Postnikov, and Alexander Buchstab. From 1967 he worked in Vladimir, and later in Kalinin (now Tver). In the 1970s and early 1980s Freiman participated in the refusenik movement. His samizdat essay It seems I am a Jew, described the discrimination against Jewish mathematicians in the Soviet Union. It was published in the US in 1980. Later, Freiman was driven out of Russia for his different views. He chose Israel as his new home country, leaving his son, daughter and wife. In Israel he became professor in Tel Aviv University and remarried. Freiman died on 19 September 2024, at the age of 98.

Selected publications Freiman, G.A. (1973). Foundations of a structural theory of set addition. Translations of Mathematical Monographs. Vol. 37. American Mathematical Society. with Boris M. Schein: Freiman, Gregory A.; Schein, Boris M. (1991). "Interconnections between the structure theory of set addition and rewritability in groups". Proc. Amer. Math. Soc. 113 (4): 899–910. doi:10.1090/s0002-9939-1991-1072338-3. MR 1072338. Freiman, G. A. (1999). "Structure Theory of Set Addition". Astérisque. 258: 1–33. MR 1701187. with Boris L. Granovsky: Freiman, Gregory A.; Granovsky, Boris L. (2005). "Clustering in coagulation-fragmentation processes, combinatorial structures and additive number systems: Asymptotic formulae and limiting laws". Trans. Amer. Math. Soc. 357 (6): 2483–2507. doi:10.1090/s0002-9947-04-03617-7. MR 2140447. Freiman, Gregory A. (2012). "On finite subsets of nonabelian groups with small doubling". Proc. Amer. Math. Soc. 140 (9): 2997–3002. doi:10.1090/s0002-9939-2012-11156-6.

Notes

Worked examples

Example 1 — a first encounter with Gregory Freiman

Start with the simplest possible case. Write down what Gregory Freiman 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 Gregory Freiman 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 Gregory Freiman 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 Gregory Freiman

In research: Gregory Freiman 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 Gregory Freiman 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: Gregory Freiman is common in secondary-school and first-year university syllabi. It links to neighbouring topics 1926 births, 2024 deaths, Academic staff of Tel Aviv University, so understanding it makes those chapters shorter.
In everyday life: Look for Gregory Freiman 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 Gregory Freiman in 20 minutes

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

Frequently asked questions

What is Gregory Freiman in simple terms?

Why does Gregory Freiman 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 Gregory Freiman?

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 Gregory Freiman.