mathematics

Gábor Szegő

Gábor Szegő 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 Gábor Szegő rather than just read about it. In short: Gábor Szegő (Hungarian: [ˈɡaːbor ˈsɛɡøː]) (January 20, 1895 – August 7, 1985) was a Hungarian-American mathematician. He was one of the foremost mathematical analysts of his generation and made fundamental contributions to the theory of orthogonal polynomials and Toeplitz matrices building on the work of his contemporary Otto Toeplitz.

Key takeaways

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Reference excerpt

Gábor Szegő (Hungarian: [ˈɡaːbor ˈsɛɡøː]) (January 20, 1895 – August 7, 1985) was a Hungarian-American mathematician. He was one of the foremost mathematical analysts of his generation and made fundamental contributions to the theory of orthogonal polynomials and Toeplitz matrices building on the work of his contemporary Otto Toeplitz.

Life

Szegő was born in Kunhegyes, Austria-Hungary (today Hungary), into a Jewish family as the son of Adolf Szegő and Hermina Neuman. He married the chemist Anna Elisabeth Neményi in 1919, with whom he had two children. In 1912 he started studies in mathematical physics at the University of Budapest, with summer visits to the University of Berlin and the University of Göttingen, where he attended lectures by Frobenius and Hilbert, amongst others. In Budapest he was taught mainly by Fejér, Beke, Kürschák and Bauer and made the acquaintance of his future collaborators George Pólya and Michael Fekete. His studies were interrupted in 1915 by World War I, in which he served in the infantry, artillery and air corps. In 1918 while stationed in Vienna, he was awarded a doctorate by the University of Vienna for his work on Toeplitz determinants. He received his Privat-Dozent from the University of Berlin in 1921, where he stayed until being appointed as successor to Knopp at the University of Königsberg in 1926. Intolerable working conditions during the Nazi regime resulted in a temporary position at the Washington University in St. Louis, Missouri in 1936, before his appointment as chairman of the mathematics department at Stanford University in 1938, where he helped build up the department until his retirement in 1966. He died in Palo Alto, California. His doctoral students include Paul Rosenbloom and Joseph Ullman. The Gábor Szegö Prize, Szegő Gábor Primary School, and Szegő Gábor Matematikaverseny (a mathematics competition in his former school) are all named in his honor.

Works Szegő's most important work was in analysis. He was one of the foremost analysts of his generation and made fundamental contributions to the theory of Toeplitz matrices and orthogonal polynomials. He wrote over 130 papers in several languages. Each of his four books, several written in collaboration with others, has become a classic in its field. The monograph Orthogonal polynomials, published in 1939, contains much of his research and has had a profound influence in many areas of applied mathematics, including theoretical physics, stochastic processes and numerical analysis.

Tutoring von Neumann At the age of 15, the young John von Neumann, recognised as a mathematical prodigy, was sent to study advanced calculus under Szegő. On their first meeting, Szegő was so astounded by von Neumann's mathematical talent and speed that, as recalled by his wife, he came back home with tears in his eyes. Szegő subsequently visited the von Neumann house twice a week to tutor the child prodigy. Some of von Neumann's instant solutions to the problems in calculus posed by Szegő, sketched out on his father's stationery, are now on display at the von Neumann archive at Budapest.

Honours

Amongst the many honours received during his lifetime were:

Julius König Prize of the Hungarian Mathematical Society (1928) Member of the Königsberger Gelehrten Gesellschaft (1928) Corresponding member of the Austrian Academy of Sciences in Vienna (1960) Honorary member of the Hungarian Academy of Sciences (1965)

Bibliography The collected Papers of Gábor Szegő, 3 Vols (ed. Richard Askey), Birkhäuser, 1982, ISBN 3-7643-3063-5 Pólya, George; Szegő, Gábor (1972) [1925], Problems and Theorems in Analysis, 2 Vols, Springer-Verlag Szegő, Gábor (1933), Asymptotische Entwicklungen der Jacobischen Polynome, Niemeyer Szegő, Gábor (1939), Orthogonal Polynomials, American Mathematical Society; 2nd edn. 1955 Pólya, George; Szegő, Gábor (2016) [1951], Isoperimetric problems in mathematical physics, Annals of Mathematics Studies, vol. 27, Princeton University Press, ISBN 0691079889 Szegő, Gábor; Grenander, Ulf (1958), Toeplitz forms and their applications, Chelsea

Selected articles Szegő, G. (1920). "Beiträge zur Theorie der Toeplitzschen Formen". Math. Z. 6 (3–4): 167–202. doi:10.1007/bf01199955. S2CID 118147030. Szegő, G. (1921). "Beiträge zur Theorie der Toeplitzschen Formen, II". Math. Z. 9 (3–4): 167–190. doi:10.1007/bf01279027. S2CID 125157848. Szegő, G. (1935). "A problem concerning orthogonal polynomials". Trans. Amer. Math. Soc. 37: 196–206. doi:10.1090/s0002-9947-1935-1501782-2. MR 1501782. Szego, Gabriel (1936). "Correction". Trans. Amer. Math. Soc. 39 (3): 500. doi:10.2307/1989765. JSTOR 1989765. MR 1501861. Szegő, Gabriel (1936). "Inequalities for the zeros of Legendre polynomials and related functions". Trans. Amer. Math. Soc. 39: 1–17. doi:10.1090/s0002-9947-1936-1501831-2. MR 1501831. Szegő, Gabriel (1936). "On some Hermitian forms associated with two given curves of the complex plane". Trans. Amer. Math. Soc. 40 (3): 450–461. doi:10.1090/s0002-9947-1936-1501884-1. MR 1501884. Szegő, G. (1940). "On the gradient of solid harmonic polynomials". Trans. Amer. Math. Soc. 47: 51–65. doi:10.1090/s0002-9947-1940-0000847-6. MR 0000847. with A. C. Schaeffer: Schaeffer, A. C.; Szegő, G. (1941). "Inequalities for harmonic polynomials in two and three dimensions". Trans. Amer. Math. Soc. 50 (2): 187–225. doi:10.1090/s0002-9947-1941-0005164-7. MR 0005164. Szegő, G. (1942). "On the oscillations of differential transforms. I". Trans. Amer. Math. Soc. 52 (3): 450–462. doi:10.1090/s0002-9947-1942-0007170-6. MR 0007170. Szegő, G. (1943). "On the oscillations of differential transforms. IV. Jacobi polynomials". Trans. Amer. Math. Soc. 53 (3): 463–468. doi:10.1090/s0002-9947-1943-0008100-4. MR 0008100. with Max Schiffer: Schiffer, M.; Szegő, G. (1949). "Virtual mass and polarization". Trans. Amer. Math. Soc. 67: 130–205. doi:10.1090/s0002-9947-1949-0033922-9. MR 0033922. Szegő, G. (1950). "On certain special sets of orthogonal polynomials". Proc. Amer. Math. Soc. 1 (6): 731–737. doi:10.1090/s0002-9939-1950-0042546-2. MR 0042546. with Albert Edrei: Edrei, A.; Szegő, G. (1953). "A note on the reciprocal of a Fourier series". Proc. Amer. Math. Soc. 4 (2): 323–329. doi:10.1090/s0002-9939-1953-0053267-7. MR 0053267.

References

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Illustrations

Worked examples

Example 1 — a first encounter with Gábor Szegő

Start with the simplest possible case. Write down what Gábor Szegő 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 Gábor Szegő 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 Gábor Szegő 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 Gábor Szegő

In research: Gábor Szegő 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 Gábor Szegő 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: Gábor Szegő is common in secondary-school and first-year university syllabi. It links to neighbouring topics 1895 births, 1985 deaths, 20th-century Hungarian Jews, so understanding it makes those chapters shorter.
In everyday life: Look for Gábor Szegő 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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Frequently asked questions

What is Gábor Szegő in simple terms?

Why does Gábor Szegő 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.

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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.

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It gives you a compact reference excerpt plus original lgStudy explanations, examples, applications and study material on Gábor Szegő.