A report on Stanislaw Ulam and Hugo Steinhaus

The Scottish Book from the Lwów School of Mathematics, which Steinhaus contributed to and probably saved during World War II.

The Scottish Café's building now houses the Universal Bank in Lviv, Ukraine.

Ivy Mike, the first full test of the Teller–Ulam design (a staged fusion bomb), with a yield of 10.4 megatons on 1 November 1952

The Sausage device of Mike nuclear test (yield 10.4 Mt) on Enewetak Atoll. The test was part of the Operation Ivy. The Sausage was the first true H-Bomb ever tested, meaning the first thermonuclear device built upon the Teller-Ulam principles of staged radiation implosion.

An artist's conception of the NASA reference design for the Project Orion spacecraft powered by nuclear propulsion

When the positive integers are arrayed along the Ulam spiral, prime numbers, represented by dots, tend to collect along diagonal lines.

An animation demonstrating the lucky number sieve. The numbers in red are lucky numbers

While in Lwów, Steinhaus co-founded the Lwów School of Mathematics and was active in the circle of mathematicians associated with the Scottish cafe, although, according to Stanislaw Ulam, for the circle's gatherings, Steinhaus would have generally preferred a more upscale tea shop down the street.

- Hugo Steinhaus

Its founders were Hugo Steinhaus and Stefan Banach, who were professors at the Jan Kazimierz University.

- Stanislaw Ulam

6 related topics with Alpha

Lwów School of Mathematics

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Group of Polish mathematicians who worked in the interwar period in Lwów, Poland (since 1945 Lviv, Ukraine).

Hugo Steinhaus

Stanisław Ulam

Stefan Banach

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Polish mathematician who is generally considered one of the 20th century's most important and influential mathematicians.

Otto Nikodym and Stefan Banach Memorial Bench in Kraków, Poland (sculpted by Stefan Dousa)

Scottish Café, meeting place of many famous Lwów mathematicians

Banach's grave, Lychakiv Cemetery, Lviv (Lwów, in Polish)

Decomposition of a ball into two identical balls - the Banach–Tarski paradox.

After completing his secondary education, he befriended Hugo Steinhaus, with whom he established the Polish Mathematical Society in 1919 and later published the scientific journal Studia Mathematica.

Stanislaw Ulam, another mathematician of the Lwów School of Mathematics, in his autobiography, quotes Banach as saying:

Lviv

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Largest city in Western Ukraine, and the sixth-largest in Ukraine, with a population of Lviv is one of the main cultural centres of Ukraine.

A satellite view of Lviv (Sentinel-2,
14 August 2017)

A 17th century portrait depicting Knyaz Lev of Galicia-Volhynia with the city of Lviv in the background

Lviv High Castle, fragment of engraving by A. Gogenberg, 17th century

John II Casimir, King of Poland, pledging an oath at Lviv's Latin Cathedral, by painter Jan Matejko. Collection of the Wrocław Museum.

The Galician Sejm (till 1918), since 1920 the Jan Kazimierz University

The Lwów Eaglets, teenage soldiers who fought on the Polish side during the Battle of Lwów

Ukrainian Sich Riflemen fought on the Ukrainian side in November 1918. The picture was made by one of the contemporaries of event.

Eastern Trade Fair (Targi Wschodnie), main entrance.

Sykhiv – Lviv's largest residential neighborhood, was built in the early 1980s under Soviet rule

E19101 electric bus – product of the Electron

Inside the Church of the Transfiguration

The Lviv Opera and Ballet Theatre, an important cultural centre for residents and visitors

The main building of Lviv National Museum

Pikkardiyska Tertsiya – Ukrainian a cappella musical formation

The front façade of the Lviv University, the oldest university in Ukraine

The former building of the Scottish Café

A clock in Lviv on Prospekt Svobody (Freedom Ave.), showing time to start of EURO 2012. Opera and Ballet Theatre in background

A confectioner makes chocolate lions at the Festival of Chocolate

Police patrol by bicycles in the tourist area of Lviv

Lviv National Stepan Gzhytsky University of Veterinary Medicine and Biotechnology.

Anatomy Department Building of Danylo Halytsky Lviv National Medical University - one of the oldest and prime medical institute of Ukraine.

Aleksander Fredro Monument, moved from Lviv to Wrocław, its sister city, after World War II

The Jesuit Church – An example of baroque style in Lviv

Bernardine church and monastery in the style of Italian and Dutch mannerism

The Nativity of the Holy Virgin Church was constructed in 1995–2001 in Sykhiv district

The mixture of modern and Soviet-era architecture in the northern part of the city

View on Old Town, a UNESCO World Heritage Site

The most well-known were the mathematicians Stefan Banach, Juliusz Schauder and Stanisław Ulam who were founders of the Lwów School of Mathematics turning Lviv in the 1930s into the "World Centre of Functional Analysis" and whose share in Lviv academia was substantial.

Stanisław Ulam who was later a participant in the Manhattan Project and the proposer of the Teller-Ulam design of thermonuclear weapons, Stefan Banach one of the founders of functional analysis, Hugo Steinhaus, Karol Borsuk, Kazimierz Kuratowski, Mark Kac and many other notable mathematicians would gather there.

Mark Kac

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Polish American mathematician.

Kac completed his Ph.D. in mathematics at the Polish University of Lwów in 1937 under the direction of Hugo Steinhaus.

Mark Kac and Stanislaw Ulam: Mathematics and Logic: Retrospect and Prospects, Praeger, New York (1968) 1992 Dover paperback reprint. ISBN: 0-486-67085-6

Scottish Book

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Thick notebook used by mathematicians of the Lwów School of Mathematics in Poland for jotting down problems meant to be solved.

The building of the Scottish cafe where the book was recorded and stored

1972: Mazur (left) acknowledges Per Enflo with the promised "live goose", the prize for having solved the problem 153.

Stanislaw Ulam recounts that the tables of the café had marble tops, so they could write in pencil, directly on the table, during their discussions.

Hugo Steinhaus contributed the last problem on 31 May 1941, shortly before the German attack on the Soviet Union; this problem involved a question about the likely distribution of matches within a matchbox, a problem motivated by Banach's habit of chain smoking cigarettes.

John von Neumann

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Hungarian-American mathematician, physicist, computer scientist, engineer and polymath.

Von Neumann's birthplace, at 16 Báthory Street, Budapest. Since 1968, it has housed the John von Neumann Computer Society.

Excerpt from the university calendars for 1928 and 1928/29 of the Friedrich-Wilhelms-Universität Berlin announcing Neumann's lectures on the theory of functions II, axiomatic set theory and mathematical logic, the mathematical colloquium, review of recent work in quantum mechanics, special functions of mathematical physics and Hilbert's proof theory. He also lectured on the theory of relativity, set theory, integral equations and analysis of infinitely many variables.

History of approaches that led to NBG set theory

Flow chart from von Neumann's "Planning and coding of problems for an electronic computing instrument," published in 1947.

The first implementation of von Neumann's self-reproducing universal constructor. Three generations of machine are shown: the second has nearly finished constructing the third. The lines running to the right are the tapes of genetic instructions, which are copied along with the body of the machines.

A simple configuration in von Neumann's cellular automaton. A binary signal is passed repeatedly around the blue wire loop, using excited and quiescent ordinary transmission states. A confluent cell duplicates the signal onto a length of red wire consisting of special transmission states. The signal passes down this wire and constructs a new cell at the end. This particular signal (1011) codes for an east-directed special transmission state, thus extending the red wire by one cell each time. During construction, the new cell passes through several sensitised states, directed by the binary sequence.

Von Neumann's wartime Los Alamos ID badge photo

Operation Redwing nuclear test in July 1956

The von Neumann crater, on the far side of the Moon.

During World War II, von Neumann worked on the Manhattan Project with theoretical physicist Edward Teller, mathematician Stanislaw Ulam and others, problem-solving key steps in the nuclear physics involved in thermonuclear reactions and the hydrogen bomb.

It solved a problem of Hugo Steinhaus asking whether an interval is And a small simplification of Hermann Minkowski's theorem for linear forms in geometric number theory.