A report on Stanislaw Ulam

Stanisław Ulam
Stanisław Ulam
The Scottish Café's building now houses the Universal Bank in Lviv, Ukraine.
Ulam's ID badge photo from Los Alamos
Stan Ulam holding the FERMIAC
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

Polish-American scientist in the fields of mathematics and nuclear physics.

- Stanislaw Ulam
Stanisław Ulam

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Lviv Polytechnic National University

Lviv Polytechnic

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Largest scientific university in Lviv.

Largest scientific university in Lviv.

Lviv Polytechnic National University
The main building is crowned with allegorical statues and the Latin inscription Litteris et Artibus
Interior main staircase of Lviv Polytechnic
Marble bust of Julian Zachariewicz at the entrance of the main building
General Sikorski was an alumnus of the Lwów Polytechnic (1902–06)

Stanislaw Ulam (mathematician, member of the Manhattan Project, major contributor to hydrogen bomb construction)

John Pasta

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American computational physicist and computer scientist who is remembered today for the Fermi–Pasta–Ulam–Tsingou experiment, the result of which was much discussed among physicists and researchers in the fields of dynamical systems and chaos theory, and as the head of the department of Computer Science at the University of Illinois at Urbana-Champaign from 1964 to 1970.

American computational physicist and computer scientist who is remembered today for the Fermi–Pasta–Ulam–Tsingou experiment, the result of which was much discussed among physicists and researchers in the fields of dynamical systems and chaos theory, and as the head of the department of Computer Science at the University of Illinois at Urbana-Champaign from 1964 to 1970.

After working alongside Enrico Fermi, Stanislaw Ulam, and Mary Tsingou, Pasta went on to work for the Atomic Energy Commission as the only computer expert, eventually developing the branch of mathematics and computers to an entire division.

Robert D. Richtmyer

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American physicist, mathematician, educator, author, and musician.

American physicist, mathematician, educator, author, and musician.

A letter sent March 11, 1947, from John von Neumann to Richtmyer outlined a technique for approximating complex problems being studied at Los Alamos by Stanislaw Ulam.

David Hawkins' Los Alamos ID badge

David Hawkins (philosopher)

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Professor whose interests included the philosophy of science, mathematics, economics, childhood science education, and ethics.

Professor whose interests included the philosophy of science, mathematics, economics, childhood science education, and ethics.

David Hawkins' Los Alamos ID badge

Hawkins saw his role as that of a go-between, mediating between the civilian scientists and the military leadership at Los Alamos, but he also found a kindred spirit in the Polish mathematician Stan Ulam, who was working in Edward Teller's "Super" Group.

Mark Kac

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Polish American mathematician.

Polish American mathematician.

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

Four ENIAC panels and one of its three function tables, on display at the School of Engineering and Applied Science at the University of Pennsylvania

ENIAC

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The first programmable, electronic, general-purpose digital computer, completed in 1945.

The first programmable, electronic, general-purpose digital computer, completed in 1945.

Four ENIAC panels and one of its three function tables, on display at the School of Engineering and Applied Science at the University of Pennsylvania
Glenn A. Beck (background) and Betty Snyder (foreground) program ENIAC in BRL building 328. (U.S. Army photo, c. 1947–1955)
Cpl. Irwin Goldstein (foreground) sets the switches on one of ENIAC's function tables at the Moore School of Electrical Engineering. (U.S. Army photo)
Programmers Betty Jean Jennings (left) and Fran Bilas (right) operate ENIAC's main control panel at the Moore School of Electrical Engineering. (U.S. Army photo from the archives of the ARL Technical Library)
The bottoms of three accumulators at Fort Sill, Oklahoma, US
A function table from ENIAC on display at Aberdeen Proving Ground museum.
Detail of the back of a section of ENIAC, showing vacuum tubes
ENIAC on a Chip, University of Pennsylvania (1995) - Computer History Museum

John von Neumann and Stanislaw Ulam realized the speed of ENIAC would allow these calculations to be done much more quickly.

Directed graph showing the orbits of small numbers under the Collatz map, skipping even numbers. The Collatz conjecture states that all paths eventually lead to 1.

Collatz conjecture

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One of the most famous unsolved problems in mathematics.

One of the most famous unsolved problems in mathematics.

Directed graph showing the orbits of small numbers under the Collatz map, skipping even numbers. The Collatz conjecture states that all paths eventually lead to 1.
Numbers from 1 to 9999 and their corresponding total stopping time
Histogram of total stopping times for the numbers 1 to 108. Total stopping time is on the x axis, frequency on the y axis.
Histogram of total stopping times for the numbers 1 to 109. Total stopping time is on the x axis, frequency on the y axis.
Iteration time for inputs of 2 to 107.
Total stopping time of numbers up to 250, 1000, 4000, 20000, 100000, 500000
frameless
The first 21 levels of the Collatz graph generated in bottom-up fashion. The graph includes all numbers with an orbit length of 21 or less.
Collatz map fractal in a neighbourhood of the real line
Directed graph showing the orbits of the first 1000 numbers.
The {{mvar|x}} axis represents starting number, the {{mvar|y}} axis represents the highest number reached during the chain to 1. This plot shows a restricted {{mvar|y}} axis: some {{mvar|x}} values produce intermediates as high as {{val|2.7e7}} (for {{math|x {{=}} 9663}})
The tree of all the numbers having fewer than 20 steps.
alt=Collatz Conjecture 100M|The number of iterations it takes to get to one for the first 100 million numbers.

conjecture, the Ulam conjecture (after Stanisław Ulam), Kakutani's problem (after Shizuo Kakutani), the Thwaites conjecture (after Sir Bryan Thwaites), Hasse's algorithm (after Helmut Hasse), or the Syracuse problem'''.

Fermi–Ulam model

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The Fermi–Ulam model (FUM) is a dynamical system that was introduced by Polish mathematician Stanislaw Ulam in 1961.

Rota in 1970.

Gian-Carlo Rota

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Italian-American mathematician and philosopher.

Italian-American mathematician and philosopher.

Rota in 1970.

Beginning in 1966 he was a consultant at Los Alamos National Laboratory, frequently visiting to lecture, discuss, and collaborate, notably with his friend Stanisław Ulam.

Ulam spiral of size 200×200. Black dots represent prime numbers. Diagonal, vertical, and horizontal lines with a high density of prime numbers are clearly visible.

Ulam spiral

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Ulam spiral of size 200×200. Black dots represent prime numbers. Diagonal, vertical, and horizontal lines with a high density of prime numbers are clearly visible.
For comparison, a spiral with random odd numbers colored black (at the same density of primes in a 200x200 spiral).
The primes of the form 4x2 − 2x + 41 with x = 0, 1, 2, ... have been highlighted in purple. The prominent parallel line in the lower half of the figure corresponds to 4x2 + 2x + 41 or, equivalently, to negative values of x.
Klauber triangle with prime numbers generated by Euler's polynomial x{{sup|2}}  −  x  +  41 highlighted.
Sacks spiral.
Ulam spiral of size 150×150 showing both prime and composite numbers.
Hexagonal number spiral with prime numbers in green and more highly composite numbers in darker shades of blue.
Number spiral with 7503 primes visible on regular triangle.

The Ulam spiral or prime spiral is a graphical depiction of the set of prime numbers, devised by mathematician Stanisław Ulam in 1963 and popularized in Martin Gardner's Mathematical Games column in Scientific American a short time later.