Bryan Bunch's Blog: S.T.E.M. History Update - Posts Tagged "alan-turing"
The Greatest Mathematician in Britain
I saw the movie The Imitation Game the other day. In one of the early scenes the actor playing Alan Turing says that he is needed for a code-breaking task in World War II because he is the greatest mathematician in Britain. I wondered if it was true.
Aside from proving in 1936 that no method can calculate all true results in mathematics (which hardly seems helpful), it would appear to the nonmathematician that before World War II Turing was not doing what we normally think of as mathematics at all. His main result was independently proved in the same year by the American mathematician Alonzo Church [1903-1995], who is barely known outside mathematical circles. This theorem, despite its negative aspect, remains one of the bases of a branch of mathematics called “foundations”—so it counts as mathematics. But Turing’s fame comes more from his work with computers than from his mathematics per se. Here are some of the relevant entries from my book The History of Science and Technology.
Alan Mathison Turing
[b. London, June 23, 1912, d. Wilmslow, Cheshire, England, June 7, 1954]
Before World War II, Turing showed that an idealized machine (a universal Turing machine) using a few simple operations can calculate the values of all functions that a mathematician can compute. Despite this, Turing proved that some mathematical results remain beyond calculation. During the war Turing was instrumental in building a machine that decoded enemy messages, a prototype for electronic computers. After the war Turing developed such computers. Turing's 1952 study of the mathematics of fluid interactions helped biologists show how organisms develop and chemists analyze fluids with periodic properties.
In August of 1936, Alan Turing's paper "On Computable Numbers with an Application to the Entscheidungsproblem" describes the "Turing machine," an imaginary machine that can solve all problems that are computable. In fact, the definition of "computable" is that the problem can be solved by a Turing machine. This paper solves Hilbert's 23rd, the decidability problem or Entscheidungsproblem, by showing that it is not possible to devise a method for determining the truth or falsity of all statements that can be made in a part of formal logic called the predicate calculus. Therefore, there is no single way to prove or disprove all logical statements. Alonzo Church [b. Washington DC, June 14, 1903, d. Hudson, OH, August 11, 1995], independently of Alan Turing, shows that there is no single method for determining whether or not a statement in mathematics is provable or even true (Church's Theorem). See also 1900 MATH.
In 1943: A team headed by Alan Turing develops Colossus at Bletchley Park in England. The Colossus, designed by Thomas Flowers and Maxwell Herman Alexander Newman [b. London, February 7, 1897, d. Comberton, England, February 22, 1984], is the first all-electronic calculating device (it uses 1500 vacuum tubes). Unlike a general-purpose computer, however, Colossus is dedicated to cracking German codes--and is very good at it, possibly influencing the course of World War II.
Most of the famous mathematicians of the 1930s also worked in the foundations branch of mathematics and also produced important theorems, but they were Austrian, Russian, or German, so Turing’s claim of being the greatest British mathematician is justified.
Aside from proving in 1936 that no method can calculate all true results in mathematics (which hardly seems helpful), it would appear to the nonmathematician that before World War II Turing was not doing what we normally think of as mathematics at all. His main result was independently proved in the same year by the American mathematician Alonzo Church [1903-1995], who is barely known outside mathematical circles. This theorem, despite its negative aspect, remains one of the bases of a branch of mathematics called “foundations”—so it counts as mathematics. But Turing’s fame comes more from his work with computers than from his mathematics per se. Here are some of the relevant entries from my book The History of Science and Technology.
Alan Mathison Turing
[b. London, June 23, 1912, d. Wilmslow, Cheshire, England, June 7, 1954]
Before World War II, Turing showed that an idealized machine (a universal Turing machine) using a few simple operations can calculate the values of all functions that a mathematician can compute. Despite this, Turing proved that some mathematical results remain beyond calculation. During the war Turing was instrumental in building a machine that decoded enemy messages, a prototype for electronic computers. After the war Turing developed such computers. Turing's 1952 study of the mathematics of fluid interactions helped biologists show how organisms develop and chemists analyze fluids with periodic properties.
In August of 1936, Alan Turing's paper "On Computable Numbers with an Application to the Entscheidungsproblem" describes the "Turing machine," an imaginary machine that can solve all problems that are computable. In fact, the definition of "computable" is that the problem can be solved by a Turing machine. This paper solves Hilbert's 23rd, the decidability problem or Entscheidungsproblem, by showing that it is not possible to devise a method for determining the truth or falsity of all statements that can be made in a part of formal logic called the predicate calculus. Therefore, there is no single way to prove or disprove all logical statements. Alonzo Church [b. Washington DC, June 14, 1903, d. Hudson, OH, August 11, 1995], independently of Alan Turing, shows that there is no single method for determining whether or not a statement in mathematics is provable or even true (Church's Theorem). See also 1900 MATH.
In 1943: A team headed by Alan Turing develops Colossus at Bletchley Park in England. The Colossus, designed by Thomas Flowers and Maxwell Herman Alexander Newman [b. London, February 7, 1897, d. Comberton, England, February 22, 1984], is the first all-electronic calculating device (it uses 1500 vacuum tubes). Unlike a general-purpose computer, however, Colossus is dedicated to cracking German codes--and is very good at it, possibly influencing the course of World War II.
Most of the famous mathematicians of the 1930s also worked in the foundations branch of mathematics and also produced important theorems, but they were Austrian, Russian, or German, so Turing’s claim of being the greatest British mathematician is justified.
S.T.E.M. History Update
The history of science, technology, engineering, and mathematics has been my main reading and writing interest for most of my life, now enriched by adding a novel, "Before Eureka!," to many works that
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