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This revolution in mathematics literally led to the invention of computers. I have been reading all about it when I go to the bookstore in the book Turing's Ca
by calhoun137 14y ago
This revolution in mathematics literally led to the invention of computers. I have been reading all about it when I go to the bookstore in the book Turing's Cathedral[1].
David Hilbert wanted to redo mathematics from square one, basing everything on set theory, axioms, and rigorous proofs. In 1900, Hilbert gave his famous address where he stated the Hilbert Problems. One of these was to prove that mathematics is "complete" in the sense that every possible statement is either provable or disprovable from the axioms.
In an effort to solve this problem, Alan Turing wrote his famous paper "On Computable Numbers" where he conceived for the first time his "Turing Machines". Although his approach didn't work to solve the Hilbert problem, it greatly inspired Von Nueman who at the time was pretty much working on pure mathematics.
Godel came along and proved that mathematics is not "complete", because there are some statements about natural numbers which cannot be proved or disproved from the axioms, but rather are undecidable.
Von Nueman was so upset by Godel's result that he decided he no longer wanted to work in pure mathematics, because if it's not complete then whats the point anyway. Instead he decided to work on applied math and physics. Since he loved the work of Turing, he wanted to build a physical Turing Machine to help out with computations, and he figured there would probably be a lot of other uses for such a machine that no one had thought of yet, and that would only become apparent once the machine was built.
While at the Institute for Advanced Study, Von Nueman fought a hard political fight to secure funding and permission to build the first computers, the MANIAC and the ENIAC, to the horror of the faculty at the time, including Einstein.
Since I am posting this at 4:30am in a thread that is 12 hours old, I will be happy if someone reads it :P
[1] http://books.google.com/books/about/Turing_s_Cathedral.html?id=6sElRNGXWFIC http://books.google.com/books/about/Turing_s_Cathedral.html?...
- stiff 14y agoThis is interesting but not completely accurate. What is most mind-blowing, is that Turing machines were Turings approach to formalizing proofs as a means towards solving the Entscheidungsproblem. In fact he was successful in "solving" the problem, in that he proved the impossibility of solving it, later than Goedel, but in a much clearer way - Goedel encoded theorems using numbers in a quite crazy way. I also don't think Turing and Von Neumann can be given that much exclusive credit in inventing the computer, while they had huge impact, I think the idea of a computer was to some extent "in the air" and there were many people working on it concurrently, sometimes unaware of each other, see: http://en.wikipedia.org/wiki/History_of_computing_hardware http://en.wikipedia.org/wiki/History_of_computing_hardware
- calhoun137 14y agoIt seems like the invention of the computer is one of the most controversial "who got there first" things in all of science. Turing's Cathedral has a ton of really interesting historical details about the history of computers, and LOTS of details about the political fight Von Nueman waged to even be allowed to work on the first computers at IAS. I didn't realize how big a role he actually played, and I would encourage people to read that book because its pretty good.
- lutusp 14y ago> In 1900, Hilbert gave his famous address where he stated the Hilbert Problems. One of these was to prove that mathematics is "consistent" in the sense that every possible statement is either provable or disprovable from the axioms. > In an effort to solve this problem, Alan Turing wrote his famous paper "On Computable Numbers" where he conceived for the first time his "Turing Machines". Whoa -- you completely skipped Gödel's Incompleteness Theorems. Gödel's Theorems answered Hilbert's inquiry, not Turing. It's true that the Turing halting problem and Gödel's Theorems are deeply connected, but the historical sequence is Hilbert, Gödel, then Turing. You can't leave Gödel out. http://en.wikipedia.org/wiki/G%C3%B6dels_incompleteness_theorems http://en.wikipedia.org/wiki/G%C3%B6dels_incompleteness_theo...
- calhoun137 14y agoI wouldn't say I left Godel out, but I suppose I got the historical order wrong, because Godel was 1931 and Turing was 1936, I didn't realize that, oops!
- blaabjerg 14y agoOnly because you have repeated your spelling of "Von Nueman" three times, I want to point out that it is in fact spelled "von Neumann".