On Jun 4, 12:51 pm, "Do any of you remember the Republican Party?" <goofin...@gmail.com> wrote: > On Jun 3, 9:39 am, Nimo <azeez...@gmail.com> wrote: >
[snip the above]
> > ________ > > > politics,philosophy religion & society > > are quite good to HIM rather than > > physics; > > > and this quote is best suited to him at this point.., > > > ?Every street urchin in our mathematical Göttingen > > knows more about four-dimensional geometry than > > Einstein. Nevertheless, it was Einstein who did the work, > > not the great mathematicians. > > > David Hilbert > > (January 23, 1862 ? February 14, 1943) > > > the quote's author had shown his sarcasm very cleverly :-) > > The tragic thing about Hilbert is how his greatest enterprise was > dashed by one young Mathematician philosopher, Kurt Godel.
Wir müssen wissen. Wir werden wissen.
As translated into English the inscriptions read:
We must know. We will know.
Ironically, the day before Hilbert pronounced this phrase at the 1930 annual meeting of the Society of German Scientists and Physicians, Kurt Gödel?in a roundtable discussion during the Conference on Epistemology held jointly with the Society meetings?tentatively announced the first expression of his (now-famous) incompleteness theorem,the news of which would make Hilbert "somewhat angry".
In 1920 he proposed explicitly a research project (in metamathematics, as it was then termed) that became known as Hilbert's program. He wanted mathematics to be formulated on a solid and complete logical foundation. He believed that in principle this could be done, by showing that:
1. all of mathematics follows from a correctly-chosen finite system of axioms; and 2. that some such axiom system is provably consistent through some means such as the epsilon calculus.
He seems to have had both technical and philosophical reasons for formulating this proposal. It affirmed his dislike of what had become known as the ignorabimus, still an active issue in his time in German thought, and traced back in that formulation to Emil du Bois-Reymond.
This program is still recognizable in the most popular philosophy of mathematics, where it is usually called formalism. For example, the Bourbaki group adopted a watered-down and selective version of it as adequate to the requirements of their twin projects of
(a) writing encyclopedic foundational works, and (b) supporting the axiomatic method as a research tool.
This approach has been successful and influential in relation with Hilbert's work in algebra and functional analysis, but has failed to engage in the same way with his interests in physics and logic.
Hilbert and the talented mathematicians who worked with him in his enterprise were committed to the project. His attempt to support axiomatized mathematics with definitive principles, which could banish theoretical uncertainties, was however to end in failure.
Gödel demonstrated that any non-contradictory formal system, which was comprehensive enough to include at least arithmetic, cannot demonstrate its completeness by way of its own axioms. In 1931 his incompleteness theorem showed that Hilbert's grand plan was impossible as stated. The second point cannot in any reasonable way be combined with the first point, as long as the axiom system is genuinely finitary.
Nevertheless, the subsequent achievements of proof theory at the very least clarified consistency as it relates to theories of central concern to mathematicians. Hilbert's work had started logic on this course of clarification; the need to understand Gödel's work then led to the development of recursion theory and then mathematical logic as an autonomous discipline in the 1930s. The basis for later theoretical computer science, in Alonzo Church and Alan Turing also grew directly out of this 'debate'.