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History, Science, and Interesting Information - The Great Library / Re: Which part of science interests you the most?
« on: August 05, 2014, 12:02:03 AM »
I think it's quite possible to understand the principle of Gödel's argument without necessarily using all the conventional mathematical apparatus. You might like to find a copy of Gödel, Escher, Bach by Douglas Hofstadter - it was popular in the 1980s, and I think an anniversary edition was published quite recently. Hofstadter summarises the basic ideas in a page or two fairly early in the book, then builds up his own apparatus to enable a more detailed exploration (somewhat more intuitive than rigorous) later on.
I agree that the interconnectedness of maths is an important part of its beauty. The polytopes I mentioned are a good example: they are geometrical objects (polygons, polyhedra and so on), but their symmetry properties are described by group theory, and the standard book on the subject draws in elements from a wide range of other areas.
I should also say I'm not a mathematician. I did maths up to A-level, and it was a minor element of my degree, but I haven't touched it in any formal way since then, and I'm sadly out of practice.
I agree that the interconnectedness of maths is an important part of its beauty. The polytopes I mentioned are a good example: they are geometrical objects (polygons, polyhedra and so on), but their symmetry properties are described by group theory, and the standard book on the subject draws in elements from a wide range of other areas.
I should also say I'm not a mathematician. I did maths up to A-level, and it was a minor element of my degree, but I haven't touched it in any formal way since then, and I'm sadly out of practice.