10 ideas
3340 | Von Neumann defines each number as the set of all smaller numbers [Neumann, by Blackburn] |
3355 | Von Neumann wanted mathematical functions to replace sets [Neumann, by Benardete,JA] |
17963 | The facts of geometry, arithmetic or statics order themselves into theories [Hilbert] |
17966 | Axioms must reveal their dependence (or not), and must be consistent [Hilbert] |
22716 | Von Neumann defined ordinals as the set of all smaller ordinals [Neumann, by Poundstone] |
17967 | To decide some questions, we must study the essence of mathematical proof itself [Hilbert] |
17965 | The whole of Euclidean geometry derives from a basic equation and transformations [Hilbert] |
17964 | Number theory just needs calculation laws and rules for integers [Hilbert] |
18284 | Particulars can be verified or falsified, but general statements can only be falsified (conclusively) [Popper] |
17968 | By digging deeper into the axioms we approach the essence of sciences, and unity of knowedge [Hilbert] |