1997 | Maths as a Science of Patterns |
One.1 | p.3 | 6295 | There are too many mathematical objects for them all to be mental or physical |
One.1 | p.9 | 6296 | Maths is pattern recognition and representation, and its truth and proofs are based on these |
One.4 | p.55 | 6297 | Euclid's geometry is synthetic, but Descartes produced an analytic version of it |
One.5.1 | p.84 | 6299 | Axioms are often affirmed simply because they produce results which have been accepted |
Three.10.1 | p.201 | 6300 | Mathematical constants and quantifiers only exist as locations within structures or patterns |
Three.10.3 | p.209 | 6301 | Congruence is the strongest relationship of patterns, equivalence comes next, and mutual occurrence is the weakest |
Three.10.4 | p.213 | 6302 | Structuralism must explain why a triangle is a whole, and not a random set of points |
Three.10.5 | p.218 | 6303 | Sets are positions in patterns |
Three.12.9 | p.271 | 6304 | Mathematical realism says that maths exists, is largely true, and is independent of proofs |