6299 | Axioms are often affirmed simply because they produce results which have been accepted |

6304 | Mathematical realism says that maths exists, is largely true, and is independent of proofs |

6297 | Euclid's geometry is synthetic, but Descartes produced an analytic version of it |

6300 | Mathematical constants and quantifiers only exist as locations within structures or patterns |

6303 | Sets are positions in patterns |

6296 | Maths is pattern recognition and representation, and its truth and proofs are based on these |

6301 | Congruence is the strongest relationship of patterns, equivalence comes next, and mutual occurrence is the weakest |

6302 | Structuralism must explain why a triangle is a whole, and not a random set of points |

6295 | There are too many mathematical objects for them all to be mental or physical |