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Full Idea
I argue that mathematical knowledge has its roots in pattern recognition and representation, and that manipulating representations of patterns provides the connection between the mathematical proof and mathematical truth.
Gist of Idea
Maths is pattern recognition and representation, and its truth and proofs are based on these
Source
Michael D. Resnik (Maths as a Science of Patterns [1997], One.1)
Book Ref
Resnik,Michael D.: 'Mathematics as a Science of Patterns' [OUP 1999], p.9
A Reaction
The suggestion that patterns are at the basis of the ontology of mathematics is the most illuminating thought I have encountered in the area. It immediately opens up the possibility of maths being an entirely empirical subject.
| 6295 | There are too many mathematical objects for them all to be mental or physical [Resnik] |
| 6296 | Maths is pattern recognition and representation, and its truth and proofs are based on these [Resnik] |
| 6299 | Axioms are often affirmed simply because they produce results which have been accepted [Resnik] |
| 6300 | Mathematical constants and quantifiers only exist as locations within structures or patterns [Resnik] |
| 6301 | Congruence is the strongest relationship of patterns, equivalence comes next, and mutual occurrence is the weakest [Resnik] |
| 6302 | Structuralism must explain why a triangle is a whole, and not a random set of points [Resnik] |
| 6303 | Sets are positions in patterns [Resnik] |
| 6304 | Mathematical realism says that maths exists, is largely true, and is independent of proofs [Resnik] |