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> The fact that non-mathematicians can produce sharp and correct criticism of an applied mathematician’s work shows us that the success of mathematics does not

> The fact that non-mathematicians can produce sharp and correct criticism of an applied mathematician’s work shows us that the success of mathematics does not rest on its abstract beauty. The ability of researchers not versed in the subtleties of mathematics to help develop models contradicts Wigner’s ‘unreasonable effectiveness’ argument. It tells us that people not trained in mathematics are also able to give deep insights to the subject. Mathematics is not there to be discovered, it is part of the patterns of reasoning in all of our brains. The key insight. It kind of reminds me of how physicists like Robbert Dijkgraaf (I think) have argued that physics and other fields are now contributing to mathematics through their own outlandish needs for weird maths.

lucideer 8y ago
I found this article a bit odd; in my mind, some parts seemed to contradict others in strange paradoxical ways. For example, from your quoted section: > Mathematics is not there to be discovered, it is part of the patterns of reasoning in all of our brains. Isn't that the very definition of elegance? He later says, talking about A.J. Ayer's definition of "non-sense": > Wigner freely admits that his idea about maths comes from a feeling that can’t be verified by known scientific methods Elegance, while there is often a wide collective understanding of what it means in mathematics, is essentially a subjective, aesthetic property; an intuitive one. Is this not exactly what: (a) Wigner means in that quote, (b) A.J. Ayer means in his definition, AND (c) the author refers to as "patterns of reasoning in all of our brains"?
- goldenkey 8y ago
  We like compression. That's our main requirement. We may not like hard coded constants in our physical theories but thats only because we'd prefer a single constant that uncompresses to all six. Or a single law about laws that uncompresses to the entire theory. Constructor theory [1] We also like symmetry but symmetry is just a way to identify attack surfaces for compression. [1] https://www.edge.org/conversation/david_deutsch-constructor-theory https://www.edge.org/conversation/david_deutsch-constructor-...

lucideer 8y ago

I found this article a bit odd; in my mind, some parts seemed to contradict others in strange paradoxical ways. For example, from your quoted section: > Mathematics is not there to be discovered, it is part of the patterns of reasoning in all of our brains. Isn't that the very definition of elegance? He later says, talking about A.J. Ayer's definition of "non-sense": > Wigner freely admits that his idea about maths comes from a feeling that can’t be verified by known scientific methods Elegance, while there is often a wide collective understanding of what it means in mathematics, is essentially a subjective, aesthetic property; an intuitive one. Is this not exactly what: (a) Wigner means in that quote, (b) A.J. Ayer means in his definition, AND (c) the author refers to as "patterns of reasoning in all of our brains"?

goldenkey 8y ago
We like compression. That's our main requirement. We may not like hard coded constants in our physical theories but thats only because we'd prefer a single constant that uncompresses to all six. Or a single law about laws that uncompresses to the entire theory. Constructor theory [1] We also like symmetry but symmetry is just a way to identify attack surfaces for compression. [1] https://www.edge.org/conversation/david_deutsch-constructor-theory https://www.edge.org/conversation/david_deutsch-constructor-...