Why does maths work? I understand that it revolves around taking and expanding basic axioms. However, even from basic calculus, I gather there is a lot of symmetry and coincidence between different areas of maths, and maths and different sciences. What different arguments are there for explaining this? Where can I read more about this?
Philosophy of maths and science
Matthew Perry
Nathan Wright
it just werks
Levi Perry
Thanks.
Nolan Morales
The explanation, I believe, is as follows:
Math is the "fundamental" science. Physics is the application of math on observed phenomena. Chemistry is the application of physics on observed phenomena. Biology is the application of chemistry on observed phenomena.
Lucas Cox
Some may even claim philosophy precedes math, since philosophy can be understood as the "study of thinking".
Connor King
>Why does maths work?
Please don't ask this question.
Angel Bell
In a few cases, our current mathematical constructs seem to fail.
Luke Edwards
No the study of thinking is neuroscience. Philosophy is the study of armchair conjectures, mental masturbation, and personality worship.
Justin Young
>What different arguments are there for explaining this?
My argument is that we are lucky. Why are integration and differentiation related? Because we are lucky. Why do complex numbers behave so nicely? Because we are lucky.
That is all there is to it. When you become a mathematician you embrace the dice of reality. What theorems are or are not true is completely about luck, the prove those that are true is the task at hand. And those theorems that cannot be proven or disproven show that there exists something beyond luck that we can't really grasp yet.
Levi Sullivan
>The Unreasonable Effectiveness of Mathematics in the Natural Sciences
>by Eugene Wigner
dartmouth.edu
>The Unreasonable Effectiveness of Mathematics
>by R. W. HAMMING
schneider.ncifcrf.gov
Nathan Edwards
Matgematics is the study of abstract relationships and patterns. There is no "works" part. It is not a machine like physics or chemistry. There is no physical manifestation for mathematics, just things that can be modeled using it.
Leo Carter
>Why does maths work?
Because instruments of mathematics derive their validity from logical proofs, and logic is the study of making of statements with the accordance to logos, the rational order of Universe.
Brody Rivera
It's just a universal law. Kind of like how gravity and electric fields are fundamental forces. There is no "why" to math's existence. It just does.
Justin Taylor
Philosophy has some really negative connotations of being useless mental masturbation, I sometimes used to think that as well, but it's not true. It's actually a very important discipline because it concerns studying the different axioms that make up different belief systems. There is a LOT to be learned by studying philosophy, or conversely, by just doing a lot of thinking about your own beliefs and values and behaviour, and why you are that way.
And neuroscience is an intricacy of biology. Philosophy is a completely separate discipline.
Gabriel Cruz
Tell me a story about the greek and in what way they discussed the foundations of math user
Mason Ortiz
So nobody knows why gravity is a thing? Just that it is?
Is it even knowable?
Nolan Barnes
>Where can I read more about this?
For an overview of philosophy of mathematics (and philisophy in general) SEP is pretty good. plato.stanford.edu
Nicholas Perry
Because our universe has causality
And because that is how everything works, as animals we have developed a sense of causality
Tracking that back we go to the fundamentals of our universe, and deduce other stuff with it
And because all that stuff has the same roots, as you said there are interesting connections between seemingly unrelated stuff
David Thomas
Logic derived from rules.
Jaxson Clark
>No the study of thinking is neuroscience
Actually, it's psychology. Neuroscience is just one small branch of psychology.
Josiah Stewart
>Neuroscience is a branch of psychology
wot