One of the dirty secrets of mathematics is that not all axiomatic systems
are equally successful. There is a kind of survivorship bias whereby
axiomatic systems that are "interesting" are studied whereas axiomatic systems
that are "boring" fall into obscurity.
For example, number theory has an incredibly rich structure that stems from
the very simple axioms of peano arithmetic. Linear algebra is another field
that has been amazingly fruitful, not just in physics but also in pure
mathematics too.
Those axiomatic systems survived infant mortality and grew to become adults,
but they are the rare exceptions.
What "the universe is math" really means is that the universe has structure.
The universe is not complete randomness, nor is it complete emptiness. The
universe has enough structure that we can use increasingly sophisticated
mathematics to describe it.
But don't think that the universe embodies all of mathematics. There are
vast wastelands of mathematics that people thought up that didn't end
up being interesting, even if internally consistent.
What is really happening is the intersection of survivorship bias in pure
mathematics with the anthropic principle in physics. We can observe the
structure of the universe only because it has structure, and there are
certain theories of mathematics that survived because they are not "boring".
Is it a surprise that the "not boring" kinds of mathematics are often the
kind required to describe the structure of the universe?
For example, number theory has an incredibly rich structure that stems from the very simple axioms of peano arithmetic. Linear algebra is another field that has been amazingly fruitful, not just in physics but also in pure mathematics too.
Those axiomatic systems survived infant mortality and grew to become adults, but they are the rare exceptions.
What "the universe is math" really means is that the universe has structure. The universe is not complete randomness, nor is it complete emptiness. The universe has enough structure that we can use increasingly sophisticated mathematics to describe it.
But don't think that the universe embodies all of mathematics. There are vast wastelands of mathematics that people thought up that didn't end up being interesting, even if internally consistent.
What is really happening is the intersection of survivorship bias in pure mathematics with the anthropic principle in physics. We can observe the structure of the universe only because it has structure, and there are certain theories of mathematics that survived because they are not "boring".
Is it a surprise that the "not boring" kinds of mathematics are often the kind required to describe the structure of the universe?