The physical universe could emerge naturally from a mathematical structure. ~ American theoretical physicist Garret Lisi & American physicist and mathematician James Weatherall
If existence is mathematical in nature, it begs the question of what the foundation of mathematics is. The answer: nothing.
The basis of all mathematics is 0 = 0. ~ American theoretical physicist John Wheeler
Mathematics is founded upon sets: groups of entities.
Math begins with the empty set. Only then can 1 be defined as the set which contains only the empty set.
To be created, something first has to not exist in space or time, and then exist. ~ Swedish American cosmologist Max Tegmark
Mathematically, space and time themselves are contained within a larger construct. If mathematics has credence as the spinner of Nature, this suggests that actuality is a subset of reality.
Space and time themselves are contained within larger mathematical structures. ~ Max Tegmark
There are salient examples which suggest that mathematics necessarily defines reality, and vice versa.
When Einstein finished his general theory of relativity in 1916, his equations elicited an unexpected message: the universe is expanding. As Einstein believed then that the universe itself was static, he ignored the implication. 13 years later, American astronomer Edwin Hubble unearthed convincing evidence of cosmic expansion.
In the 1960s, several researchers found lurking in their models of particle physics a fundamental field whose interactions formulate existence. Almost a half-century later, the field revealed itself as the Higgs.
The quantum fields that pervade all of space encode within themselves the potential for particles and antiparticles and dictate the rules of how they behave. ~ American physicist Brian Skinner
All of the fields which give rise to quanta dictate the properties that quanta possess. Quantum fields, which are mathematical expressions of energy, bestow upon their creations the behaviors which define them; behaviors which are entirely mathematical.
Maybe it’s because math is reality. ~ American theoretical physicist Brian Greene