“All things are number.” — Pythagoras (582 BCE - 496 BCE)
I once thought as follows:
As a result, two questions haunted me for a long time:
Today, however, I have changed my mind: I regard the world itself as a mathematical fact, on a par with certainties such as
The largest of those 26 sporadic simple groups is called the “Monster group.”
The Riemann Hypothesis itself remains unproven, yet Hardy (1914) and Hardy & Littlewood (1921) showed that infinitely many zeros lie on Re(s)=1/2. Thus the statement “infinitely many zeros line up on one straight line” is a solid mathematical fact.
In 1984 the physicist Steven Weinberg remarked:
The Universe is an enormous direct product of representations of symmetry groups. It's hard to say it any more strongly than that.
I suspect the universe may literally be the direct product of representations of those 26 sporadic simple groups.
Mathematical facts exist independent of time; asking “When were they born?” makes no sense.
Mathematical facts are also location‑free; there is no need to ask “Where are they?”
Imagine a state with no time, no space, no matter—before the birth of the cosmos. The only thing that could exist there is mathematical fact.
Among those facts might even be sentient beings who understand that their own world is a mathematical fact—a striking self‑reference.
To close, here is a 1983 passage by the physicist Freeman Dyson:
I have a sneaking hope, a hope unsupported by any facts or any evidence, that sometime in the twenty first century physicists will stumble upon the Monster group, built in some unsuspected way into the structure of the universe.
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