In recent years, a rapidly expanding body of work has been making unexpected, seemingly unrelated connections between the mysterious distribution of prime numbers and various branches of physics. Note that in general, mathematics ‘informs’ physics, but not vice versa. That is, mathematicians have traditionally been able to provide physicists with useful insights and techniques, but this has been largely a one-way process. What we are considering here is the reverse process, where insights and techniques derived from physics are shedding new light on pure mathematical (in particular, number theoretical) concerns. The number theory and physics archive pages are an attempt to document and archive this material as comprehensively as possible.

These pages are part of the more general site “Inexplicable secrets of creation” of Matthew R. Watkins. The author provides a good summary of current research on number theory as the ultimate physical theory, including his own research: “In some previously unexplored context, the familiar ’shape’ of the sequence of prime numbers is the result of a kind of dynamic or evolutionary process.”

My feeling is that match “describe” better because it reaches deeply, but not precisely in the nature of the external world, but in the nature that is both “inside” and “outside” our minds.

I will not attempt to explain more this, as I lack time at this moment, but what Im trying to say is that we see (always) through a set of concepts instead of seeing with just our senses. Those concepts rely on our language, and deep inside our language resides the language of mathematics, maybe the first set of abstractions we developed as a race.

What we see “outside” or what we want to explain is always more in our minds than in the so called external universe, in this sense, math not only deal with that external world, but with our most intimate self.

And Dirac (I think), who posited the existence of the anti-electron (nee positiron) because the theory had a mathematical symmetry that suggested it should be there. He was laughed at, at first. Eventually there were experimental data whose only explanation was a positron. Anti-matter is now very well accepted (indeed, even created).

Math is amazing. As someone finishing up a BS in math and physics, I find that physics is often trivial — it is always the math that is hard. Well, the math and finding the patterns among the experimental data that might lead one to the math. Our favorite geek joke among my physics friends is that we are mathematicians with realistic boundary conditions. Indeed, the term theoretical physics really implies a branch of math: that of making mathematical models to try and model the physical world.