If the universe turns out to be granular (meaning there is a smallest length and a smallest unit of time), is mathematics as it exists today a flawed, or even the wrong tool to describe reality?

That’s irrational. Sure I will agree will you.

I thought we already knew there was a smallest length, the Planck length?

Mathematics as it exists today can deal with discrete quantities.

Still perfectly valid as far as I know. May be able to reproduce it as well.
Also what @Mariah said

I presume it could still describe reality, but also be able to describe concepts that do not exist in reality.

Honest answer: I don’t believe there is any tool that can describe reality. I don’t believe that anything that could reasonably be termed “reality” is within the scope of our perceptions. At best we can reach some level of practical concurrence on phenomena that seem to be external to us, but I think that’s as much a matter of our common makeup—the configuration of the human brain and sensory apparatus—as it is of any supposedly objective experience.

Well, the math can still work. If you draw a perfect circle with a protractor, you can describe the circumference of 2 pi r. But if you zoom into it, the perfect line you draw is filled with jagged edges. That doesn’t make the formula any less true.

If you go to a very small level, extremely small, you get quantum foam. Quantum mechanics works at this level, and there is math to describe this. Relativity breaks down at this level, but it doesn’t make Relativity any less true.

So the math is still valid.

Wasn’t it mathematics that gave rise to the idea that the universe might be granular? It isn’t something that we observe in our daily lives or can have any direct knowledge of.

@Rarebear – Warning: I know less than nothing about physics

So, do you think we could ultimately figure out exactly where we go from jagged to foam? and what would be the significance of that finding?

Mathematics had no problem going from Newtonian physics to relativity and quantum mechanics. Why do you suppose it would have problems with new models? There is currently a problem of reconciling relativity and quantum mechanics. There are plenty of theories on how to do it, but difficulty in being able to prove any of them.

From a purely practical point of view, our understanding of physics works just fine. We are not running into any barriers due to lack of understanding of fundamental laws. We use quantum mechanics for designing computer circuits and general relativity for operating GPS devices.

@Seek Well, the quantum foam is at the quantum level—the level of quarks, electrons, protons, etc. Even if you look at an electron micrograph of something extremely smooth, it’s jagged. But the maths work.