The idea that the forces, particles and interactions that we see today are all manifestations of a single, overarching theory is an attractive one, requiring extra dimensions and lots of new particles and interactions. Many such mathematical constructs exist to explore, but without a physical Universe to compare it to, we’re unlikely to learn anything meaningful about our Universe. (Credit: Rogilbert/public domain via Wikimedia Comons)

No, our Universe isn’t made of pure mathematics

Unless you confront your theory with what’s actually out there in the Universe, you’re playing in the sandbox, not engaging in science.

At the frontiers of theoretical physics, many of the most popular ideas have one thing in common: they begin from a mathematical framework that seeks to explain more things than our currently prevailing theories do. Our current frameworks for General Relativity and Quantum Field Theory are great for what they do, but they don’t do everything. They’re fundamentally incompatible with one another, and cannot sufficiently explain dark matter, dark energy, or the reason why our Universe is filled with matter and not antimatter, among other puzzles.

It’s true that mathematics enables us to quantitatively describe the Universe, it’s an incredibly useful tool when applied properly. But the Universe is a physical, not mathematical entity, and there’s a big difference between the two. Here’s why mathematics alone will always be insufficient to reach a fundamental theory of everything.

One of the great puzzles of the 1500s was how planets moved in an apparently retrograde fashion. This could either be explained through Ptolemy’s geocentric model (L), or Copernicus’ heliocentric one (R). However, getting the details right to arbitrary precision was something that would require theoretical advances in our understanding of the rules underlying the observed phenomena, which led to Kepler’s laws and eventually Newton’s theory of universal gravitation. (Credit: E. Siegel/Beyond the Galaxy)