Imagine if everything around you – your phone, the stars, even your thoughts – wasn’t just described by mathematical equations but was actually made of maths. This is exactly what physicist Max Tegmark’s Mathematical Universe Hypothesis (MUH) proposes: that reality itself is a mathematical structure, and every possible mathematical equation represents a different universe.

Sounds like a conspiracy theorist made this up, right? Well actually, Tegmark is an MIT professor with over 300 publications, a Fellow of the American Physical Society, and one of Times Magazine’s Most Influential People in AI 2023. 

MUH does not mean we live in a world where numbers float around like characters from a kids’ TV show, whispering equations into our ears. Instead, the MUH suggests that our universe is an embodiment of all mathematical laws, from particle behaviour to galaxy formation. Not just that maths describes our universe (which we already know – it’s the foundation of physics), but that our universe literally is a mathematical structure. Inside the world of Minecraft, everything runs on code. The characters can’t see this code, but it completely determines their reality. Tegmark dares us to ask – what if our universe works the same way? 

This would have some bizarre implications. For one, reality isn’t made of atoms – it’s made of equations. Every mathematically possible universe exists, which means infinite versions of you, doing infinite things. Tegmark begins his best-selling novel, Our Mathematical Universe,  with an overview of some very well accepted cosmological theories, such as inflation theory, and a discussion of our cosmic origins. Towards the end of the book, he delves deep into his most radical idea, the MUH and its multiverses. This is Tegmark’s view that parallel universes are simply a direct implication of cosmological theory.

Image: Doodle of parallel universes, taken from Tegmark’s website, https://space.mit.edu/home/tegmark/crazy.html

So, is the MUH actually scientific or is it just mathematical mysticism? For this we can turn to one of the great philosophers of science, Karl Popper. Popper argued that for a theory to be scientific, there must be a way to prove it wrong. If there’s no possible observation that could contradict it, then it’s just an idea – not science. Popper’s approach embodies the self-correcting nature of inquiry and aims to provide unbiased criteria that science should follow.

At first glance, by a strict Popperian approach, the MUH is closer to sci-fi than science. Falsificationism, at its core, involves devising a hypothesis, making a prediction based upon this, and comparing with observations. Popper hugely admired Einstein’s daring relativity theories which were risky and had highly improbable predictions. Crucially, however, these theories were always potentially falsifiable and eventually advancements in physics provided evidence in support. MUH, like Einstein’s relativity, is bold and creative, but unlike relativity, it isn’t testable. We cannot directly test the implications of MUH, meaning there is nothing to refute it with. This is why many scientists cannot class the MUH as genuinely scientific, and probably why a lot of physicists think Tegmark is a bit nuts. Perhaps you agree with Sabina Hossenfeld, a physicist-YouTuber, when she said, “Frankly, I think Tegmark came up with the mathematical universe only to make sure everyone knows he is a seriously weird fellow.”

Yet Tegmark dares to dream, and he argues the following: space continuation inside black holes is a prediction of general relativity, and we cannot falsify this in isolation. However, we can provide several observations in support of general relativity, such as Mercury’s orbit around the Sun. This implies the theory’s validity, and hence its predictions are also valid. Thus, although we cannot directly observe what transpires inside black holes (well, you could fall into one and find out, but you wouldn’t be alive to tell anyone), we still consider this factual. Mathematical theories can be tested without examining all their implications, and by the same logic as before, this does not render the concept of a multiverse non-scientific. 

The MUH is fascinating, but it pushes the limits of Popper’s falsificationism. Some theories, like multiverses and string theory, are difficult to test, but that doesn’t mean they aren’t valuable ideas. At the end of the day, falsificationism keeps science honest, but Tegmark’s ideas show that some theories might require new ways of thinking. Maybe the next breakthrough in physics will give us the tools to finally test if we’re all just living inside an equation. 

Whether or not the MUH is true, one thing is undeniable – mathematics works. From the equations that predict planetary motion to the formulas governing electricity, maths appears to be woven into the fabric of reality with an elegance that seems almost too perfect. Perhaps it’s just a coincidence. Or perhaps, as Max Tegmark suggests, it’s because mathematics is reality itself. As Nobel Prize-winning physicist Eugene Wigner put it, “The enormous usefulness of mathematics in the natural sciences is something bordering on the mysterious.” And perhaps, that mystery is one we may never fully unravel…