Did mathematics create the universe?

 The short answer is no; there is no ‘fire in the equations’. One needs to be careful not to conflate epistemology with ontology. Let’s look at the wave function (ψ) which is a fundamental entity in quantum mechanics (QM). It’s a mathematical formula that gives probabilities of finding a particle existing before the particle is actually ‘observed’. However, there is also some debate about whether the wave function exists in reality. 

 

Mathematics, from a human perspective, is a set of symbols that can be arranged in formulae that can describe and predict physical phenomena. The symbols are human-made, but the relationships, that are entailed in the formulae, are not. In other words, mathematical relationships appear to have a life of their own independent of human minds.

 

So there is a relationship between mathematics, the physical world and the human mind, (probably best explored, if not explained, by Roger Penrose’s 3 worlds philosophy). The relationship between the human mind and the physical world is epistemological - epitomised by the discipline called physics. And mathematics is the medium we use in pursuing that epistemology.

 

Eugene Wigner famously wrote an essay called The unreasonable effectiveness of mathematics in the natural sciences, and it still causes debate half a century after it was written. Wigner refers to the 2 miracles inherent in the Universe’s capacity to be self-comprehending: 

 

It is difficult to avoid the impression that a miracle confronts us here… or the two miracles of the existence of laws of nature and of the human mind’s capacity to divine them.

 

Or to quote Einstein: The most incomprehensible thing about the Universe is that it’s comprehensible.

 

The point is that Wigner’s ‘miracles’ or Einstein’s ‘incomprehensible thing’ are completely dependent on mathematics. But Wigner, in particular, brings together epistemology and ontology under one rubric. Ontology is ‘the nature of being’ (dictionary definition). At its deepest level, the ‘nature of being’ appears to be mathematical.

 

None other than Richard Feynman weighed into the discussion in his book, The Character of Physical Law, specifically in a chapter titled The Relation of Mathematics to Physics, where he expounds:

 

...what turns out to be true is that the more we investigate, the more laws we find, and the deeper we penetrate nature, the more this disease persists. Every one of our laws is a purely mathematical statement in rather complex and abstruse mathematics... Why? I have not the slightest idea. It is only my purpose to tell you about this fact.

 

The ’disease’ he’s referring to and the ‘fact’ he can’t explain is best expressed in his own words:

 

The strange thing about physics is that for the fundamental laws we still need mathematics.

 

In conclusion, he says the following:

 

Physicists cannot make a conversation in any other language. If you want to learn about nature, to appreciate nature, it is necessary to understand the language that she speaks in. She offers her information only in one form.

 

Many scientists and philosophers argue that we create mathematical models that give very reliable and accurate descriptions of reality. All these ‘models’ have epistemological limits, which means we use different mathematics for different scenarios. Nevertheless, there are natural constants and mathematical ‘laws’ that are requisite for complex life to exist. Terry Bollinger (in a Quora post) explained the significance of Planck’s constant in determining the size and stability of atoms, from which everything we can see and touch is made, including ourselves. The fine structure constant is another fundamental dimensionless number that determines the ‘nature of being’ upon which the reality we all know depends.

 

So mathematics didn’t create the Universe, but, at a fundamental level, it determines the Universe we inhabit.

Footnotes: 

1) This was in answer to a question posted on Quora. I did receive an 'upvote' from Masroor Bukhari, who is a former Research Fellow and PhD in Particle Physics at Houston University.

2) Will Singourd, who asked the question, wrote the following:

Thank you for that outstanding answer. This is the most thorough & best answer I've seen on Quora. I've printed it out for reference.

I appreciate all the thought you put in it, plus your elucidating writing skills.