My answer would be **yes**, the universe could be simply a mathematical abstraction.

Why? Because I have never heard about a proof that refutes your question (*title*). In fact, I've read in magazines -- a very long time ago (when the movie Matrix was popular) -- that we cannot refute the hypothesis that we live inside a simulation.

In other words: "the universe could be simply a mathematical abstraction" is a valid hypothesis. Today, we are unable to disprove it.

Regarding your other question (*body* - "can we create our own simulation?"): my answer would be **no**.

It has to do with the fact that it is computationally and physically impossible to run a simulation -- complete, perfect, lossless, bit precise -- of our universe from inside our universe (*please* someone verify that sentence, as I'm not 100% sure about that, it's just vague memory).

I'll quote myself (curiously, I've written down the following a few days ago):

The simulated beings will never have enough computational power to run a complete and perfect simulation like the simulation inside which they live.

Again, I might be completely wrong. But if I'm not wrong, I'll be very happy because I like that quote (I've written it down for a reason :)

1I've heard the proposal before by a mathematician but I don't understand it. Mathematical models are developed by modeling something else: If you model the travel of a particle by distance = rate * time, you establish some numerical principles to explain how to use this equation, and then observe reality to check that it models reality well. If existence is a mathematical model, what would you check it against? Mathematical models are the mental constructs of humans, so it seems unintelligible to me that existence would be a mathematical model, which is a thing in the mind of a human. – Addem – 2014-04-02T20:47:33.723

@Addem You're describing the broad field of physics, and possibly other sciences that use math. I think mathematics may be more universal than just in

our heads. Maybe beings outside our observable universe also do similar mathematics. – StudySmarterNotHarder – 2014-04-02T21:00:11.800@Addem what about dreams? We can have seemingly real dreams without any input from the world except our memories. So our brains are capable of of modelling worlds. What I'm saying is, without addressing the imaginer, could we simply be a points in some space that can be mathematically defined. Maybe outside our everyday experience, we

don't existexcept in some abstract mathematical structure, that is so detailed that even though the structure remains the same, it contains a dimension calledtimeand beings in it that can observe and think, but on the outside, we don't exist to "them." – StudySmarterNotHarder – 2014-04-02T21:26:31.943What makes you think the beings are conscious? When you play a video game, do you think the monsters and space aliens are conscious? – user4894 – 2014-04-02T22:07:13.403

Certainly other beings may do mathematics, but that doesn't imply that it exists outside our minds. I'm not saying that it doesn't have a correspondence to objective reality, but I don't see how it could be reality. The proposal just doesn't make sense to me, like proposing that all of reality is the color blue. The color blue seems like a thing that describes a part of reality--it couldn't be that a

descriptionof apartisidenticalwith thewhole. – Addem – 2014-04-03T01:52:33.153@EnjoysMath, we can certainly mistake dreams for reality--and I can even make sense of, and debate about, the proposal that all of reality "is a dream". I take that to be a loose and poetic way of saying that our perceptions do not stand in a relationship to an object that is in existentially independent of but responsible for those perceptions. That seems like a well-formed (but dubious) proposal to me. But I don't know what it is for a mathematical structure to exist independent of its conception by thinking creatures. – Addem – 2014-04-03T01:57:08.270

This is essentially Pythagoras's view. More recently Max Tegmark has advocated this view in his "Mathematical Universe Hypothesis."

– Geremia – 2014-04-03T17:42:19.807This is a good critical review of notion as a scientific hypothesis. http://www.scottaaronson.com/blog/?p=1753

– Tim kinsella – 2014-04-05T02:30:43.987