Tegmark does not clain that the universe is math. He proposes that it has only mathematical properties.....difference. On the face of that sounds reasonable to me. I cannot conceive of a universe which does not have mathematical properties. Even chaos is a mathematical term. Well, as bookkeeper my maths were an accurate accounting and reflection of the real assets and liabilities of the company, as verified by our yearly inventory count and cash in the bank. This is not trivial. I would not compare mathematics to a game, but more to the rules of how a game is played....difference. Tegmark says that the universe could not exist unless it followed some form of mathematical function because all physical things in the universe have values and values interact through mathematical functions. As to our ability to represent the mathematical values and functions with a symbolic language is considered to be our greatest evolutionary asset. But humans are not the only ones who can perform mathematical calculations. A Lemur and many other species can tell the difference between more and less, and are able to do a form of rudimentary calculus based on that mental ability. It is not necessecary for our symbolic language to be reality as long as it can represent universal functions accurately. Thank you and suit yourself if you do wish to pursue this perspective. I have problems myself with some of Tegmarks presentations, but as have dealt with mathematics for a greater part of my life, I find the concept of a certain mathematical aspect to the very creation and evolution of the universe. David Bohm called this progreesion as the "enfolded order" (potential values and functions) becoming expressed in the physical world as the "unfolded order". The word "order" being key. Well , perhaps they are right, I am not qualified to judge, but many scientist seem to accept the premise and I can only ask, "how does the universe function if not by some form of mathematics?" I haven't read his book either. But I see no other option to his premise and I haven't read anything that can replace the power of mathematics in all of reality. All patterns are fundamentally mathematical in essence, as are equations which merely show that one thing has the same value as another thing, but seen from a different persective. And to say mathematical structures are very abstract, I recommend this short but delightful Ted Talk by Roger Antonsen, who clearly demonstrates the connection between ratios and reality. https://www.ted.com/talks/roger_antonsen_math_is_the_hidden_secret_to_understanding_the_world Thank you for the link, I now feel compelled to read it, just to confirm if my first impression is correct. And I agree with you that any assumption of a mathematical nature to the universe has nothing to do with infinity per se.