Mathematical universe hypothesis

The proposal that physical reality is a mathematical structure, not merely something mathematics describes. It treats mathematical existence and physical existence as the same.

Max Tegmark: A Swedish-American cosmologist who proposed that all mathematical structures exist physically. He developed and popularized the hypothesis in its modern form.
Mathematical Structure: A collection of objects together with specified relations or operations among them. The hypothesis identifies each physically real universe with such a structure.
Instrumentalism: The view that theories are tools for predicting observations rather than true descriptions of reality. It rejects the hypothesis's claim that mathematical theories can be identical to physical reality.
Empirical Testability: The capacity of a claim to be assessed through observations that could count against it. The hypothesis risks accommodating every possible observation by including its structure among mathematical possibilities.
Mathematical Platonism: The view that mathematical objects exist independently of human minds and conventions. The hypothesis extends mathematical realism from abstract objects to physical reality.
Isomorphism: A structure-preserving correspondence between two mathematical structures. Isomorphic descriptions may encode the same structure rather than distinct physical realities.
Mathematical Modeling: The use of mathematical structures to represent selected features of real-world systems. Modeling distinguishes a mathematical representation from the physical system it represents.
Measure Problem in Cosmology: The problem of assigning consistent probabilities when cosmological theory allows infinitely many regions or universes. A multiverse of mathematical structures needs a measure to predict which observations are typical.
Indispensability Argument: An argument that commitment to mathematical entities follows from their indispensable role in scientific theories. It supports belief in mathematics, but does not establish that the world is mathematical.
Scientific Realism: The view that successful scientific theories describe a mind-independent world, including unobservable entities. The hypothesis takes realism further by identifying the world with a mathematical theory's structure.

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PlatonismBroader topic: It extends mathematical realism by identifying the physical world with mathematical structure.