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The Physicalization of Metamathematics and Its Implications for the Foundations of Mathematics

Stephen Wolfram

1 Mathematics and Physics Have the Same Foundations. 2 The Underlying Structure of Mathematics and Physics. 23 The Physicalized Laws of Mathematics. 29 Counting the Emes of Mathematics and Physics. 1 | Mathematics and Physics Have the Same Foundations. 3 The Metamodeling of Axiomatic Mathematics. Graphical Key.

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Even beyond Physics: Introducing Multicomputation as a Fourth General Paradigm for Theoretical Science

Stephen Wolfram

One might have thought it was already exciting enough for our Physics Project to be showing a path to a fundamental theory of physics and a fundamental description of how our physical universe works. Part of what this achieves is to generalize beyond traditional mathematics the kind of constructs that can appear in models.

Physics 64
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Observer Theory

Stephen Wolfram

But what we’ve discovered particularly dramatically in our Physics Project is that the nature of us as observers is critical even in determining the most fundamental laws we attribute to the universe. But in observer theory what we want to do is just characterize the equivalencing that’s achieved.

Physics 120
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How to Master Math Wooden Manipulatives Get Your High Score

STEM Education Shopping

By physically manipulating these blocks, you can practice counting, addition, and subtraction. By placing them side by side, you can physically see that when you combine 2 and 3, you get 5. By physically removing the blocks, you can see how the quantity decreases, reinforcing the concept of subtraction.

Math 52
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The Concept of the Ruliad

Stephen Wolfram

It’s yet another surprising construct that’s arisen from our Physics Project. In the language of our Physics Project, it’s the ultimate limit of all rulial multiway systems. And here is a rulial multiway system made from hypergraph rewriting of the kind used in our Physics Project , using all rules with signature : &#10005.

Physics 121
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Can AI Solve Science?

Stephen Wolfram

A key idea—ultimately supported at a foundational level by our Physics Project —is that we can think of everything that happens as a computational process. A lot of science—and technology—has been constructed specifically around computationally reducible phenomena. The system is doing a computation to determine its behavior.

Science 122
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The Story Continues: Announcing Version 14 of Wolfram Language and Mathematica

Stephen Wolfram

So many discoveries, so many inventions, so much achieved, so much learned. And key to everything we do is leveraging what we have already done—often taking what in earlier years was a pinnacle of technical achievement, and now using it as a routine building block to reach a level that could barely even be imagined before.

Computer 102