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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. 3 The Metamodeling of Axiomatic Mathematics. 4 Simple Examples with Mathematical Interpretations. 15 Axiom Systems of Present-Day Mathematics. 21 What Can Human Mathematics Be Like? Graphical Key.

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Can AI Solve Science?

Stephen Wolfram

Three centuries ago science was transformed by the idea of representing the world using mathematics. A lot of science—and technology—has been constructed specifically around computationally reducible phenomena. And that’s for example why things like mathematical formulas have been able to be as successful in science as they have.

Science 122
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Navigating the Three Dimensions of NGSS: A Guide for 4th and 5th Grade Teachers

The Science Penguin

The DCI states, “Support an argument that plants get the materials they need for growth chiefly from air and water.” It also encourages students to be flexible and creative and to develop their ideas over time. In our NGSS-aligned Phenomena-Based Science Units , each unit is aligned to a specific DCI.

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How Did We Get Here? The Tangled History of the Second Law of Thermodynamics

Stephen Wolfram

It began partly as an empirical law, and partly as something abstractly constructed on the basis of the idea of molecules, that nobody at the time knew for sure existed. There were still mathematical loose ends, as well as issues such as its application to living systems and to systems involving gravity.

Energy 88
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Boost Literacy with STEAM

PCS Edventures

While sciences and mathematics may take center stage, literacy skills have always been waiting in the wings, ready to make their debut. Both Discover Digital Video LAB and Traveling Artist kits are flexible for in-person or distance learning. Mathematics and Literacy. We can’t forget literacy in math!

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The New World of LLM Functions: Integrating LLM Technology into the Wolfram Language

Stephen Wolfram

And for example doing a very simple piece of machine learning , we again get a symbolic object which can be used as a function and applied to an argument to get a result: And so it is with LLMFunction. By giving a second argument to LLMFunction you can say you want actual, structured computable output. are symbolic objects.

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

Stephen Wolfram

Its key idea is to think of things in the world as being constructed from some kind of simple-to-describe elements—say geometrical objects—and then to use something like logical reasoning to work out what will happen with them. In the mathematical paradigm one imagines having a mathematical equation and then separately somehow solving it.

Physics 65