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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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How to Master Math Wooden Manipulatives Get Your High Score

STEM Education Shopping

Each block represents a specific number, allowing you to visually understand mathematical operations. By using these manipulatives, you can actively participate in the learning process and visually understand mathematical concepts. By combining two of these bars, you can visually see that two-fourths is equal to one-half.

Math 52
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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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Observer Theory

Stephen Wolfram

But here we want to think not about what’s “mathematically describable”, but instead about what in general is actually implemented —say by our senses, our measuring devices, or our ways of analyzing things. How Observers Construct Their Perceived Reality Our view of the world is ultimately determined by what we observe of it.

Physics 120
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How can first-year STEM university students be better supported?

Futurum

Biology is often combined with engineering, medicine, psychology, sociology, chemistry, physics or mathematics, so that scientists can tackle complex, real-world problems. If you have the option, take a statistics course and mathematics courses beyond algebra,” says Barbara. Do you have a question for Barbara or Olivia?

Biology 81
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How Inevitable Is the Concept of Numbers?

Stephen Wolfram

Presumably it’s that we can sample space without having to think about time, or in other words, that we can consistently construct a stable notion of space. Fast numbers-based ways to do particular computations are often viewed as representing “ exact solutions ” to corresponding mathematical problems. But which axioms should these be?

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Aggregation and Tiling as Multicomputational Processes

Stephen Wolfram

But the general concept of a multiway system, with its discrete branching at discrete steps, depends on a level of fundamental discreteness that’s quite unfamiliar from traditional statistical mechanics—though is perfectly straightforward to define in a computational, or even mathematical, way. For the 8:{3} rule something surprising happens.

Physics 87