Remove doubt-proof-and-what-it-means-to-do-mathematics
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Why Mastery Based Learning is a Good Option

Ask a Tech Teacher

Without doubt, we teachers recognize this as a problem but what do we do about it? What is MBL. Students who don’t understand a topic and don’t do well on the summative assessment for that subject, aren’t automatically moved on because time allotted for that topic ran out. Characteristics.

Learning 188
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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. 11 Proofs in Accumulative Systems. 15 Axiom Systems of Present-Day Mathematics. 20 The Notion of Truth.

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The Concept of the Ruliad

Stephen Wolfram

And—it should be said at the outset—we’re still only at the very beginning of nailing down those technical details and setting up the difficult mathematics and formalism they involve.) But to ground things here, let’s start with a slightly technical discussion of what the ruliad is. The Entangled Limit of Everything. &#10005.

Physics 122
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Will AIs Take All Our Jobs and End Human History—or Not? Well, It’s Complicated…

Stephen Wolfram

The Shock of ChatGPT Just a few months ago writing an original essay seemed like something only a human could do. What will AIs be able to do? My goal here is to explore some of the science, technology—and philosophy—of what we can expect from AIs. So what is ChatGPT ? But so what do we get in the end?

Computer 105
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How Did We Get Here? The Tangled History of the Second Law of Thermodynamics

Stephen Wolfram

And to check myself I’ve been keen to know just where this conventional wisdom came from, how it’s been validated, and what might have made it go astray. 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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How Inevitable Is the Concept of Numbers?

Stephen Wolfram

What is there to count? Now here’s what we get: &#10005. And we can imagine describing what we’re seeing by just saying for example “There are 11 objects…”. What Underlies the Idea of Numbers? What Underlies the Idea of Numbers? It doesn’t matter what kinds of things they are.

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Computational Foundations for the Second Law of Thermodynamics

Stephen Wolfram

What does it really depend on? What would be needed to “prove it”? But it is only now—with ideas that have emerged from our Physics Project —that I think I can pull all the pieces together and finally be able to construct a proper framework to explain why—and to what extent—the Second Law is true. Why does the Second Law work?