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Don’t Give Up on Algebra: Let’s Shift the Focus to Instruction

National Science Foundation

In its current form, school algebra serves as a gatekeeper to higher-level mathematics. Researchers and policy makers have pushed to open that gate—providing more students access to algebra, focusing in particular on those students historically denied access to higher-level mathematics. Let’s Not Be So Quick to Give Up on Algebra.

Algebra 76
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The Concept of the Ruliad

Stephen Wolfram

The global structures of metamathematics , economics , linguistics and evolutionary biology seem likely to provide examples—and in each case we can expect that at the core is the ruliad, with its unique structure. And we can trace the argument for this to the Principle of Computational Equivalence. But what if our knowledge changed?

Physics 122
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Even beyond Physics: Introducing Multicomputation as a Fourth General Paradigm for Theoretical Science

Stephen Wolfram

Part of what this achieves is to generalize beyond traditional mathematics the kind of constructs that can appear in models. Events are like functions, whose “arguments” are incoming tokens, and whose output is one or more outgoing tokens. Economics.

Physics 65
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Multicomputation: A Fourth Paradigm for Theoretical Science

Stephen Wolfram

Part of what this achieves is to generalize beyond traditional mathematics the kind of constructs that can appear in models. Events are like functions, whose “arguments” are incoming tokens, and whose output is one or more outgoing tokens. Economics.

Science 64
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Remembering the Improbable Life of Ed Fredkin (1934–2023) and His World of Ideas and Stories

Stephen Wolfram

Ed was never officially a “test pilot”, but he told me stories about figuring out how to take his plane higher than anyone else—and achieving weightlessness by flying his plane in a perfect free-fall trajectory by maintaining an eraser floating in midair in front of him. Then McCarthy started to explain ways a computer could do algebra.

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Can AI Solve Science?

Stephen Wolfram

In 2000 I was interested in what the simplest possible axiom system for logic (Boolean algebra) might be. of what’s now Wolfram Language —we were trying to develop algorithms to compute hundreds of mathematical special functions over very broad ranges of arguments. Back in 1987—as part of building Version 1.0

Science 122