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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 Physicalization of Metamathematics and Its Implications for the Foundations of Mathematics

Stephen Wolfram

How Math Relates to Humans. One can view a symbolic expression such as f[g[x][y, h[z]], w] as a hierarchical or tree structure , in which at every level some particular “head” (like f ) is “applied to” one or more arguments. and at t steps gives a total number of rules equal to: &#10005. 22 Going below Axiomatic Mathematics.

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LLM Tech and a Lot More: Version 13.3 of Wolfram Language and Mathematica

Stephen Wolfram

we’ve finally finished doing the math and creating the algorithms to introduce AppellF2 , AppellF3 and AppellF4. And, yes, when you try to run the function, it’ll notice it doesn’t have correct arguments and options specified. In technical documents it’s common to see math that’s at least formatted elegantly. But in Version 13.3

Computer 118
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Can AI Solve Science?

Stephen Wolfram

But in a sense the ultimate reason that “math is hard” is that we’re constantly seeing evidence of computational irreducibility: we can’t get around actually having to compute things. In 2000 I was interested in what the simplest possible axiom system for logic (Boolean algebra) might be. Back in 1987—as part of building Version 1.0

Science 122
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The Problem of Distributed Consensus

Stephen Wolfram

In the basic definition of a standard cellular automaton, the rule “takes its arguments” in a definite order. But what kind of integro-differential-algebraic equation can reproduce the time evolution isn’t clear. RandomGraph[{20, 40}, EdgeStyle -> Gray, VertexStyle -> Table[i -> (RandomInteger[] /. {0