National Science Foundation

SEPTEMBER 22, 2021

Yet we have not seen equal advances in achievement (National Center for Education Statistics, 2019). Arguments that suggest we do away with school algebra frame algebra itself as the problem and leave unexamined how and in what ways that algebra is taught. 2017; Stein et al., Boaler & Leavitt, 2019). Compared with what?

Algebra 76

Algebra Mathematics Flexibility Research 76

Stephen Wolfram

MAY 23, 2023

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.

Technology 69

Technology Argumentation Computer Publication 69

Stephen Wolfram

JANUARY 31, 2023

But he had a second hypothesis too—based, he said, on the ideas of “that most ingenious gentleman, Monsieur Descartes”: that instead air consists of “flexible particles” that are “so whirled around” that “each corpuscle endeavors to beat off all others”.

Energy 89

Energy Argumentation Physics Mathematics 89

Stephen Wolfram

MARCH 7, 2022

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. which we can read as “there exists something a for which equals a ”.

Mathematics 114

Mathematics Physics Computer Algebra 114

Stephen Wolfram

FEBRUARY 3, 2023

Sometimes textbooks will gloss over everything; sometimes they’ll give some kind of “common-sense-but-outside-of-physics argument”. The energy of the particles is indicated here by the size of the “token dots”: Continuing this a few more steps we get: At the beginning we started with all particles having equal energies.

Computer 91

Computer Energy Physics Construction 91

Stephen Wolfram

MARCH 5, 2024

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. Yes, there can be a lot of flexibility in this model. Back in 1987—as part of building Version 1.0 But one can’t have a truly “model-less model”.

Science 115

Science Sciences Computer Mathematics 115