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 88

Energy Physics Argumentation Mathematics 88

National Science Foundation

SEPTEMBER 22, 2021

Similarly, reformers have focused on the timing of the course, aiming to enroll students as early as possible to open pathways to calculus and to diversify access to higher level mathematics. Yet we have not seen equal advances in achievement (National Center for Education Statistics, 2019). 2017; Stein et al.,

Algebra 76

Algebra Mathematics Flexibility Research 76

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 120

Mathematics Physics Computer Algebra 120

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”. Once one has the idea of “equilibrium”, one can then start to think of its properties as purely being functions of certain parameters—and this opens up all sorts of calculus-based mathematical opportunities.

Computer 92

Computer Energy Physics Construction 92