National Science Foundation

SEPTEMBER 22, 2021

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. Yet we have not seen equal advances in achievement (National Center for Education Statistics, 2019). Domina et al.,

Algebra 76

Algebra Mathematics Flexibility Research 76

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

Stephen Wolfram

DECEMBER 13, 2021

When you do operations on Around numbers the “errors” are combined using a certain calculus of errors that’s effectively based on Gaussian distributions—and the results you get are always in some sense statistical. Also in the area of calculus we’ve added various conveniences to the handling of differential equations.

Construction 67

Construction Computer Physics Accessibility 67

Stephen Wolfram

MARCH 7, 2022

But beginning a little more than a century ago there emerged the idea that one could build mathematics purely from formal axioms, without necessarily any reference to what is accessible to sensory experience. and at t steps gives a total number of rules equal to: &#10005. But what can we do with this statement? &#10005.

Mathematics 120

Mathematics Physics Computer Algebra 120

Stephen Wolfram

FEBRUARY 3, 2023

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. That anything like this makes sense depends, however, yet again on “perfect randomness as far as the observer is concerned”.

Computer 92

Computer Energy Physics Construction 92