National Science Foundation

SEPTEMBER 22, 2021

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

Algebra Mathematics Flexibility Research 76

Futurum

SEPTEMBER 12, 2023

Library and research skills cover areas such as knowing how to reference and cite authors properly, being able to discern between reliable and unreliable sources of information, accessing scientific literature and giving accurate evidence-based arguments when writing scientific essays and reports. What do students learn from studying this?

Biology 81

Biology STEM Critical Thinking Chemistry 81

Stephen Wolfram

JUNE 28, 2023

And in Mathematica and the Wolfram Language that’s achieved with Integrate. And over the years that’s exactly what we’ve achieved—for integrals, sums, differential equations, etc. It’s the end of a long journey, and a satisfying achievement in the quest to make as much mathematical knowledge as possible automatically computable.

Computer 118

Computer Calculus Construction Mathematics 118

Stephen Wolfram

MARCH 7, 2022

And in what follows we’ll see the great power that arises from using this to combine the achievements and intuitions of physics and mathematics—and how this lets us think about new “general laws of mathematics”, and view the ultimate foundations of mathematics in a different light. 3 | The Metamodeling of Axiomatic Mathematics. &#10005.

Mathematics 120

Mathematics Physics Computer Algebra 120

Stephen Wolfram

MAY 17, 2021

Traditional blockchains achieve consensus through what amounts to a centralized mechanism (even though there are multiple “decentralized” copies of the blockchain that is produced). In both these cases, the rule successfully achieves “global consensus”. So what other cellular automaton rules achieve consensus like this?

Computer 52

Computer Achievement Mathematics Physics 52

Stephen Wolfram

NOVEMBER 10, 2021

For integers, the obvious notion of equivalence is numerical equality. For example, we know (as I discovered in 2000) that (( b · c ) · a ) · ( b · (( b · a ) · b )) = a is the minimal axiom system for Boolean algebra , because FindEquationalProof finds a path that proves it.

Physics 122

Physics Mathematics Computer Construction 122

Stephen Wolfram

MARCH 5, 2024

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

Science Sciences Computer Mathematics 122