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

Stephen Wolfram

JANUARY 23, 2025

Introducing Tabular Manipulating Data in Tabular Getting Data into Tabular Cleaning Data for Tabular The Structure of Tabular Tabular Everywhere Algebra with Symbolic Arrays Language Tune-Ups Brightening Our Colors; Spiffing Up for 2025 LLM Streamlining & Streaming Streamlining Parallel Computation: Launch All the Machines!

Computer 65

Computer Algebra Data Science Construction 65

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. So how about logic, or, more specifically Boolean algebra ?

Mathematics 116

Mathematics Physics Computer Algebra 116

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 Chemistry Critical Thinking 81

Stephen Wolfram

JUNE 28, 2023

And, yes, when you try to run the function, it’ll notice it doesn’t have correct arguments and options specified. But what if we ask a question where the answer is some algebraic expression? The issue is that there may be many mathematically equal forms of that expression. And, yes, it’s taken a while, but now in Version 13.3

Computer 120

Computer Construction Calculus Mathematics 120

Stephen Wolfram

SEPTEMBER 27, 2024

Some involve alternate functional forms; others involve introducing additional functions, or allowing multiple arguments to our function f. But it turns out that the fact that this can happen depends critically on the Ackermann function having more than one argument—so that one can construct the “diagonal” f [ m , m , m ].

Computer 108

Computer Mathematics Argumentation Science 108

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 117

Physics Mathematics Computer Construction 117