Algebra Elementary Equality 
CSTEM
JULY 30, 2024
Elementary students rarely encounter computer science or engineering, and advanced science courses in high school favor higher-income, non-minority students. In middle schools offering algebra, white students make up 50% of the attendees, but 58% of those enrolled in algebra classes. Changing placement policies.
Stephen Wolfram
MARCH 7, 2022
In more explicit form we could write this as Equal [f[x_, y_], f[f[y_, x_],y_]] —where Equal ( ) has the “known meaning” of representing equality. and at t steps gives a total number of rules equal to: ✕. So how about logic, or, more specifically Boolean algebra ? ✕. ✕.
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Stephen Wolfram
JUNE 28, 2023
As an example, here’s a small piece of code (from my An Elementary Introduction to the Wolfram Language ), shown in the default way it’s rendered in notebooks: But in Version 13.3 But what if we ask a question where the answer is some algebraic expression? But in Version 13.3 Sometimes that’s easy to determine.
Stephen Wolfram
MAY 25, 2021
Instead, what happens is that the universe evolves by virtue of lots of elementary updating events happening throughout the network. The same is true of axioms for areas of abstract algebra like group theory—as well as basic Euclidean geometry (at least for integers). But at the lowest level in our models, time doesn’t work that way.
Stephen Wolfram
DECEMBER 11, 2023
In observing the metamathematical universe the analogy is basically different possible kinds of theories or abstractions—say, algebraic vs. geometrical vs. topological vs. categorical, etc. With our concept of “elementary equivalencings” we have a way to measure both in terms of computational operations.
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.
Stephen Wolfram
MARCH 5, 2024
My first big success came in 1981 when I decided to try enumerating all possible rules of a certain kind (elementary cellular automata) and then ran them on a computer to see what they did: I’d assumed that with simple underlying rules, the final behavior would be correspondingly simple.
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