Algebra Argumentation Calculus Computer Science 
Robert Talbert, Ph.D.
FEBRUARY 10, 2023
As I teach my Linear Algebra and Differential Equations class this semester, which uses more computing than ever, I'm thinking even more about these topics. If anything, over the past seven years, my feelings about the centrality of computing in the mathematics major have gotten even more entrenched.
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. So how about logic, or, more specifically Boolean algebra ? We’ve looked at axioms for group theory and for Boolean algebra.
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Stephen Wolfram
SEPTEMBER 29, 2023
Since the standard Wolfram Language evaluator evaluates arguments first (“leftmost-innermost evaluation”), it therefore won’t terminate in this case—even though there are branches in the multiway evaluation (corresponding to “outermost evaluation”) that do terminate. As the Version 1.0
Stephen Wolfram
AUGUST 22, 2023
It didn’t help that his knowledge of physics was at best spotty (and, for example, I don’t think he ever really learned calculus). “Lick” Licklider —who persuaded Ed to join BBN to “teach them about computers”. Then McCarthy started to explain ways a computer could do algebra. It was all algebra.
Stephen Wolfram
SEPTEMBER 9, 2021
At the level of individual events, ideas from the theory and practice of computation are useful. Events are like functions, whose “arguments” are incoming tokens, and whose output is one or more outgoing tokens. And the same issue arose for Alonzo Church’s lambda calculus (introduced around 1930).
Stephen Wolfram
SEPTEMBER 9, 2021
At the level of individual events, ideas from the theory and practice of computation are useful. Events are like functions, whose “arguments” are incoming tokens, and whose output is one or more outgoing tokens. And the same issue arose for Alonzo Church’s lambda calculus (introduced around 1930).
Stephen Wolfram
NOVEMBER 10, 2021
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. But what about other models of computation—like cellular automata or register machines or lambda calculus?
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