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
MARCH 5, 2024
But the computer let me discover just by systematic enumeration the 2-state, 3-color machine that in 2007 was proved universal (and, yes, it’s the simplest possible universal Turing machine). In 2000 I was interested in what the simplest possible axiom system for logic (Boolean algebra) might be.
Stephen Wolfram
AUGUST 22, 2023
. “Lick” Licklider —who persuaded Ed to join BBN to “teach them about computers”. It didn’t really come to light until he was at BBN, but while at Lincoln Lab Ed had made what would eventually become his first lasting contribution to computer science. Then McCarthy started to explain ways a computer could do 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. The systems can be based on Boolean algebra, database updating or other kinds of ultimately computational rules.
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. The systems can be based on Boolean algebra, database updating or other kinds of ultimately computational rules.
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