Stephen Wolfram

OCTOBER 27, 2023

It’s a new paradigm—that actually seems to unlock things not only in fundamental physics, but also in the foundations of mathematics and computer science , and possibly in areas like biology and economics too. You know, I talked about building up the universe by repeatedly applying a computational rule.

Computer 134

Computer Physics Mathematics Achievement 134

Futurum

JUNE 28, 2022

Machine learners use a mix of mathematics and computer science to develop and test their algorithms. I enjoy developing algorithms, deriving theory for them, and finally implementing them as a computer program to solve problems,” he says. “I WHAT INSPIRED YOU TO BECOME A COMPUTER SCIENTIST? Explore all your options.

Artificial Intelligence 88

Artificial Intelligence Learning Computer Science Computer 88

Robert Talbert, Ph.D.

FEBRUARY 11, 2022

Here's the one from Winter 2021 for calculus and here's the one for modern algebra. This semester I taught two sections of Discrete Structures for Computer Science 1, an entry-level course for Computer Science majors on the mathematical foundations of computing.

Mathematics 52

Mathematics Algebra Communications Computer Science 52

Stephen Wolfram

MARCH 7, 2022

So how about logic, or, more specifically Boolean algebra ? The axiom system we’ve used for Boolean algebra here is by no means the only possible one. And in terms of that operator the very simplest axiom system for Boolean algebra contains ( as I found in 2000 ) just one axiom (where here ? and Not ) is: &#10005.

Mathematics 121

Mathematics Physics Computer Algebra 121

PCS Edventures

MARCH 4, 2020

Algebra , which incorporates unknown variables into arithmetic equations. Calculus , which calculates rates of change and infinites. Science, technology, engineering and arts careers often rely upon at least one of these math specializations, so jobs with a math focus are often talked about under the other STEAM categories. (The

Mathematics 52

Mathematics Energy Architecture Government 52

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.

Mathematics 52

Mathematics Computer Algebra Calculus 52

Stephen Wolfram

SEPTEMBER 9, 2021

Mathematics is normally done at the level of “specific mathematical concepts” (like, say, algebraic equations or hyperbolic geometry)—that are effectively the “populated places” (or “populated reference frames”) of metamathematical space. And the same issue arose for Alonzo Church’s lambda calculus (introduced around 1930).

Science 65

Science Sciences Physics Mathematics 65

Stephen Wolfram

SEPTEMBER 9, 2021

Mathematics is normally done at the level of “specific mathematical concepts” (like, say, algebraic equations or hyperbolic geometry)—that are effectively the “populated places” (or “populated reference frames”) of metamathematical space. And the same issue arose for Alonzo Church’s lambda calculus (introduced around 1930).

Physics 64

Physics Science Sciences Mathematics 64

Stephen Wolfram

SEPTEMBER 29, 2023

Such abstract functions could be used both “symbolically” to represent things, and explicitly to “compute” things. All sorts of (often ornate) formalism was developed in mathematical logic, with combinators arriving in 1920 , and lambda calculus in 1935.

Physics 108

Physics Computer Argumentation Construction 108

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.

Computer 67

Computer Physics Science Sciences 67

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?

Physics 122

Physics Mathematics Computer Construction 122