Stephen Wolfram

DECEMBER 13, 2021

Any integral of an algebraic function can in principle be done in terms of our general DifferentialRoot objects. there are now many integrals that could previously be done only in terms of special functions, but now give results in elementary functions. And a third of a century later—in Version 13.0—we’re it can: &#10005.

Construction 67

Construction Computer Physics Accessibility 67

Stephen Wolfram

JUNE 28, 2023

Line, Surface and Contour Integration “Find the integral of the function ” is a typical core thing one wants to do in calculus. But particularly in applications of calculus, it’s common to want to ask slightly more elaborate questions, like “What’s the integral of over the region ?”, or “What’s the integral of along the line ?”

Computer 118

Computer Calculus Construction Mathematics 118

Stephen Wolfram

SEPTEMBER 9, 2021

In physics, those “topological phenomena” presumably correspond to things like elementary particles , with all their various elaborate symmetries. Ultimately one wants to see how the structure and behavior of the system can be broken down into elementary “tokens” and “events”.

Physics 65

Physics Science Sciences Mathematics 65

Stephen Wolfram

SEPTEMBER 9, 2021

In physics, those “topological phenomena” presumably correspond to things like elementary particles , with all their various elaborate symmetries. Ultimately one wants to see how the structure and behavior of the system can be broken down into elementary “tokens” and “events”.

Science 64

Science Sciences Physics Mathematics 64

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). Then McCarthy started to explain ways a computer could do algebra. It was all algebra. Gliders are usually transported with their wings removed, with the wings attached in order to fly.

Computer 68

Computer Physics Science Sciences 68

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