Stephen Wolfram

DECEMBER 13, 2021

Any integral of an algebraic function can in principle be done in terms of our general DifferentialRoot objects. When you do operations on Around numbers the “errors” are combined using a certain calculus of errors that’s effectively based on Gaussian distributions—and the results you get are always in some sense statistical.

Construction 67

Construction Computer Physics Accessibility 67

Stephen Wolfram

MARCH 23, 2023

But then mathematical notation was invented, and math took off—with the development of algebra, calculus, and eventually all the various mathematical sciences. Back before about 500 years ago, pretty much the only way to “express math” was in natural language.

Computer 145

Computer Mathematics Math Achievement 145

Stephen Wolfram

SEPTEMBER 9, 2021

Its key idea is to think of things in the world as being constructed from some kind of simple-to-describe elements—say geometrical objects—and then to use something like logical reasoning to work out what will happen with them. It’s not difficult to construct multiway system models. There are multiway Turing machines.

Physics 64

Physics Science Sciences Mathematics 64

Stephen Wolfram

SEPTEMBER 9, 2021

Its key idea is to think of things in the world as being constructed from some kind of simple-to-describe elements—say geometrical objects—and then to use something like logical reasoning to work out what will happen with them. It’s not difficult to construct multiway system models. There are multiway Turing machines.

Science 64

Science Sciences Physics Mathematics 64

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

JANUARY 9, 2024

Then for each function (or other construct in the language) there are pages that explain the function, with extensive examples. So did that mean we were “finished” with calculus? Somewhere along the way we built out discrete calculus , asymptotic expansions and integral transforms. But even now there are still frontiers.

Computer 102

Computer Calculus Construction Accessibility 102

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). He was going for what he saw as the big prize: using them to “construct the universe”. 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

It’s yet another surprising construct that’s arisen from our Physics Project. In some ways it’s a bit like our efforts to construct the ruliad. In constructing it, one can imagine using Turing machines or hypergraph rewriting systems or indeed any other kind of computational system. As an analogy, consider the real numbers.

Physics 121

Physics Mathematics Computer Construction 121

Robert Talbert, Ph.D.

APRIL 15, 2022

Those assessments can take on various forms, and in well-constructed courses they do have varying forms, corresponding to different levels of Bloom's Taxonomy. But no matter the form, they are are typically one-and-done: Students turn them in, and the work is graded, and that's that. Limit the frequency of reassessments.

Academic Standards 52

Academic Standards Communications Calculus Argumentation 52