Stephen Wolfram

JANUARY 9, 2024

So many discoveries, so many inventions, so much achieved, so much learned. Of course one of our great achievements has been to maintain across all that functionality a tightly coherent and consistent design that results in there ultimately being only a small set of fundamental principles to learn.

Computer 100

Computer Calculus Construction Accessibility 100

National Science Foundation

SEPTEMBER 22, 2021

Similarly, reformers have focused on the timing of the course, aiming to enroll students as early as possible to open pathways to calculus and to diversify access to higher level mathematics. This necessitates that we turn our attention to how to support students in learning algebraic ideas. Let’s Not Be So Quick to Give Up on Algebra.

Algebra 76

Algebra Mathematics Flexibility Research 76

Robert Talbert, Ph.D.

APRIL 15, 2022

How it traditionally works In traditional, points-based grading systems, the evidence that students present about their learning is almost always in the form of one-and-done assessments: Tests, exams, homework, presentations, and the like. One-and-done assessment is clearly a terrible way to measure student learning.

Academic Standards 52

Academic Standards Communications Calculus Algebra 52

Stephen Wolfram

SEPTEMBER 9, 2021

Because what we seem to be learning is that in fact our whole universe is operating as a giant multiway system. Events are like functions, whose “arguments” are incoming tokens, and whose output is one or more outgoing tokens. But I suspect there’s even more to learn by looking at something closer to the underlying token-event graph.

Physics 67

Physics Science Sciences Mathematics 67

Stephen Wolfram

SEPTEMBER 9, 2021

Because what we seem to be learning is that in fact our whole universe is operating as a giant multiway system. Events are like functions, whose “arguments” are incoming tokens, and whose output is one or more outgoing tokens. But I suspect there’s even more to learn by looking at something closer to the underlying token-event graph.

Science 61

Science Sciences Physics Mathematics 61

Stephen Wolfram

JUNE 29, 2022

You can give Threaded as an argument to any listable function, not just Plus and Times : &#10005. we’re adding SymmetricDifference : find elements that (in the 2-argument case) are in one list or the other, but not both. Now we can use the path function to make a “spiralling” tour video: College Calculus. In Version 13.1

Calculus 116

Calculus Construction Computer Argumentation 116

Stephen Wolfram

JANUARY 31, 2023

But in 1798 Benjamin Thompson (Count Rumford) (1753–1814) measured the heat produced by the mechanical process of boring a cannon, and began to make the argument that, in contradiction to the caloric theory, there was actually some kind of correspondence between mechanical energy and amount of heat.

Energy 91

Energy Physics Argumentation Mathematics 91

Stephen Wolfram

AUGUST 29, 2024

I later learned that a century earlier many well-known physicists were beginning to think in a similar direction (matter is discrete, light is discrete; space must be too) but back then they hadn’t had the computational paradigm or the other tools needed to move this forward. There was still much to do (and there still is today).

Physics 114

Physics Computer Biology Mathematics 114

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. and zero arguments: α[ ]. &#10005. One step of substitution already gives: &#10005. &#10005. &#10005. or: &#10005.

Mathematics 119

Mathematics Physics Computer Algebra 119

Stephen Wolfram

DECEMBER 14, 2022

Calculus & Its Generalizations. Is there still more to do in calculus? But in more recent times—with increased sophistication from machine learning—we’ve been adding more and more sophisticated forms of cluster analysis. For example, you might have a function with several arguments that are each large expressions.

Computer 77

Computer Astronomy Construction Algebra 77

Stephen Wolfram

FEBRUARY 3, 2023

Sometimes textbooks will gloss over everything; sometimes they’ll give some kind of “common-sense-but-outside-of-physics argument”. And, yes, one can try all sorts of methods from statistics , machine learning , cryptography and so on. This argument is quite rough, but it captures the essence of what’s going on.

Computer 93

Computer Energy Physics Construction 93

Stephen Wolfram

AUGUST 22, 2023

He used to like to tell people I’d learned a lot from him. 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). And in fact I think it was only in writing this piece that I even learned he’d grown up in Los Angeles (specifically, East Hollywood).

Computer 70

Computer Physics Sciences Science 70