Stephen Wolfram

MARCH 7, 2022

And in what follows we’ll see the great power that arises from using this to combine the achievements and intuitions of physics and mathematics—and how this lets us think about new “general laws of mathematics”, and view the ultimate foundations of mathematics in a different light. So how about logic, or, more specifically Boolean algebra ?

Mathematics 114

Mathematics Physics Computer Algebra 114

Magic EdTech

MAY 13, 2022

In language arts, students can create two contrasting media messages that employ persuasive techniques to capture opposing sides of an issue, instead of just examining the impact of persuasive techniques in a formal argument. The curriculum for algebra classes, for example, will move at a faster and more efficient pace.

Curriculum 52

Curriculum Algebra Argumentation Personalized Learning 52

Stephen Wolfram

JANUARY 9, 2024

So many discoveries, so many inventions, so much achieved, so much learned. And key to everything we do is leveraging what we have already done—often taking what in earlier years was a pinnacle of technical achievement, and now using it as a routine building block to reach a level that could barely even be imagined before.

Computer 96

Computer Calculus Construction Accessibility 96

Stephen Wolfram

SEPTEMBER 27, 2024

Some involve alternate functional forms; others involve introducing additional functions, or allowing multiple arguments to our function f. But functions that for example test whether a Turing machine will ever halt (or give the state that it achieves if and when it does halt) are not in general primitive recursive.

Computer 107

Computer Mathematics Argumentation Sciences 107

Robert Talbert, Ph.D.

APRIL 1, 2022

Both grades and marks are shorthand indicators of some level of achievement; the mark is given at the level of an individual piece of student work. This is the concept behind ungrading , which both David and I have tried and have written about ( here’s David’s article , here’s mine ).

Primary 52

Primary Mathematics Algebra Argumentation 52

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. And we can trace the argument for this to the Principle of Computational Equivalence.

Physics 116

Physics Mathematics Computer Construction 116

Stephen Wolfram

AUGUST 29, 2024

In the end—after all sorts of philosophical arguments, and an analysis of actual historical data —the answer was: “It’s Complicated”. An idea that was someone’s great achievement had been buried and lost to the world. A test example coming soon is whether I can easily explain math ideas like algebra and calculus this way.)

Physics 110

Physics Computer Biology Mathematics 110

Stephen Wolfram

SEPTEMBER 9, 2021

Part of what this achieves is to generalize beyond traditional mathematics the kind of constructs that can appear in models. Events are like functions, whose “arguments” are incoming tokens, and whose output is one or more outgoing tokens. But there is something else too—and it’s from this that the full computational paradigm emerges.

Physics 65

Physics Science Sciences Mathematics 65

Stephen Wolfram

SEPTEMBER 9, 2021

Part of what this achieves is to generalize beyond traditional mathematics the kind of constructs that can appear in models. Events are like functions, whose “arguments” are incoming tokens, and whose output is one or more outgoing tokens. But there is something else too—and it’s from this that the full computational paradigm emerges.

Science 60

Science Sciences Physics Mathematics 60

Stephen Wolfram

MAY 17, 2021

Traditional blockchains achieve consensus through what amounts to a centralized mechanism (even though there are multiple “decentralized” copies of the blockchain that is produced). In both these cases, the rule successfully achieves “global consensus”. So what other cellular automaton rules achieve consensus like this?

Computer 52

Computer Achievement Mathematics Physics 52

Stephen Wolfram

AUGUST 22, 2023

Ed was never officially a “test pilot”, but he told me stories about figuring out how to take his plane higher than anyone else—and achieving weightlessness by flying his plane in a perfect free-fall trajectory by maintaining an eraser floating in midair in front of him. Then McCarthy started to explain ways a computer could do algebra.

Computer 68

Computer Physics Science Sciences 68

Stephen Wolfram

MARCH 5, 2024

In 2000 I was interested in what the simplest possible axiom system for logic (Boolean algebra) might be. of what’s now Wolfram Language —we were trying to develop algorithms to compute hundreds of mathematical special functions over very broad ranges of arguments. Back in 1987—as part of building Version 1.0

Science 115

Science Sciences Computer Mathematics 115

Stephen Wolfram

MAY 20, 2021

1”) releases that deliver our latest R&D achievements—both fully fleshed out, and partly as “coming attractions”—much more frequently. Particularly notable is significantly faster rendering on Windows platforms, achieved by using DirectWrite and making use of GPU capabilities. We released Version 12.2 on December 16, 2020.

Computer 52

Computer Construction Physics Technology 52