Stephen Wolfram

MARCH 23, 2023

The whole process of “prompt engineering” feels a bit like animal wrangling: you’re trying to get ChatGPT to do what you want, but it’s hard to know just what it will take to achieve that. In the past, one might have tried to achieve this “by hand” by starting with “boilerplate” pieces, then modifying them, “gluing” them together, etc.

Computer 145

Computer Mathematics Math Achievement 145

Stephen Wolfram

DECEMBER 13, 2021

Any integral of an algebraic function can in principle be done in terms of our general DifferentialRoot objects. Turning from calculus to algebra, we’ve added the function PolynomialSumOfSquaresList that provides a kind of “certificate of positivity” for a multivariate polynomial. And a third of a century later—in Version 13.0—we’re

Construction 67

Construction Computer Physics Accessibility 67

Stephen Wolfram

MARCH 5, 2024

A lot of science—and technology—has been constructed specifically around computationally reducible phenomena. In 2000 I was interested in what the simplest possible axiom system for logic (Boolean algebra) might be. Once again, I had no idea this was “out there”, and certainly I would never have been able to construct it myself.

Science 122

Science Sciences Computer Mathematics 122

ED Surge

NOVEMBER 7, 2023

These are the students who end up hitting a wall when math courses move from easier algebra to more advanced concepts in, say, calculus, he argues. “At So how do you achieve change in any setting if that's the case? So they left their habits at the door and then they were willing to construct new habits inside this setting.

Research 354

Research Research Teaching Calculus 354

Stephen Wolfram

MAY 25, 2021

How do we achieve this? Presumably it’s that we can sample space without having to think about time, or in other words, that we can consistently construct a stable notion of space. Let’s say that we’re trying to achieve the objective of having an efficient transportation system for carrying people around.

Mathematics 53

Mathematics Physics Computer Algebra 53

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

ED Surge

NOVEMBER 7, 2022

Teachers spend a lot of time teaching students to work in groups, identifying different roles and practicing how to give feedback on a game or a project in a way that's constructive. In ninth grade algebra, they create food trucks and pitch them to judges in a Shark Tank-style final project.

Learning 273

Learning Algebra Creativity Communications 273

Stephen Wolfram

JUNE 28, 2023

And in Mathematica and the Wolfram Language that’s achieved with Integrate. And over the years that’s exactly what we’ve achieved—for integrals, sums, differential equations, etc. It’s the end of a long journey, and a satisfying achievement in the quest to make as much mathematical knowledge as possible automatically computable.

Computer 118

Computer Calculus Construction Mathematics 118

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). And for example in 1978 the following “radius 3” rule (operating on size-7 neighborhoods) was constructed (and we’ll call it the “GKL rule”): &#10005.

Computer 52

Computer Achievement Mathematics Physics 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 102

Computer Calculus Construction Accessibility 102

Stephen Wolfram

MAY 16, 2022

It’s that underneath everything is all possible computation, encapsulated in the single unique construct that is the ruliad. And in a sense it’s the ultimate computational construct. My stated goal at the beginning of A New Kind of Science was to go beyond the mathematical paradigm, and that’s exactly what was achieved.

Science 63

Science Sciences Mathematics Physics 63

Stephen Wolfram

AUGUST 22, 2023

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. And the only conclusion we can arrive at is that a person can’t do this much algebra with the hope of getting it right.” But Ed wasn’t interested.

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

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. Having this as a single function makes it easier to use in functional programming constructs like this: &#10005. In earlier times we used to release the results of efforts only every few years.

Computer 52

Computer Construction Physics Technology 52