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

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. In the mathematical paradigm one imagines having a mathematical equation and then separately somehow solving it.

Physics 65

Physics Science Sciences Mathematics 65

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. In the mathematical paradigm one imagines having a mathematical equation and then separately somehow solving it.

Science 64

Science Sciences Physics Mathematics 64

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. Fast numbers-based ways to do particular computations are often viewed as representing “ exact solutions ” to corresponding mathematical problems.

Mathematics 53

Mathematics Physics Computer Algebra 53

Stephen Wolfram

MAY 16, 2022

My original goal in A New Kind of Science was to take a step beyond the mathematical paradigm that had defined the state of the art in science for three centuries—and to introduce a new paradigm based on computation and on the exploration of the computational universe of possible programs. But there’s more.

Science 63

Science Sciences Mathematics Physics 63

Stephen Wolfram

DECEMBER 13, 2021

Any integral of an algebraic function can in principle be done in terms of our general DifferentialRoot objects. the same integral could still be done, but only in terms of elliptic integrals : Mathematical Functions: A Milestone Is Reached. has lots of specific mathematical enhancements. we’re delivering another jump forward.

Construction 67

Construction Computer Physics Accessibility 67

ED Surge

NOVEMBER 7, 2023

That’s the argument of Peter Liljedahl, a professor of mathematics education at Simon Fraser University in Vancouver, who has spent years researching what works in teaching. 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

Research 354

Research Research Teaching Calculus 354

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. And, of course, it has to be mathematically accurate. It's very much scaffolded, especially when students come into sixth grade.

Learning 272

Learning Algebra Creativity Communications 272

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

JUNE 28, 2023

And in Mathematica and the Wolfram Language that’s achieved with Integrate. They’re mathematically more complex, but each one we successfully cover makes a new collection of problems accessible to exact solution and reliable numerical and symbolic computation. or “What’s the integral of along the line ?” But now in Version 13.3

Computer 118

Computer Calculus Construction Mathematics 118

Stephen Wolfram

NOVEMBER 10, 2021

It’s yet another surprising construct that’s arisen from our Physics Project. And—it should be said at the outset—we’re still only at the very beginning of nailing down those technical details and setting up the difficult mathematics and formalism they involve.) In some ways it’s a bit like our efforts to construct the ruliad.

Physics 122

Physics Mathematics Computer Construction 122

Stephen Wolfram

AUGUST 22, 2023

He was going for what he saw as the big prize: using them to “construct the universe”. It explains that III has four divisions: Mathematical and Programming Services, Behavioral Science, Operations, and “New York”. Then McCarthy started to explain ways a computer could do algebra. It was all algebra.

Computer 68

Computer Physics Science Sciences 68

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 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. Sometimes the result involves explicit mathematical functions: &#10005.

Computer 52

Computer Construction Physics Technology 52