Futurum

SEPTEMBER 12, 2023

The scope of objectives Olivia and Barbara are aiming for students to achieve demands a range of learning experiences. If you have the option, take a statistics course and mathematics courses beyond algebra,” says Barbara. One of my proudest career achievements thus far is successfully completing my PhD.

Biology 81

Biology STEM Chemistry Critical Thinking 81

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 95

Computer Calculus Construction Accessibility 95

Stephen Wolfram

DECEMBER 11, 2023

But in observer theory what we want to do is just characterize the equivalencing that’s achieved. Sometimes then the crucial step of equivalencing different detailed inputs is achieved by simple “numerical aggregation”, most often by accumulation of objects (atoms, raindrops, etc.) or physical effects (forces, currents, etc.).

Physics 112

Physics Computer Mathematics Communications 112

Futurum

JULY 13, 2022

Mathematically, these records make it fairly easy to construct a supply chain network,” says Zach. There are many branches of maths, including algebra, geometry, calculus and statistics. Linear algebra, statistics and computer programming are particularly useful. “If WHAT ARE YOUR PROUDEST CAREER ACHIEVEMENTS SO FAR?

Mathematics 82

Mathematics Artificial Intelligence Math Research 82

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

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 116

Physics Mathematics Computer Construction 116

Stephen Wolfram

SEPTEMBER 27, 2024

Just like in our original f [0] = 1 case, we can construct “blue graph trees” rooted at each of the initial conditions. 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. are also primitive recursive.

Computer 106

Computer Mathematics Argumentation Science 106

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 115

Science Sciences Computer Mathematics 115

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 52

Mathematics Physics Computer Algebra 52

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 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. It’s not difficult to construct multiway system models. There are multiway Turing machines.

Science 59

Science Sciences Physics Mathematics 59

Stephen Wolfram

AUGUST 29, 2024

Even if I hadn’t been able to imagine quite what could be built on them, I’d been able to construct solid foundations, that successfully encapsulated things in the cleanest and simplest ways. In a sense, computation constructs sequences of new things, say with time. And I’m then usually left with a strong sense of responsibility.

Physics 110

Physics Computer Biology Mathematics 110

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

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 64

Science Sciences Mathematics Physics 64

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 69

Computer Physics Science Sciences 69

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 68

Construction Computer Physics Accessibility 68

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