Stephen Wolfram

MARCH 5, 2024

So what about science? But that certainly doesn’t mean AI can’t importantly help the progress of science. But what I want to do here is to discuss what amount to deeper questions about AI in science. Three centuries ago science was transformed by the idea of representing the world using mathematics.

Science 124

Science Sciences Computer Mathematics 124

Futurum

FEBRUARY 9, 2023

Dr Craig Nitschke of the University of Melbourne uses plant science and sophisticated computer modelling to study how the distribution of tree species in Australia could evolve as the climate changes. Simulation and statistical models (SSMs) are types of mathematical models used in ecology.

Research 78

Research Research Science Sciences 78

STEM Education Shopping

AUGUST 27, 2023

We can draw upon various fields such as science, humanities, social sciences, and arts to enrich our understanding. For instance, by combining critical thinking skills from philosophy with problem-solving skills from mathematics, I can approach challenges from multiple perspectives and develop innovative solutions.

Critical Thinking 52

Critical Thinking Learning Problem Solving Communications 52

Stephen Wolfram

MARCH 7, 2022

1 Mathematics and Physics Have the Same Foundations. 2 The Underlying Structure of Mathematics and Physics. 3 The Metamodeling of Axiomatic Mathematics. 4 Simple Examples with Mathematical Interpretations. 15 Axiom Systems of Present-Day Mathematics. 21 What Can Human Mathematics Be Like? Graphical Key.

Mathematics 122

Mathematics Physics Computer Algebra 122

Robert Talbert, Ph.D.

FEBRUARY 10, 2023

In the original article, I gave a list of what computing skills mathematics majors should learn and when they should learn them. If anything, over the past seven years, my feelings about the centrality of computing in the mathematics major have gotten even more entrenched. Mostly this is because of two things.

Mathematics 52

Mathematics Computer Algebra Calculus 52

Stephen Wolfram

JANUARY 31, 2023

But by the end of the 1800s, with the existence of molecules increasingly firmly established, the Second Law began to often be treated as an almost-mathematically-proven necessary law of physics. There were still mathematical loose ends, as well as issues such as its application to living systems and to systems involving gravity.

Energy 89

Energy Physics Argumentation Mathematics 89

Stephen Wolfram

SEPTEMBER 9, 2021

But what I’ve increasingly been realizing is that actually it’s showing us something even bigger and deeper: a whole fundamentally new paradigm for making models and in general for doing theoretical science. Part of what this achieves is to generalize beyond traditional mathematics the kind of constructs that can appear in models.

Science 65

Science Sciences Physics Mathematics 65

Stephen Wolfram

SEPTEMBER 9, 2021

But what I’ve increasingly been realizing is that actually it’s showing us something even bigger and deeper: a whole fundamentally new paradigm for making models and in general for doing theoretical science. Part of what this achieves is to generalize beyond traditional mathematics the kind of constructs that can appear in models.

Physics 65

Physics Science Sciences Mathematics 65

Stephen Wolfram

NOVEMBER 10, 2021

And it’s one that I think has extremely deep implications—both in science and beyond. 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.) Experiencing the Ruliad. But in the ruliad there are no choices.

Physics 123

Physics Mathematics Computer Construction 123

Stephen Wolfram

FEBRUARY 2, 2023

Statistical Mechanics and Simple Programs Back in 1973 I never really managed to do much science on the very first computer I used. And finally I gave what the 22-year-old me thought at the time was the most plausible explanation: All of this was in a sense rooted in a traditional mathematical physics style of thinking.

Physics 95

Physics Computer Mathematics Science 95

Stephen Wolfram

JANUARY 9, 2024

And in the past few months we’ve been steadily adding connections to the full range of popular LLMs, making Wolfram Language a unique hub not only for LLM usage, but also for studying the performance—and science—of LLMs. You need to be able to easily define mathematically complicated boundary conditions. are Comap and ComapApply.

Computer 104

Computer Calculus Construction Accessibility 104

Stephen Wolfram

FEBRUARY 3, 2023

The Second Law of thermodynamics is considered one of the great general principles of physical science. Sometimes textbooks will gloss over everything; sometimes they’ll give some kind of “common-sense-but-outside-of-physics argument”. How does one tie all this down with rigorous, mathematical-style proofs?

Computer 93

Computer Energy Physics Construction 93

Stephen Wolfram

MAY 17, 2021

In preparation for a conference entitled “ Distributed Consensus with Cellular Automata & Related Systems ” that we’re organizing with NKN (= “New Kind of Network”) I decided to explore the problem of distributed consensus using methods from A New Kind of Science (yes, NKN “rhymes” with NKS) as well as from the Wolfram Physics Project.

Computer 52

Computer Achievement Mathematics Physics 52

Stephen Wolfram

AUGUST 22, 2023

Ed was someone who wanted to independently figure things out for himself, and delighted in presenting his often somewhat-outlandish conclusions—whether about technology, science, business or the world—with dramatic showman-like panache. I wrote about this in one chapter of my 2002 book A New Kind of Science.

Computer 68

Computer Physics Science Sciences 68