Robert Talbert, Ph.D.

FEBRUARY 10, 2023

As I teach my Linear Algebra and Differential Equations class this semester, which uses more computing than ever, I'm thinking even more about these topics. If anything, over the past seven years, my feelings about the centrality of computing in the mathematics major have gotten even more entrenched.

Mathematics 52

Mathematics Computer Algebra Calculus 52

Stephen Wolfram

OCTOBER 27, 2023

It’s a new paradigm—that actually seems to unlock things not only in fundamental physics, but also in the foundations of mathematics and computer science , and possibly in areas like biology and economics too. You know, I talked about building up the universe by repeatedly applying a computational rule.

Computer 134

Computer Physics Mathematics Achievement 134

Futurum

DECEMBER 6, 2022

Nguyen Do, “Direct-Sense Brain-Computer Interfaces and Wearable Computers,” IEEE Transactions on Systems, Man, and Cybernetics – Systems, 50th Anniversary Issue, Vol. Fields of research: Computer Science, Artificial Intelligence (AI), Brain Computer Interfaces (BCIs). Explore careers in computer science. •

Computer 70

Computer Computer Science Artificial Intelligence Research 70

Stephen Wolfram

SEPTEMBER 9, 2021

But among the examples I’ve at least begun to investigate are metamathematics, molecular biology, evolutionary biology, molecular computing, neuroscience, machine learning, immunology, linguistics, economics and distributed computing. Chemistry / Molecular Biology. There are many.

Physics 67

Physics Sciences Science Mathematics 67

Stephen Wolfram

SEPTEMBER 9, 2021

But among the examples I’ve at least begun to investigate are metamathematics, molecular biology, evolutionary biology, molecular computing, neuroscience, machine learning, immunology, linguistics, economics and distributed computing. Chemistry / Molecular Biology. There are many.

Sciences 61

Sciences Science Physics Mathematics 61

Stephen Wolfram

NOVEMBER 10, 2021

The global structures of metamathematics , economics , linguistics and evolutionary biology seem likely to provide examples—and in each case we can expect that at the core is the ruliad, with its unique structure. Some correspond to theoretical computer science. Still, finding such paths is what automated theorem provers do.

Physics 121

Physics Mathematics Computer Construction 121

Stephen Wolfram

MAY 16, 2022

And what determines our experience—and the science we use to summarize it—is what characteristics we as observers have in sampling the ruliad. And these ideas build crucially on the paradigm of A New Kind of Science. But in biology (for example in connection with membranes), or in molecular computing, they may be crucial.

Sciences 65

Sciences Science Mathematics Physics 65

Stephen Wolfram

MAY 17, 2021

But what kind of integro-differential-algebraic equation can reproduce the time evolution isn’t clear. The “consensus result” in this case should be a constant function whose value is effectively the sign of the integral of this function. To do more than this requires in effect defining “directions” in the graph.

Computer 52

Computer Achievement Mathematics Physics 52

Stephen Wolfram

AUGUST 29, 2024

The fall of 2021 involved really leaning into the new multicomputational paradigm , among other things giving a long list of where it might apply : metamathematics, chemistry, molecular biology, evolutionary biology, neuroscience, immunology, linguistics, economics, machine learning, distributed computing.

Physics 114

Physics Computer Biology Mathematics 114

Stephen Wolfram

MARCH 7, 2022

So how about logic, or, more specifically Boolean algebra ? The axiom system we’ve used for Boolean algebra here is by no means the only possible one. And in terms of that operator the very simplest axiom system for Boolean algebra contains ( as I found in 2000 ) just one axiom (where here ? and Not ) is: &#10005.

Mathematics 119

Mathematics Physics Computer Algebra 119

Stephen Wolfram

MARCH 5, 2024

But the computer let me discover just by systematic enumeration the 2-state, 3-color machine that in 2007 was proved universal (and, yes, it’s the simplest possible universal Turing machine). In 2000 I was interested in what the simplest possible axiom system for logic (Boolean algebra) might be. So why does this work?

Sciences 120

Sciences Science Computer Mathematics 120

Stephen Wolfram

AUGUST 22, 2023

. “Lick” Licklider —who persuaded Ed to join BBN to “teach them about computers”. It didn’t really come to light until he was at BBN, but while at Lincoln Lab Ed had made what would eventually become his first lasting contribution to computer science. Then McCarthy started to explain ways a computer could do algebra.

Computer 70

Computer Physics Sciences Science 70