Stephen Wolfram

SEPTEMBER 27, 2024

Some involve alternate functional forms; others involve introducing additional functions, or allowing multiple arguments to our function f. But it turns out that the fact that this can happen depends critically on the Ackermann function having more than one argument—so that one can construct the “diagonal” f [ m , m , m ].

Computer 112

Computer Mathematics Argumentation Science 112

Stephen Wolfram

JUNE 28, 2023

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. 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 121

Computer Calculus Construction Mathematics 121

Stephen Wolfram

NOVEMBER 10, 2021

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.) Mathematically this can be thought of as being like decomposing the ruliad structure in terms of fibrations and foliations.). The View from Mathematics.

Physics 121

Physics Mathematics Computer Construction 121

Stephen Wolfram

SEPTEMBER 29, 2023

Since the standard Wolfram Language evaluator evaluates arguments first (“leftmost-innermost evaluation”), it therefore won’t terminate in this case—even though there are branches in the multiway evaluation (corresponding to “outermost evaluation”) that do terminate. If you set , then you set , you should get (not ) if you asked for.

Physics 106

Physics Computer Argumentation Construction 106

Stephen Wolfram

SEPTEMBER 9, 2021

Many would say that modern exact science was launched in the 1600s with the introduction of what we can call the “ mathematical paradigm ”: the idea that things in the world can be described by mathematical equations—and that their behavior can be determined by finding solutions to these equations.

Physics 67

Physics Sciences Science Mathematics 67

Magic EdTech

MAY 13, 2022

Academic enrichment in mathematics instruction could be prompting students with open-ended questions that don’t have a single right solution. The curriculum for algebra classes, for example, will move at a faster and more efficient pace. How Can Academic Enrichment Boost Student Success? Enriched Knowledge.

Curriculum 52

Curriculum Algebra Argumentation Personalized Learning 52

Stephen Wolfram

SEPTEMBER 9, 2021

Many would say that modern exact science was launched in the 1600s with the introduction of what we can call the “ mathematical paradigm ”: the idea that things in the world can be described by mathematical equations—and that their behavior can be determined by finding solutions to these equations.

Sciences 61

Sciences Science Physics Mathematics 61

Robert Talbert, Ph.D.

MARCH 30, 2022

Last semester, when I learned I would be teaching Modern Algebra a third-year level course on number theory, rings, and fields in January, I knew I wanted to make some changes to how I'd taught it in the past. I decided to revamp my course to be ungraded because most of the work consists of written mathematical proofs of theorems.

Mathematics 52

Mathematics Algebra Argumentation Communications 52

Stephen Wolfram

JANUARY 9, 2024

The function Map takes a function f and “maps it” over a list: Comap does the “mathematically co-” version of this, taking a list of functions and “comapping” them onto a single argument: Why is this useful? You need to be able to easily define mathematically complicated boundary conditions. are Comap and ComapApply.

Computer 100

Computer Calculus Construction Accessibility 100

Robert Talbert, Ph.D.

APRIL 1, 2022

In fact, although points are numbers, we typically use them not as numerical data , where mathematical calculations such as averages have real meaning, but as categorical data — that is, as labels that represent our professional judgment on the student’s work.

Primary 52

Primary Mathematics Algebra Argumentation 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 119

Mathematics Physics Computer Algebra 119

Robert Talbert, Ph.D.

APRIL 15, 2022

An argument for traditional grading goes like this: Sure, a single assessment might have a grade on it that doesn't accurately reflect student understanding. Nobody likes traditional grading because it is so soul-sucking and time-consuming, so why do it more often than necessary? This has a connection with the next point.

Academic Standards 52

Academic Standards Communications Calculus Algebra 52

Stephen Wolfram

MAY 17, 2021

In the basic definition of a standard cellular automaton, the rule “takes its arguments” in a definite order. But what kind of integro-differential-algebraic equation can reproduce the time evolution isn’t clear. It was difficult to establish ergodicity mathematically. There is one immediate issue here.

Computer 52

Computer Achievement Mathematics Physics 52

Stephen Wolfram

AUGUST 29, 2024

Pleasantly enough, given our framework, many modern areas of mathematical physics seemed to fit right in.) I had realized that one of the places the ideas of the Physics Project should apply was to the foundations of mathematics, and to metamathematics. And now the responsibility had fallen on us to do this.

Physics 114

Physics Computer Biology Mathematics 114

Stephen Wolfram

MAY 20, 2021

Version 1 of Mathematica was billed as “A System for Doing Mathematics by Computer” , and—for more than three decades—in every new version of Wolfram Language and Mathematica there’ve been innovations in “doing mathematics by computer”. Sometimes the result involves explicit mathematical functions: &#10005. For Version 12.3

Computer 52

Computer Construction Physics Technology 52

Stephen Wolfram

MARCH 5, 2024

Three centuries ago science was transformed by the idea of representing the world using mathematics. And that’s for example why things like mathematical formulas have been able to be as successful in science as they have. In 2000 I was interested in what the simplest possible axiom system for logic (Boolean algebra) might be.

Sciences 120

Sciences Science Computer Mathematics 120

Futurum

SEPTEMBER 12, 2023

Library and research skills cover areas such as knowing how to reference and cite authors properly, being able to discern between reliable and unreliable sources of information, accessing scientific literature and giving accurate evidence-based arguments when writing scientific essays and reports. What do students learn from studying this?

Biology 81

Biology STEM Chemistry Argumentation 81

Stephen Wolfram

AUGUST 22, 2023

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. So what happened is Marvin [Minsky] and I basically fleshed out the idea of a mathematical thing.

Computer 70

Computer Physics Science Sciences 70