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.

Science 65

Science Sciences Physics Mathematics 65

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 64

Physics Science Sciences Mathematics 64

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 Argumentation Algebra Communications 52

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 Argumentation Algebra 52

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 357

Research Research Teaching Calculus 357

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 Argumentation 52

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 117

Computer Calculus Construction Mathematics 117

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 67

Computer Physics Science Sciences 67

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 122

Physics Mathematics Computer Construction 122

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 Argumentation Algebra Personalized Learning 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

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 103

Computer Calculus Construction Accessibility 103

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