National Science Foundation

DECEMBER 13, 2022

I teach four classes of 8 th grade Pre-Algebra every day. My school has a high percentage of Hispanic students, many of whom speak Spanish and English with equal facility. Only the most heartless among us would deny this young man access to a suitable class—he had literally moved to the country from Venezuela the day before.

Math 75

Math Mathematics Communications Algebra 75

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.

Biology 81

Biology STEM Critical Thinking Chemistry 81

Robert Talbert, Ph.D.

FEBRUARY 11, 2022

Here's the one from Winter 2021 for calculus and here's the one for modern algebra. This worked out really well since students got access to helpful resources and a break from time pressure, and I got more explanations of reasoning which led (in my view) to better data about student learning. These are both big leaps for me.

Mathematics 52

Mathematics Algebra Communications Computer Science 52

STEM Education Shopping

JULY 19, 2023

For example, if you have a fraction bar that’s divided into four equal parts, you can see that each part represents one-fourth. By combining two of these bars, you can visually see that two-fourths is equal to one-half. This hands-on approach makes it much easier to grasp the concept of fractions and perform operations with them.

Math 52

Math Algebra Data analysis Problem Solving 52

Stephen Wolfram

JUNE 28, 2023

The Wolfram Language is important to LLMs—in providing a way to access computation and computational knowledge from within the LLM. We’ve always built—and deployed—Wolfram Language so it can be accessible to as many people as possible. But the advent of LLMs—and our new Chat Notebooks —opens up Wolfram Language to vastly more people.

Computer 118

Computer Calculus Construction Mathematics 118

Futurum

AUGUST 11, 2022

LIGHT-YEAR – the distance travelled by light in one year (equal to ~9,000,000,000,000 km). I have also been advocating for STEM programmes to develop more flexibility and to be more accessible. I work with the Project for Inmate Education programme at UCSC, where I teach algebra and astronomy in Santa Cruz jail facilities.

Astronomy 98

Astronomy Equality Research Research 98

Stephen Wolfram

MARCH 7, 2022

But beginning a little more than a century ago there emerged the idea that one could build mathematics purely from formal axioms, without necessarily any reference to what is accessible to sensory experience. and at t steps gives a total number of rules equal to: &#10005. So how about logic, or, more specifically Boolean algebra ?

Mathematics 120

Mathematics Physics Computer Algebra 120

Stephen Wolfram

MAY 25, 2021

The same is true of axioms for areas of abstract algebra like group theory—as well as basic Euclidean geometry (at least for integers). We also can’t tell whether numbers were just “convenient for proofs” or whether in fact the actual mathematical results picked to formalize were somehow based on their “accessibility” through numbers.

Mathematics 53

Mathematics Physics Computer Algebra 53

Stephen Wolfram

MARCH 5, 2024

Should we think of it essentially as a practical tool for accessing existing methods, or does it provide something fundamentally new for science? In 2000 I was interested in what the simplest possible axiom system for logic (Boolean algebra) might be. Will they be “accessible” to neural nets? So how does AI stack up?

Science 122

Science Sciences Computer Mathematics 122

Stephen Wolfram

OCTOBER 7, 2021

or ) must for example be equal to 1 mod 2, 3 and 6. But it seems at least conceivable that this one might be more accessible to proof than most. This structure is very dependent on the algebraic properties of. These could be algebraic constructs (such a polynomials) based on ordinary real or complex numbers. &#10005.

Physics 52

Physics Mathematics Algebra Construction 52

Stephen Wolfram

DECEMBER 11, 2023

And through our technology we also have access to a few thousand other kinds of measurements. In a physics analogy to the behavior of a gas, typical human mathematics operates not at the “molecular” level of individual emes (or even axioms) but rather at the “fluid dynamics” level of “human-accessible” mathematical concepts.

Physics 120

Physics Mathematics Computer Communications 120

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 67

Construction Computer Physics Accessibility 67

Stephen Wolfram

MAY 17, 2021

But what kind of integro-differential-algebraic equation can reproduce the time evolution isn’t clear. And in fact such probabilities tend to have the effect of hiding whatever complexity is intrinsically produced—even if they do “smooth out average behavior” to make things more accessible to traditional mathematical methods.

Computer 52

Computer Achievement Mathematics Physics 52