Stephen Wolfram

JANUARY 9, 2024

So many discoveries, so many inventions, so much achieved, so much learned. And key to everything we do is leveraging what we have already done—often taking what in earlier years was a pinnacle of technical achievement, and now using it as a routine building block to reach a level that could barely even be imagined before.

Computer 102

Computer Calculus Construction Accessibility 102

Stephen Wolfram

JUNE 28, 2023

Line, Surface and Contour Integration “Find the integral of the function ” is a typical core thing one wants to do in calculus. And in Mathematica and the Wolfram Language that’s achieved with Integrate. And over the years that’s exactly what we’ve achieved—for integrals, sums, differential equations, etc. And in Version 13.3

Computer 118

Computer Calculus Construction Mathematics 118

Stephen Wolfram

MARCH 7, 2022

And in what follows we’ll see the great power that arises from using this to combine the achievements and intuitions of physics and mathematics—and how this lets us think about new “general laws of mathematics”, and view the ultimate foundations of mathematics in a different light. So how about logic, or, more specifically Boolean algebra ?

Mathematics 120

Mathematics Physics Computer Algebra 120

ED Surge

DECEMBER 12, 2022

And like so much during the pandemic, the losses were worse for some communities, with achievement gaps having widened during the pandemic. billion in the hopes of closing achievement gaps in K-12 math education. We believe that it's critical for some kids to be exposed to calculus.

Math 250

Math Algebra Calculus Achievement 250

Stephen Wolfram

AUGUST 22, 2023

It didn’t help that his knowledge of physics was at best spotty (and, for example, I don’t think he ever really learned calculus). Then McCarthy started to explain ways a computer could do algebra. It was all algebra. Ed was assigned to an airbase in Arizona , and by the summer of 1955 he had qualified as a fighter pilot.

Computer 68

Computer Physics Science Sciences 68

Stephen Wolfram

NOVEMBER 10, 2021

For example, we know (as I discovered in 2000) that (( b · c ) · a ) · ( b · (( b · a ) · b )) = a is the minimal axiom system for Boolean algebra , because FindEquationalProof finds a path that proves it. But what about other models of computation—like cellular automata or register machines or lambda calculus?

Physics 122

Physics Mathematics Computer Construction 122

Stephen Wolfram

SEPTEMBER 9, 2021

Part of what this achieves is to generalize beyond traditional mathematics the kind of constructs that can appear in models. In physics, those “topological phenomena” presumably correspond to things like elementary particles , with all their various elaborate symmetries. It’s very much like in the emergence of physical space.

Physics 65

Physics Science Sciences Mathematics 65

Stephen Wolfram

SEPTEMBER 9, 2021

Part of what this achieves is to generalize beyond traditional mathematics the kind of constructs that can appear in models. In physics, those “topological phenomena” presumably correspond to things like elementary particles , with all their various elaborate symmetries. It’s very much like in the emergence of physical space.

Science 64

Science Sciences Physics Mathematics 64

Stephen Wolfram

DECEMBER 13, 2021

Any integral of an algebraic function can in principle be done in terms of our general DifferentialRoot objects. there are now many integrals that could previously be done only in terms of special functions, but now give results in elementary functions. And a third of a century later—in Version 13.0—we’re it can: &#10005.

Construction 67

Construction Computer Physics Accessibility 67