Stephen Wolfram

JUNE 28, 2023

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. 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 118

Computer Calculus Construction Mathematics 118

Stephen Wolfram

MAY 25, 2021

How do we achieve this? Let’s say that we’re trying to achieve the objective of having an efficient transportation system for carrying people around. The same is true of axioms for areas of abstract algebra like group theory—as well as basic Euclidean geometry (at least for integers). One person wants to get a cookie.

Mathematics 53

Mathematics Physics Computer Algebra 53

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

NOVEMBER 10, 2021

For integers, the obvious notion of equivalence is numerical equality. 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.

Physics 121

Physics Mathematics Computer Construction 121