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 120

Mathematics Physics Computer Algebra 120

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.

Science 122

Science Sciences Computer Mathematics 122

Stephen Wolfram

MARCH 23, 2023

And in the end, as we’ll discuss later, that’s a more flexible and powerful way to communicate. There’s a big example of this historically, in mathematics. But then mathematical notation was invented, and math took off—with the development of algebra, calculus, and eventually all the various mathematical sciences.

Computer 145

Computer Mathematics Math Achievement 145

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 65

Physics Science Sciences 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.

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. has lots of specific mathematical enhancements. it can: &#10005.

Construction 67

Construction Computer Physics Accessibility 67

Stephen Wolfram

JANUARY 9, 2024

In addition to whole courses, we have “miniseries” of lectures about specific topics: And we also have courses —and books—about the Wolfram Language itself, like my Elementary Introduction to the Wolfram Language , which came out in a third edition this year (and has an associated course, online version, etc.): are Comap and ComapApply.

Computer 102

Computer Calculus Construction Accessibility 102