Stephen Wolfram

JANUARY 31, 2023

But by the end of the 1800s, with the existence of molecules increasingly firmly established, the Second Law began to often be treated as an almost-mathematically-proven necessary law of physics. There were still mathematical loose ends, as well as issues such as its application to living systems and to systems involving gravity.

Energy 88

Energy Physics Argumentation Mathematics 88

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

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. But particularly in applications of calculus, it’s common to want to ask slightly more elaborate questions, like “What’s the integral of over the region ?”, or “What’s the integral of along the line ?”

Computer 118

Computer Calculus Construction Mathematics 118

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). It explains that III has four divisions: Mathematical and Programming Services, Behavioral Science, Operations, and “New York”. It says that “From a one-man operation [in 1962], I.I.I.

Computer 68

Computer Physics Science Sciences 68

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

Stephen Wolfram

FEBRUARY 3, 2023

Sometimes textbooks will gloss over everything; sometimes they’ll give some kind of “common-sense-but-outside-of-physics argument”. How does one tie all this down with rigorous, mathematical-style proofs? But one never quite gets there ; it always seems to need something extra. But the mystery of the Second Law has never gone away.

Computer 92

Computer Energy Physics Construction 92