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 23, 2021

And at first I did so in the main scientific paradigm I knew : models based on mathematics and mathematical equations. From mathematics. Mathematical physics. By the late 1970s, though, there were other initiatives emerging, particularly coming from mathematics and mathematical physics. Synergetics.

Computer 55

Computer Mathematics Science Sciences 55

Stephen Wolfram

JANUARY 9, 2024

So did that mean we were “finished” with calculus? Somewhere along the way we built out discrete calculus , asymptotic expansions and integral transforms. And in Version 14 there are significant advances around calculus. Another advance has to do with expanding the range of “pre-packaged” calculus operations.

Computer 103

Computer Calculus Construction Accessibility 103

Stephen Wolfram

JUNE 29, 2022

Now “characters” could be 16-bit constructs, with nearly 65536 possible “glyphs” allocated across different languages and uses (including some mathematical symbols that we introduced). Needless to say, you can do this computationally—though the “calculus” of what’s been defined so far in Unicode is fairly bizarre: &#10005.

Calculus 114

Calculus Construction Computer Argumentation 114

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 65

Science Sciences Physics 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.

Physics 64

Physics Science Sciences Mathematics 64

Futurum

MAY 16, 2023

Because these processes typically take place over very long timescales, we have to rely on models by expressing these processes as mathematical formulas,” explains Denise. “To For a geoscience degree, you will generally need a good understanding of chemistry and physics, as well as calculus,” she says. “I

Geology 52

Geology Research Research Energy 52

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). In 2015 Ed told me a nice story about his time at Caltech: In 1952–53, I was a student in Linus Pauling’s class where he lectured Freshman Chemistry at Caltech. And it was agreed that we would do it.

Computer 67

Computer Physics Science Sciences 67

Stephen Wolfram

SEPTEMBER 29, 2023

A different tradition—originating in mathematics in the late 1800s—involved the routine use of “abstract functions” like f ( x ). All sorts of (often ornate) formalism was developed in mathematical logic, with combinators arriving in 1920 , and lambda calculus in 1935.

Physics 108

Physics Computer Argumentation Construction 108

Stephen Wolfram

FEBRUARY 3, 2023

How does one tie all this down with rigorous, mathematical-style proofs? Once one has the idea of “equilibrium”, one can then start to think of its properties as purely being functions of certain parameters—and this opens up all sorts of calculus-based mathematical opportunities. Well, it’s difficult.

Computer 92

Computer Energy Physics Construction 92

Stephen Wolfram

DECEMBER 13, 2021

the same integral could still be done, but only in terms of elliptic integrals : Mathematical Functions: A Milestone Is Reached. Special functions are in a sense a way of packaging mathematical knowledge : once you know that the solution to your equation is a Lamé function , that immediately tells you lots of mathematical things about it.

Construction 66

Construction Computer Physics Accessibility 66