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 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 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

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 67

Construction Computer Physics Accessibility 67

Stephen Wolfram

JANUARY 9, 2024

And we’ve been steadily doing the engineering to let AIs call on Wolfram Language as easily as possible. 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.

Computer 102

Computer Calculus Construction Accessibility 102

Stephen Wolfram

SEPTEMBER 29, 2023

But insofar as we’re only looking at the evaluation of expressions we’ve engineered for particular computational purposes, we’re not yet used to seeing “generic bulk expression evaluation”. A different tradition—originating in mathematics in the late 1800s—involved the routine use of “abstract functions” like f ( x ).

Physics 108

Physics Computer Argumentation Construction 108

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). His father ’s university engineering studies had been cut short by the Russian Revolution, and he now had a one-man wholesale electronic parts business. Petersburg; his mother in Odessa ; they met in LA).

Computer 68

Computer Physics Science Sciences 68

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