Achievement Equality Natural Sciences 
Stephen Wolfram
NOVEMBER 10, 2021
For integers, the obvious notion of equivalence is numerical equality. Then (by the assumed properties of equality) it follows that. In other words, we’re concerned more with what computational results are obtained, with what computational resources, rather than on the details of the program constructed to achieve this.
STEM Sport
DECEMBER 12, 2023
As the air rushes out of the balloon, it propels the balloon forward, vividly illustrating Newton’s Third Law of Motion – for every action, there is an equal and opposite reaction. Homemade Pendulum: Construct a simple pendulum by suspending a weight from a string.
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Stephen Wolfram
JANUARY 31, 2023
But, first and foremost, the story of the Second Law is the story of a great intellectual achievement of the mid-19th century. There’s a discussion about H for systems that interact, and how there’s an equilibrium value achieved. It’s exciting now, of course, to be able to use the latest 21st-century ideas to take another step.
Stephen Wolfram
MARCH 7, 2022
And in what follows we’ll see the great power that arises from using this to combine the achievements and intuitions of physics and mathematics—and how this lets us think about new “general laws of mathematics”, and view the ultimate foundations of mathematics in a different light. 3 | The Metamodeling of Axiomatic Mathematics. ✕.
Stephen Wolfram
MARCH 15, 2023
Given a defined “goal”, an AI can automatically work towards achieving it. Most of our existing intuition about “machinery” and “automation” comes from a kind of “clockwork” view of engineering—in which we specifically build systems component by component to achieve objectives we want. And that’s where we humans come in.
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. No doubt there’ll at least be some “natural-science-like” characterizations of what’s going on. Will there still be “human-level descriptions” that involve numbers?
Stephen Wolfram
JANUARY 9, 2025
It is, I think, an interesting challengethat gets at the heart of what one can (and cant) expect to achieve with formalized mathematics. But what about something more like a theory in natural science? And in this respect its very different from natural science. So, OK, weve got a complicated proof.
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