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The Physicalization of Metamathematics and Its Implications for the Foundations of Mathematics

Stephen Wolfram

When most working mathematicians do mathematics it seems to be typical for them to reason as if the constructs they’re dealing with (whether they be numbers or sets or whatever) are “real things”. And we can think of that ultimate machine code as operating on things that are in effect just abstract constructs—very much like in mathematics.

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Numbers and networks: how can we use mathematics to assess the resilience of global supply chains?

Futurum

Mathematically, these records make it fairly easy to construct a supply chain network,” says Zach. There are many branches of maths, including algebra, geometry, calculus and statistics. Linear algebra, statistics and computer programming are particularly useful. “If WHAT DOES A DAY IN THE LIFE OF A MATHEMATICIAN LOOK LIKE? .

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The Concept of the Ruliad

Stephen Wolfram

It’s yet another surprising construct that’s arisen from our Physics Project. And it’s one that I think has extremely deep implications—both in science and beyond. In some ways it’s a bit like our efforts to construct the ruliad. The whole continuum of all real numbers is “from the outside” in many ways a simple construct.

Physics 122
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How Inevitable Is the Concept of Numbers?

Stephen Wolfram

Presumably it’s that we can sample space without having to think about time, or in other words, that we can consistently construct a stable notion of space. 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?