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

Stephen Wolfram

1 Mathematics and Physics Have the Same Foundations. 2 The Underlying Structure of Mathematics and Physics. 23 The Physicalized Laws of Mathematics. 29 Counting the Emes of Mathematics and Physics. 1 | Mathematics and Physics Have the Same Foundations. 3 The Metamodeling of Axiomatic Mathematics. Graphical Key.

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Calculus 187
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Even beyond Physics: Introducing Multicomputation as a Fourth General Paradigm for Theoretical Science

Stephen Wolfram

One might have thought it was already exciting enough for our Physics Project to be showing a path to a fundamental theory of physics and a fundamental description of how our physical universe works. Despite this, however, fundamental physics always seemed to resist its advance. The Path to a New Paradigm.

Physics 67
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How can smart contact lenses monitor and treat eye conditions?

Futurum

Wearable sensors can be tailored to monitor a range of physical (e.g., Therefore, wearable biomedical devices must have mechanical softness, flexibility, stretchability and breathability, without side effects such as discomfort, pain or tissue damage.”. At school, study maths, physics, biology and chemistry.

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How Did We Get Here? The Tangled History of the Second Law of Thermodynamics

Stephen Wolfram

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. The theory of heat will hereafter form one of the most important branches of general physics. physics) in Glasgow—began to be curious about.

Energy 91
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The Story Continues: Announcing Version 14 of Wolfram Language and Mathematica

Stephen Wolfram

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 100
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Computational Foundations for the Second Law of Thermodynamics

Stephen Wolfram

The Second Law of thermodynamics is considered one of the great general principles of physical science. Sometimes textbooks will gloss over everything; sometimes they’ll give some kind of “common-sense-but-outside-of-physics argument”. But our Physics Project has changed that picture. Why does the Second Law work?