Remove Accessibility Remove Argumentation Remove Calculus Remove Equality
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How Did We Get Here? The Tangled History of the Second Law of Thermodynamics

Stephen Wolfram

But in 1798 Benjamin Thompson (Count Rumford) (1753–1814) measured the heat produced by the mechanical process of boring a cannon, and began to make the argument that, in contradiction to the caloric theory, there was actually some kind of correspondence between mechanical energy and amount of heat.

Energy 88
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Don’t Give Up on Algebra: Let’s Shift the Focus to Instruction

National Science Foundation

Researchers and policy makers have pushed to open that gate—providing more students access to algebra, focusing in particular on those students historically denied access to higher-level mathematics. Yet we have not seen equal advances in achievement (National Center for Education Statistics, 2019). Domina et al.,

Algebra 76
educators

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LLM Tech and a Lot More: Version 13.3 of Wolfram Language and Mathematica

Stephen Wolfram

The Wolfram Language is important to LLMs—in providing a way to access computation and computational knowledge from within the LLM. We’ve always built—and deployed—Wolfram Language so it can be accessible to as many people as possible. But the advent of LLMs—and our new Chat Notebooks —opens up Wolfram Language to vastly more people.

Computer 118
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The Physicalization of Metamathematics and Its Implications for the Foundations of Mathematics

Stephen Wolfram

But beginning a little more than a century ago there emerged the idea that one could build mathematics purely from formal axioms, without necessarily any reference to what is accessible to sensory experience. and at t steps gives a total number of rules equal to: &#10005. But what can we do with this statement? &#10005.

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Computational Foundations for the Second Law of Thermodynamics

Stephen Wolfram

Sometimes textbooks will gloss over everything; sometimes they’ll give some kind of “common-sense-but-outside-of-physics argument”. 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.