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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. 3 The Metamodeling of Axiomatic Mathematics. 4 Simple Examples with Mathematical Interpretations. 15 Axiom Systems of Present-Day Mathematics. 21 What Can Human Mathematics Be Like? Graphical Key.

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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. There were still mathematical loose ends, as well as issues such as its application to living systems and to systems involving gravity.

Energy 88
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Assessing My First Semester of ‘Ungrading’

ED Surge

They were eager to get back to normal (whatever that means) and I credit that desire with bringing much of the extra energy into our class. They learn about the subtleties of mathematical argument by presenting to each other in class. I just had to help them on their way. So, what did I notice about learning?

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Navigating the Three Dimensions of NGSS: A Guide for 4th and 5th Grade Teachers

The Science Penguin

The DCI states, “Support an argument that plants get the materials they need for growth chiefly from air and water.” In our NGSS-aligned Phenomena-Based Science Units , each unit is aligned to a specific DCI. For example, in the Plants Phenonema-Based Science Unit , the fifth grade DCI for LS1-1 is the focus of the content within the unit.

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Loop Quantum Gravity: The Answer to What Space is

STEMe

He suggested that time dilates, space contracts, and energy and mass are the same things. Separate from this, Einstein published a paper in 1905 saying that monochromatic radiation behaves discontinuously and is made up of energy quanta; we then later figured out that the energy quanta were photons.

Energy 52
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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”. With hard spheres there’s built-in conservation of energy, momentum and number of particles. How does one tie all this down with rigorous, mathematical-style proofs? Why does the Second Law work?

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How machine learning is revolutionising materials science

Futurum

For the growing ML aspects of the field, backgrounds in computing, coding and mathematics are helpful. My father taught science and mathematics, and our house was full of science books. I had great arguments about mathematical proofs with my amazing grade school maths teachers and was a regular at Boston’s science museum.

Science 98