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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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Behind the screens: the crystals that flow like rain down a windowpane

Futurum

Mathematically, a sphere is the shape that minimises the surface area of a fixed volume, explaining why small water droplets on a flat surface take the shape of a spherical cap. JOSEPH’S MATHEMATICAL MODELS. Joseph builds mathematical models for the height of rivulets, based on mathematical equations. Pinterest.

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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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How we read: the neuroscience behind literacy

Futurum

In goal-based training, individuals set their own goals associated with reading and we design activities to help them achieve them.” The enthusiasm and energy that emerging scientists bring to research is a constant rejuvenation! “An We found that both programmes improved reading performance in adults with dyslexia,” says Jacqueline.

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On the frontline of the biomedical revolution

Futurum

I loved building things, such as with LEGO, and enjoyed mathematics – I was always quite good at it. “I I think I’ve achieved a lot. Dr Jiajia Zhou, Associate Professor at UTS’s School of Mathematical and Physical Sciences, is leading the research and development of a range of innovative detection methods.

Biology 98
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How can intelligent systems revolutionise healthcare?

Futurum

In the world’s fight against climate change, AI algorithms can help by monitoring carbon emissions, predicting changes to weather patterns and optimising our energy use. What successes has this project achieved so far? “We This method also significantly reduced the time and resources needed to achieve successful detection.

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The Concept of the Ruliad

Stephen Wolfram

And—it should be said at the outset—we’re still only at the very beginning of nailing down those technical details and setting up the difficult mathematics and formalism they involve.) Mathematically this can be thought of as being like decomposing the ruliad structure in terms of fibrations and foliations.). The View from Mathematics.

Physics 122