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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?

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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. AKHSHAY’S PHYSICAL EXPERIMENTS. JOSEPH’S MATHEMATICAL MODELS. For larger volumes of fluid, gravity also becomes important.”. Download the article.

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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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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 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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Imaging the invisible: how can research software and imaging techniques help scientists study the things we can’t see?

Futurum

Scientific model — a conceptual or mathematical representation of a real-world phenomenon that allows scientists to study the phenomenon in more detail. Scientists can now turn their theories into mathematical models, which can then be expressed in software as simulations. GrantRef=EP/R025819/1 ). Joanna’s research.

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How can intelligent systems revolutionise healthcare?

Futurum

Whether it’s tracking physical activity, monitoring vital signs, analysing sleep patterns or brain activities, intelligent systems can provide real-time feedback and recommendations to encourage healthier habits, behaviours, and early and accurate diagnosis and prognosis that may not be evident to the human eyes,” explains Narges.

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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 the language of our Physics Project, it’s the ultimate limit of all rulial multiway systems. In many ways, the ruliad is a strange and profoundly abstract thing.

Physics 122