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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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On the frontline of the biomedical revolution

Futurum

It is likely you can answer yes to both questions because biomedical science is booming – and for good reason. Diagnostics, imaging, materials science – people now realise how important it is.” Into the light Jin specialises in using photonics – the science of light – within biomedicine. “We

Biology 98
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How we read: the neuroscience behind literacy

Futurum

Literacy skills have a profound impact on a person’s life,” says Dr Jacqueline Cummine, a professor at the Faculty of Rehabilitation Medicine – Communication Science and Disorders at the University of Alberta. The enthusiasm and energy that emerging scientists bring to research is a constant rejuvenation! “An

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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. From miniscule sub-atomic particles to gargantuan black holes, the world of science deals with a dramatic range of sizes. Research computing is a sub-discipline of computer science.

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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. This natural inclination towards science and technology sparked my interest in pursuing a field where I could delve into the intricacies of electrical and computer systems.