article thumbnail

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.

article thumbnail

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.

educators

Sign Up for our Newsletter

This site is protected by reCAPTCHA and the Google Privacy Policy and Terms of Service apply.

article thumbnail

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
article thumbnail

How we read: the neuroscience behind literacy

Futurum

The enthusiasm and energy that emerging scientists bring to research is a constant rejuvenation! “An There is a lot of ‘tradition’ with regards to ideas and approaches, which I feel can sometimes impede our ability to move science forward efficiently. An ongoing challenge for my field is trying to buck the status quo.

article thumbnail

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. I started my career as an experimental scientist.

Biology 98
article thumbnail

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. Chemistry with Dr Nicole Hondow and Stuart Micklethwaite.

article thumbnail

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. Meet Hadi From a young age, I was naturally drawn to mathematics and science.