Constructive mathematics reconsiders traditional foundational approaches by emphasising explicit constructions and algorithmic content rather than relying solely on non-constructive existence proofs.

“Crystal Math” uses equations—and minimal resources—to rapidly predict the 3D structures of molecular crystals, which could speed up R&D for drugs and electronic devices. Researchers at New York ...

Reverse mathematics is a vibrant programme in mathematical logic that investigates the axioms necessary to establish fundamental theorems throughout mathematics. Central to this endeavour are ...

The mysteries of infinity could lead us to a fantastic structure above and beyond mathematics as we know it WHEN David Hilbert left the podium at the Sorbonne in Paris, France, on 8 August 1900, few ...

For more than a century, scientists have wondered why physical structures like blood vessels, neurons, tree branches, and other biological networks look the way they do. The prevailing theory held ...

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