Viewers like you help make PBS (Thank you đ). Support your local PBS Member Station here: https://to.pbs.org/DonateSPACE
Be sure to check out the Infinite Series episode Singularities Explained ⹠Singularities Explained | Infinite Se⊠or How I Learned to Stop Worrying and Divide by Zero.
Data assimilation is a mathematical discipline that integrates observed data and numerical models to improve the interpretation and prediction of dynamical systems. It is a crucial component of Earth sciences, particularly in numerical weather prediction (NWP).
Officials of the U.S. Defense Advanced Research Projects Agency (DARPA) in Arlington, Va., issued a broad agency announcement (HR001124S0029) for the Artificial Intelligence Quantified (AIQ) project.
AIQ seeks to find ways of assessing and understanding the capabilities of AI to enable mathematical guarantees on performance. Successful use of military AI requires ensuring safe and responsible operation of autonomous and semi-autonomous technologies.
What does âequalsâ mean? For mathematicians, this simple question has more than one answer, which is causing issues when it comes to using computers to check proofs. The solution might be to tear up the foundations of maths.
By Alex Wilkins
Emergent phenomena: large-scale patterns and organization arise from innumerable interactions between component parts.
The behavior of a complex system might be considered emergent if it canât be predicted from the properties of the parts alone.
The puzzle of emergence asks how regularities emerge on macro scales out of uncountable constituent parts. A new framework has researchers hopeful that a solution is near.
Fields Medalist Terence Tao explains how proof checkers and AI programs are dramatically changing mathematics.
Mathematics is traditionally a solitary science. In 1986 Andrew Wiles withdrew to his study for seven years to prove Fermatâs theorem. The resulting proofs are often difficult for colleagues to understand, and some are still controversial today. But in recent years ever larger areas of mathematics have been so strictly broken down into their individual components (âformalizedâ) that proofs can be checked and verified by computers.
This is a series of videos that I decided to make on Georg Cantorâs groundbreaking works published in 1,895 and 1,897 titled Contributions to the Founding of the Theory of Transfinite Numbers.
This work could probably be counted among the most influential and significant works in mathematical history â Cantorâs transfinite numbers changed the face of mathematics completely (although, not to everyoneâs pleasure). The impact of Cantorâs work canât be underestimated.
A simple concept of decay and fission of âmagnetic quiversâ helps to clarify complex quantum physics and mathematical structures.
Researchers employed magnetic quivers to delve into the fundamentals of quantum physics, specifically through the lens of supersymmetric quantum field theories. They have provided a novel interpretation of the Higgs mechanism, illustrating how particles gain mass and the potential decay and fission within QFTs.
Pioneering Quantum Physics Study
The American theoretical physicist, Brian Greene explains various hypotheses about the causation of the big bang. Brian Greene is an excellent science communicator and he makes complex cosmological concepts more easy to understand.
The Big Bang explains the evolution of the universe from a starting density and temperature that is currently well beyond humanityâs capability to replicate. Thus the most extreme conditions and earliest times of the universe are speculative and any explanation for what caused the big bang should be taken with a grain of salt. Nevertheless that shouldnât stop us to ask questions like what was there before the big bang.
Continue reading “Brian Greene â What Was There Before The Big Bang?” »
Four mathematicians have estimated the chances that thereâs a clear path through a random maze.
