Mathematicians used “magic functions” to prove that two highly symmetric lattices solve a myriad of problems in eight- and 24-dimensional space. The points could be an infinite collection of electrons ...

Most people probably don’t think of mathematics when they hear ... The busy beaver function is the first example of a noncalculable mathematical expression. The function itself is easy ...

The Bottom Line Probability distribution functions (PDFs) describe the expected values of random variables drawn from a sample. The shape of the PDF explains how likely it is that an observed ...