After finding the homeschooling life confining, the teen petitioned her way into a graduate class at Berkeley, where she ended up disproving a 40-year-old conjecture. It’s not that anyone ever said ...

Most people probably don’t think of mathematics when they hear “busy beavers.” But these eager little animals symbolize one of the most amazing concepts of the knotty field: not everything can be ...

If OpenAI's new model can solve grade-school math, it could pave the way for more powerful systems. This story is from The Algorithm, our weekly newsletter on AI. To get stories like this in your ...

In the paper, the authors extend a function arising from the Bernoulli trials in probability and involving the gamma function to its largest ranges, nd logarithmically complete monotonicity of these ...

“There are five fundamental operations in mathematics,” the German mathematician Martin Eichler supposedly said. “Addition, subtraction, multiplication, division and modular forms.” Part of the joke, ...

ABSTRACT: In this paper, we characterize lower semi-continuous pseudo-convex functions f : X → R ∪ {+ ∞} on convex subset of real Banach spaces K ⊂ X with respect to the pseudo-monotonicity of its ...

Abstract: We consider the problem of constructing a penalty function associated with a given monotone function. We provide a construction that allows the monotone function to be discontinuous or ...

Activation functions are essential components in any neural network model; they play a crucial role in determining the network’s expressive power through their introduced non-linearity. Rectified ...