By replacing the most fundamental concept in topology, Peter Scholze and Dustin Clausen are taking the first step in a far ...

Machine Learning is concerned with computer programs that automatically improve their performance through experience (e.g., programs that answer questions, diagnose diseases, recommend music and ...

I show how to solve math problems online during a live classroom. This is my way of providing free tutoring for the students in my class and for students anywhere in the world. Every video is a short ...

Penn researchers have developed a smarter AI method for solving notoriously difficult inverse equations, which help scientists uncover hidden causes behind observable effects. By introducing ...

The "prisoner's dilemma" is one of the most famous ideas in game theory. For decades, this game has been used to explain why selfishness often beats cooperation. In the prisoner's dilemma, two players ...

THAT the late Prof. A. N. Whitehead's little volume should establish itself as a classic is not surprising. It was published in the "Home University Library" in 1911, was reprinted about eight times ...

Mathematics provides tools for explanation and analysis in the physical, engineering, business and social sciences. These tools can help in areas as diverse as planning and evaluating market research, ...

Grothendieck is revered in the world of math; outside of it, he’s known for his unusual life, if he’s known at all. But what ...

Mathematics and computing is the study and analysis of abstract concepts, such as numbers and patterns. Mathematics is the language of choice for scientifically describing and modelling the universe ...

An introduction is the opening paragraph of an essay. It should briefly introduce the topic and outline your key ideas to answer the question. These ideas are then explored in more detail in the rest ...

Classifying a variable as a particular type of data is important when considering how to present the data. Data can be presented in a number of ways, which depends on the type of variable and the uses ...