In a note to clients on Friday, FactSet's John Butters highlighted what is, forever and always, the most irrational chart in the market. The green line going up is the S&P 500, which, since the ...

Investor expectations and portfolio allocations reflect exuberance. There are some positives in the fundamentals that could justify calling it rational exuberance, yet bearish warning signs may beg to ...

Katie has a PhD in maths, specializing in the intersection of dynamical systems and number theory. She reports on topics from maths and history to society and animals. Katie has a PhD in maths, ...

Irrational numbers are numbers that cannot be expressed as the ratio of two whole numbers. This is opposed to rational numbers, like 2, 7, one-fifth and -13/9, which can be, and are, expressed as the ...

The ancient Greeks wondered when “irrational” numbers can be approximated by fractions. By proving the longstanding Duffin-Schaeffer conjecture, two mathematicians have provided a complete answer. The ...