The proof resolves a nearly 80-year-old problem known as the Duffin-Schaeffer conjecture. In doing so, it provides a final answer to a question that has preoccupied mathematicians since ancient times: ...
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 ...
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 ...
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, ...
A new proof illuminates the hidden patterns that emerge when addition becomes impossible. The simplest ideas in mathematics can also be the most perplexing. Take addition. It’s a straightforward ...
Most people rarely deal with irrational numbers—it would be, well, irrational, as they run on forever, and representing them accurately requires an infinite amount of space. But irrational constants ...
The ancient scholar Hippasus of Metapontum was punished with death for his discovery of irrational numbers—or at least that’s the legend. What actually happened in the fifth century B.C.E. is far from ...
I was reading about π (pi) today, and of course, went to wikipedia to read about it. One thing that I don't remember so clearly from math class (sad, since I was a mathematics minor....) was ...
Most people rarely deal with irrational numbers—it would be, well, irrational, as they run on forever, and representing them accurately requires an infinite amount of space. But irrational constants ...
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