The Rocky Mountain Journal of Mathematics, Vol. 17, No. 2 (SPRING 1987), pp. 371-384 (14 pages) Let Cn(x; β\q) be the continuous q-ultra-spherical polynomial and Dn(x; β\q) be the q-ultraspherical ...

Proceedings of the National Academy of Sciences of the United States of America, Vol. 93, No. 26 (Dec. 24, 1996), pp. 15004-15008 (5 pages) In this paper, we give two infinite families of explicit ...

Important update, Jan. 17 at 18:00 UTC: There have been a lot of objections raised about the video mentioned below and the way I describe the math therein. It’s more than I can simply add or update ...

This is what happens when you mess with infinity. You might think that if you simply started adding the natural numbers, 1 plus 2 plus 3 and so on all the way to infinity, you would get a pretty big ...

Yesterday, I posted an article about a math video that showed how you can sum up an infinite series of numbers to get a result of, weirdly enough, -1/12. A lot of stuff happened after I posted it.

When you have an infinitely decreasing number does it ever hit a point where it is indistinguishable from the number it’s approaching? Does 0.999999999…, for instance, ever finally just become 1? A ...

A hundred and one years ago, in 1913, the famous British mathematician G. H. Hardy received a letter out of the blue. The Indian (British colonial) stamps and curious handwriting caught his attention, ...

Mathematics is often about uncovering patterns. For example, certain areas of topology revolve around categorizing knots or geometric shapes, and number theory explores properties such as the ...

Our July Insights column was inspired by the mathematics of the phenomenal 20th-century number theorist Srinivasa Ramanujan, whose romantic and tragic life story was the subject of the recent film The ...

Several years ago, I tried to explain infinity to a class of fifth graders. In the story that I told them, I was preparing to eat a piece of cake when a friend walked in on me. Being polite, I gave ...