9/15/2023 0 Comments Terence tao stephen colbertWhere the denominators are all perfect squares. Then we’ll move on to an infinite series that is not geometric: Of course, this one converges since it’s an infinite geometric series. For example, when discussing infinite series, I’ll ask my students to debate whether or not this series converges: In this series, I’m compiling some of the quips and one-liners that I’ll use with my students to hopefully make my lessons more memorable for them.Įvery once in a while, I’ll discuss something in class which is at least tangentially related to an unsolved problems in mathematics. (I like sharing this story with my students to convince them that not everything that can be known about mathematics has been figure out yet - a misconception encouraged by the structure of the secondary curriculum - and that research continues to this day.) Specifically, it was recently shown that, for some integer that is less than 70 million, there are infinitely many pairs of primes that differ by. Still, research continues, and some major progress has been made in the past few years. Indeed, this has been one of the most popular unsolved problems in mathematics - not necessarily because it’s important, but for the curiosity that a conjecture so simply stated has eluded conquest by the world’s best mathematicians. While most mathematicians believe the twin prime conjecture is correct, an explicit proof has not been found. The twin prime conjecture (see here, here and here for more information) asserts that there are infinitely many primes that have a difference of 2.
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