At the beginning of 2014 Numberphile published an incredible interview with Ed Frenkel with the provocative title: “Why do people hate mathematics?””
There is a particularly interesting exchange around the 5:00 mark:
Numberphile: “Let’s apportion some blame. Let’s blame someone. Sounds to me like you are blaming high school teachers . . . . back in our school days they were making us paint fences instead of showing us Picasso.”
Frenkel: “Well, if I really were to assign blame, I would assign the blame to myself and to my colleagues – professional mathematicians. We don’t do nearly enough of exposing these ideas to the public in an accessible way. Often times we aren’t willing to come up with good metaphors and analogies.
That exchange has really stayed with me.
Later in the year, actually about a month ago, David Coffey wrote a nice piece in which he answered a similar question – Whose fault is it that you aren’t good at math?:
Whose Fault is it that you aren’t good at math?
I like his answer a lot -> you aren’t good at math because you didn’t have the experiences that you needed to be good at math. I wrote a little too long of a response to Coffey’s piece here where I suggested some places where students (and, well, everyone) might find fun math experiences:
Responding to Cafid Coffey’s Challenge
Despite writing way too much last time, I want to write more because I’ve seen so many great math experiences just in the last few days.
(1) Let’s start with this incredible public lecture from Terry Tao at New York’s Museum of Mathematics:
This lecture seems to be almost exactly what Frenkel was taking about in the piece of his interview that I quoted above. Tao shows some wonderful ideas of mathematics and how those ideas helped us understand how to measure distance in the universe. A beautiful and accessible lecture from one of the world’s top mathematicians. It has been online since the beginning of June and as of today doesn’t even have 700 views!! Ugh, though to be fair I try to look out for stuff like this and didn’t even see it until yesterday. I hope more people find out about this lecture and are able to watch it.
(2) Speaking of the Museum of Math, this weekend they finished their portion of the MegaMenger project: http://www.megamenger.com/ . My family went down to participate in the build and it was really fun to see all of the kids helping out and playing around in the Museum. Hopefully there will be more projects like this one that can show kids that math is more than their 20 question algebra assignment. Here’s a picture of my son standing inside of the finished product:
(3) Fawn Nguyen’s digit puzzle.
Last week Fawn Nguyen shared a wonderful digit problem that she did with her class. A few days later the online math world was buzzing left and right about her problem. On Sunday morning 5 different people had shared it on my twitter feed. So fun and I’m so happy for Fawn’s incredible work is being recognized by an ever-growing audience. But don’t take my word that this is an “utterly kick-ass” exercise. Try it out, too:
(4) Continued Fractions
Continued fractions have a special place in my heart because my high school math teacher, Mr. Waterman, loved them. He taught us out of the book pictured below (sorry I only have the picture side by side with Geometry Revisited, but trust me, that’s a great book as well!):
Amazingly I saw two ideas in the last week where continued fractions either have or could have played a role. It really is a beautiful subject and it is a shame that it no longer has much of a place in high school or college math programs.
In any case, here’s a really neat blog post from Sam Shah showing how he incorporated continued fractions into a lesson in his class:
Substitution and Continued Fractions
and here’s a fun tweet from Steven Strogatz from this morning showing a problem in which continued fractions could help students make a fun connection:
Since the picture from Gilbert Strang’s book doesn’t come through, let me expand a little on the continued fraction connection. On page 36 of the book Strang mentions the pattern he’s showing comes from a connection that 
Anyway, it has been great to see all of this fun math online (and in person) during the last week. Hopefully there will be many more weeks like this one to come.
Mike's Math Page 
You might be amused to know that there is another link between the [1,1,1,…] continued fraction and the nested square roots from Sam Shah’s calculus class problem. Try alternating positive and negative roots instead of always taking positive roots . . .