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The cosmic distance ladder
I gave a non-technical talk today to the local chapter of the Pi Mu Epsilon society here at UCLA. I chose to talk on the cosmic distance ladder – the hierarchy of rather clever (yet surprisingly...
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The blue-eyed islanders puzzle
Given that there has recently been a lot of discussion on this blog about this logic puzzle, I thought I would make a dedicated post for it (and move all the previous comments to this post). The text...
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An airport-inspired puzzle
I was recently at an international airport, trying to get from one end of a very long terminal to another. It inspired in me the following simple maths puzzle, which I thought I would share here:...
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The cosmic distance ladder
I am uploading another of my Clay-Mahler lectures here, namely my public talk on the cosmic distance ladder (4.3MB, PDF). These slides are based on my previous talks of the same name, but I have...
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A demonstration of the non-commutativity of the English language
This will be a more frivolous post than usual, in part due to the holiday season. I recently happened across the following video, which exploits a simple rhetorical trick that I had not seen before: If...
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245A: Problem solving strategies
This is going to be a somewhat experimental post. In class, I mentioned that when solving the type of homework problems encountered in a graduate real analysis course, there are really only about a...
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The “no self-defeating object” argument, and the vagueness paradox
This is the third in a series of posts on the “no self-defeating object” argument in mathematics – a powerful and useful argument based on formalising the observation that any object or structure that...
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Gamifying algebra?
High school algebra marks a key transition point in one’s early mathematical education, and is a common point at which students feel that mathematics becomes really difficult. One of the reasons for...
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New version of algebra game
Just a quick update on my previous post on gamifying the problem-solving process in high school algebra. I had a little time to spare (on an airplane flight, of all things), so I decided to rework the...
View ArticleRequest for comments from the ICM Structure Committee
[This post is collectively authored by the ICM structure committee, whom I am currently chairing – T.] The International Congress of Mathematicians (ICM) is widely considered to be the premier...
View ArticleTwo announcements
Now that Google Plus is closing, the brief announcements that I used to post over there will now be migrated over to this blog. (Some people have suggested other platforms for this also, such as...
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The spherical Cayley-Menger determinant and the radius of the Earth
Given three points in the plane, the distances between them have to be non-negative and obey the triangle inequalities but are otherwise unconstrained. But if one has four points in the plane, then...
View ArticleIllustrating the Impact of the Mathematical Sciences
Over the last few years, I have served on a committee of the National Academy of Sciences to produce some posters and other related media to showcase twenty-first century and its applications in the...
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AI Mathematical Olympiad – Progress Prize Competition now open
The first progress prize competition for the AI Mathematical Olympiad has now launched. (Disclosure: I am on the advisory committee for the prize.) This is a competition in which contestants submit an...
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