Math News and Blogs

Good math content can be hard, especially content that explains or explores topics outside of a conventional textbook approach. Let's face it, the vast majority of math resources out there are dry and old-fashioned. And a lot of times, that's the best or most straightforward way to teach or learn math - after all, many areas of math are inherently very logical and filled with symbol manipulation and detailed proofs. But I'm always on the lookout for new or interesting ways to explore math, or places to read about the modern frontier of math. If you are mathematically inclined, or are tired of the textbook approach to math, or are simply curious, I highly recomment that you check these out.

News and Blogs

• Quanta Magazine is an online magazine about advances in STEM fields, written in a clear expositional manner to be read by anyone. In particular, it has some great articles about mathematical concepts and breakthroughs. They put out a new article a couple times a week, and it is always high-quality.
• What's New by Terrence Tao is some of the best math writing that I have seen: everything is explained in a straight-forward manner. The concepts are all advanced, and the blog requires some mathematical maturity to be read. Terrence Tao is one of the world's premier mathematics researchers (and a bit of a math celebrity). His blog contains expositions of his research and notes and courses he is teaching. I have learned a lot from it.
• Stephen Wolfram's Blog has posts on mathematics, computation, and philosophy. I found his post on the concept of numbers really interesting.
• 3Blue1Brown is the best math YouTuber I have seen. He explains concepts with plenty of diagrams, and his videos have a unique style that makes them really satisfying to watch.
• Vi Hart makes videos about confused triangles, as well as other content. See also her Youtube Channel.

Geometry

Geometry is for many the most easily accessible facet of mathematics. As a result, there are a lot of website that specialize in geometric puzzles or visualization. Here are a few of my favorites.

• Geometry Games!

  • Zeno Rogue has an article full of non-Euclidean games. Many of the entries here come from their list.
  • Hyperbolica looks like a really fun non-Euclidean goemetry 3D game. Explore the world, or the way it would be if space had positive or negative curvature. Set to be
    released in late 2021. I haven't played it, but it looks really interesting. Not free.
  • Hyper Rogue is a 2D roguelike game, except the world is a hyperbolic plane. It is a turn-based puzzle/ strategy game. It's worth playing if you have trouble wrapping your mind around hyperbolic space.
  • Curved Spaces is a neat simulator for, you guessed it, curved space. Specifically, curved 3D space. Fly around and watch your surroundings grow, shrink, and bend with the strange properties of curved space.
  • Hyperbolic Maze is a maze in 2D hyperbolic space. Try to reach the center of the maze, or just explore! Neat features include using different projections of the hyperbolic plane, and a version of the maze in a quotient of hyperbolic space.
  • HYPERNOM is a cute browser game where you eat the polyhedra that tile some (compact) 3D curved space.
  • Curved Space is an action game played on the (curved) surface of a spaceship. I have not played it, but the announcement trailer looks interesting.

Number Theory

Number Theory is all about finding and answering really deep questions about the integers, $\mathbb{Z}$. In their quest to understand $\mathbb{Z}$, number theories have bound their field up with countless other fields of mathematics. Here is some food for thought about numbers.

• The Online Encyclopedia of Integer Sequences is famous, and not just among number theories. It is a collection of more than 120,000 sequences of integers. If you ever have the start of a sequence, and want to know the rest of it, or you just want to learn more abot it, then look no further! You can also listen to the integer sequences as music.
• The Ramanujan Machine is a mesh of number theory and computer science. Its creators have a program that can efficiently search for continued fraction representations of common numbers. These computer-found identities can be proved by humans. This has led to a few new continued fraction representations for $\pi$ and $e$ found completely by computer!

Problem-Solving

While I believe that mathematics is, at its core, about solving interesting problems, there are some settings where this is especially true. Here are some fun mathematical problems or problem-solving resources.

• The Putnam Archive is an archive of past Putnam Exam questions and answers maintained by Kiran Kedlaya. The Putnam exam is a very challenging math exam that college students in the US can take. Don't be discouraged if you get stumped by these problems: the median score on the exam is 0 or 1 out of 120, meaning that more than half of the participants don't solve any problems. If you are looking for resources to learn or teach with in preparation for the Putnam exam, this is your best option. If you are looking for challenging problems to play with, I would also recommend the Putnam Archive.
• The Art of Problem Solving is a website where people can discuss math problems. It also sells online math courses and resources, but I don't have any experience with them.

Miscellaneous Links

Sometime math doesn't fit into neat divisions. Here are some math-related links that I couldn't find a good category for.

• Graphical Linear Algebra is part blog, part textbook. It teaches linear algebra using diagrams (which look a lot like circuit diagrams). It's a cool idea, but I haven't looked at it in detail.
• Desmos is a very intuitive and easy-to-use online graphing calculator.