The main issue is that, by the time you get to the frontiers of math, the words to describe the concepts don’t really exist yet. Communicating these ideas is a bit like trying to explain a vacuum cleaner to someone who has never seen one, except you’re only allowed to use words that are four letters long or shorter.

A mathematician volunteers to teach a class at a women’s prison and learns an unexpected lesson. Told live at our Man Behind the Curtain Show on June 16, 2018 at The ArtsCenter in Carrboro, NC.

via: https://geometrynyc.wixsite.com/home/combinatorics-reu

Hi! I’m Misha. I do research in combinatorics and teach math, occasionally to high-school students.

via: https://vertex.degree/

In mathematics it happens at times that one and the same concept is given two different names to indicate a specific perspective, a certain attitude as to what to do with such objects.

I’m a fifth-year Ph.D. student in the Department of Mathematics at The Ohio State University. I’m interested in algebraic topology, semigroup theory, and computer science.

via: https://www.youtube.com/watch?v=CxGtAuJdjYI

This is the kind of mathematics I was put on this earth to do. The equation explorer is also just a genuinely useful tool for looking up equations; did so earlier this year as part of preparations for a lecture I gave.

Such an aesthetic problem.

A counterexample is any exception to a generalization. Counterexamples  are often used in science (and philosophy), as a means to setting boundaries. In mathematics at large,  well-chosen counterexamples may  bound possible theorems, disprove certain conjectures. This conspectus is (mostly) meant to gather and share counterexample book references (on algebra, analysis, calculus, logic, philosophy, probability, statistics, topology).

In general, if you’re trying to prove something, you can think of the various techniques and tools you have much like chess moves or Hanabi lines. Just like in turn-based games, you’ll find there are dead ends, e.g. trying to apply so-and-so theorem to reduce the problem to proving X, but X turns out to be false. Or there will be lots of paths that look more promising, but you can’t see far enough into the future to completely evaluate them all, and then you have to use heuristics and intuition to prioritize between approaches.

Most of us are familiar with the Fibonacci sequence. What’s the largest Fibonacci number you can compute in 1 second? I’m not setting any world records, here; I don’t own a supercomputer.

A very nerdy talk on baseball using analogies to logic and probability.

Mathematics and science Braille textbooks are expensive and require an enormous effort to produce — until now. A team of researchers has developed a method for easily creating textbooks in Braille, with an initial focus on math textbooks. The new process is made possible by a new authoring system which serves as a “universal translator” for textbook formats, combined with enhancements to the standard method for putting mathematics in a Web page. Basing the new work on established systems will ensure that the production of Braille textbooks will become easy, inexpensive, and widespread.

We introduce a versatile method for finding prime numbers that display surprisingly intricate visual patterns— hypothetically, any desired pattern is possible, with only mild distortion. We use this method to locate several examples of large prime numbers that are, in and of themselves, self-referential works of art.

Zvezdelina Stankova discusses the raffle function - and her epic proof ends with an interesting connection.

Beautiful, beautiful problem. Abstract algebra, calculus, number theory, and combinatorics all wrapped up into a bow. :)

Love using mathematics to prove weird facts like this.

Knot theory is far more complicated than I initially gave it credit. Would love to learn how they found the counter example via computer search.

What is infinity? Can there be different sizes of infinity? Surprisingly, the answer is yes. In fact, there are many different ways to make bigger infinite sets. In this video, a few different sets of infinities will be explored, including their surprising differences and even more surprising similarities.

Thomas Bloom’s erdosproblems.com site hosts nearly a thousand questions that originated, or were communicated by, Paul Erdős, as well as the current status of these questions (about a third of which are currently solved). The site is now a couple years old, and has been steadily adding features, the most recent of which has been…

via: https://www.youtube.com/watch?v=itRV2jEtV8Q