Welcome to the 186th Carnival of Mathematics, with your host Abhik Jain (if you don’t know about Carnival of Mathematics, check here).

Lets start off with some fun facts about the number 186:

  • The sum of factors of 186 is greater than 186.
  • Kepler-186f is an exoplanet, is one of the first planets observed by astronomers which has same radius as earth, and was in the Goldilocks Zone of it’s star (the distance range from star where water can exist in liquid state).
  • It is a product of 3 distinct primes (\(186 = 2 \times 3 \times 31\)), and thus can have only 8 divisors formed by their combination (\(2^3 = 8\))
  • Hexadecimal representation of 186 is \(\text{BA}\)
  • the SHA-256 hash of a file containing ‘186’ is \(\text{aaeeefc8f66b433fc4079c06b096c2d63fb9e012d5038eeb8d35cbb9d2110d84}\)

Now, moving onto the interesting maths stuff that happened this month.

Many people are now attending online meeting, either via zoom, Google Meets etc. which are often boring. Add some fun to those meeting with these card tricks that can be performed in online meetings.

9th marks the birthday of Dennis Ritchie, a famous computer scientist and the creator of many things on which modern computer infrastructure depends upon (including, but not limited to C programming language and the Unix operating system).

What do you do when you come across a bunch of cubes with missing edges? Obviously, you put them in a soap solution and see what sort of soap films form around the loops of the incomplete cube (hint: they try to cover the minimum surface area). Kartik Chandra (aka hardmath123) has written the code to simulate this for us so we don’t need to. You can read more about this on his blog post

Often proofs in geometry are accompanied by beautiful (or sometimes not so beautiful) diagrams. Some of these diagrams have inspired people to create art based on them. Check out this post on Futility Closet to find out more about them.

Speaking of geometry, want to try out a cool geometry problem that can be solved using high school mathematics? In this post by Benjamin Leis, where he presents the problem and an interesting solution to it.

In the famous science fiction book The Hitchhiker’s Guide to the Galaxy by Douglas Adams, the super computer Deep Thought, created to answer the “Great Question” of “Life Universe and Everything”, gave the answer 42 (and later they discover that the answer is right but the question was itself wrong, and so they created another supercomputer “Earth” to find the right question). The answer now is famous, appearing on various shows and even shows on Googling the question. Jean-Paul Delahaye discusses more about the number and it’s various apperances here.

Mathematics has had great discoveries in last century, yet most of the curricula used in teaching mathematics has largely remained unchanged. The origins of the current curriculum can be traced back to 1892. Is it about time we change that? I don’t know the answer, but maybe you can find some insights in this post by Daniel Rockmore.

Often time people new to mathematics beyond high school (myself included) find ourselves stuck with some problem or some theorem we can not understand. This state of being stuck is normal, but we are not taught that in high school, instead we are required to produce correct answers. Being stuck is a part of the process while learning and doing maths. Ben Orlin discusses more about it on his blog.

In the September podcast of My Favorite Theorem, in which Susan D’Agostino talks about her favourite theorem, the Jordan Curve Theorem, which tells us that every simple closed curve separates a 2D plane into 2 parts (inside and outside). This theorem seemed so intuitively obvious that no one bother proving it, but it is rather difficult to prove.

Recently, David Conlon and Asaf Ferber have released a paper on ArXiv talking about new lower limit to Ramsey’s theorem, which states that in a complete graph with \(n\) or greater vertices (where \(n\) is finite), if we color it with \(l\) different colors, we will certainly find get complete graph of order \(t\). Gil Kalai talks more about it in his blogpost here. (If you don’t understand any of this graph theory jargon, I highly recommend checking out these small lectures by Kaj Hensen).

In the 61st International Mathematical Olympiad, we have now Artificial Intelligence competing against humans. IMO provides a ideal place to test AI in a field humans are still better, in Mathematical Thinking.

Sir Vaughan Jones, a Fields Medal winning mathematician who has contributed significantly to knot theory, sadly passed on 6th September, 2020 at the age of 67.