## A short video on Ramsey numbers

I was recently involved in making a 1 minute maths video for a contest organised by Veritasium. Here is the main requirement for the video

We are looking for videos that clearly and creatively explain complex or counterintuitive concepts in the fields of Science, Technology, Engineering, and Mathematics.

This project started with Aditya Potukuchi telling me about the contest some weeks back after which we immediately started brainstorming for possible topics. I then suggested that we include my brother Anup Bishnoi and his wife Jyoti Arora in the project as they love creating various forms of learning content. In fact, they have founded a company around this called Not A Bot Studios (go check it out!). I introduced to them what Ramsey numbers were, as Aditya and I decided that could be a suitable topic for a 1 minute video. They seemed quite amazed by this mathematical concept and especially surprised by the fact that we don’t even know what the Ramsey number R(5) is. Thus, that became the punchline of our video. We worked on this video for about a week and had a lot of fun doing it! The involvement of my partner Aparajita Nath later on made it even better. I am quite happy with the final outcome as we have been getting some great comments.

As this is the first time I have been involved with something like this, I though I’ll share my experience and learnings, with the aim of encouraging other mathematicians to do something similar.

Here are some of my key learnings from this project:

• Parsing mathematical statements is really hard.
As mathematics students we get trained in parsing statements like “Either A or B is true” and using quantifiers like “for all”, “there exists”, etc. This is not the case for most people and they can find it extremely difficult to understand such statements, especially in such a short video. We tried to make it easier by using some visual aids. For example, we showed a bunch of possible arrangements of allies/enemies (as a two-edge-colouring of the complete graph) when saying that you can always find 3 mutual allies or 3 mutual enemies. Even after that it didn’t look like it’ll be immediately clear to a first time viewer that we are talking about all possible arrangement and so we decided to make it interactive by asking the viewer to pause the video and try it out on their own.
• Get a lot of feedback!
When we made the first version of this video all of us were pretty happy with the outcome, until we tried it out with a bunch of our friends who had no idea about the topic. Many of them couldn’t follow it at all. Even after multiple watchings! The feedback we got from them made us realise that because we had already spent a lot of time working on this, we all had a good idea of what Ramsey numbers were, and so we just started focussing on making it visually appealing and fun. The explanation part took a back seat. Because of the feedback, we were able to fix this. Even though it required a lot of rewriting of the script and redoing of the animation, I am so glad that we didn’t put out that version of the video.
• Make it fun to watch, without compromising the subject matter.
No matter what audience you are aiming for, it is going to be really helpful to add fun elements that they can all enjoy. Make them laugh and make them care about what you are teaching. Memes are your friends!
One important thing to ensure though is that these fun elements don’t take away anything from the actual concept that you are trying to explain. For example, we based our script around the world of the widely popular tv series Game of Thrones (which also had a widely unpopular last season), but made sure that the specific characters and all the insider jokes are not necessary in any way to understand Ramsey numbers. A friend pointed out how he started recalling the tv show instead of focussing on the maths. We tried to fix this in the final version of the video, but I am not sure if we have still managed to remove all such distractions.

• Keep it clear and simple
Both the script and visuals should be as clear and simple as possible. Complicated mathematical terms or english words can be very confusing, especially in a short video like this. It took as many iterations to get to the final version, but I am glad that we made a conscious effort of keeping it simple.

As I said before, it was great fun to make this video that can explain Ramsey numbers to a general audience in one minute and I wish I can do more such things in future, especially with such great collaborators. Go check out the video and share it around!