re: Visualizations, Inspirations, and the Super Ultimate Graphing Challenge
MM: Our blog is mostly for middle school students (ages 10-13 maybe). What was math like for you at that age? Were you always into math(s)?
JD: I was very interested in maths and science at that age. I remember spending a long time trying to prove Fermat’s Last Theorem, and I was very disappointed to discover that someone else (Andrew Wiles) had already proven it in 1997! There was some consolation in realising that the proof was over 200 pages long and only a few people in the world could understand all of it, though.
MM: How did you get interested in visualization? What do you find interesting/exciting about these pieces?
JD: My maths teacher’s top tip for doing mechanics questions was always to start off by drawing a good diagram containing all of the information in the question. Answering the question usually became much easier.
I find visualisation appealing because of its power to engage and clarify an otherwise opaque or full topic. Modern technology allows us to quickly create interactive visualisations that can be explored endlessly.
MM: You mentioned that drawing diagrams is a great way to start solving mechanics questions. Can you say a bit more about what you mean? Do you mean mathematics? Physics questions?
JD: In the UK, mechanics is one of the A-level maths modules. Roughly, it’s the study of physical objects in motion when forces are applied, so it’s very similar to the same module in Physics covering Newton’s laws of motion. Which is great, because you get taught the same thing twice!
MM: Do you think of your work as mathematical art?
JD: I create these visualisations both to understand things better myself, and to make it possible for others to understand things better. I think aesthetics are important in making something pleasant to play with, and hence to gain understanding quicker. But the primary purpose is the utility, so any semblance to art is a bonus!
MM: Do you have a favorite piece from your site? Can you remember your first visualization?
JD: At an early age I kept records of temperature and plotted graphs. During my undergraduate degree I also worked for Cambridge University on interactive fluid dynamics visualisations. Probably the first visualisation to spark off my current “season” though was this one – suggested by Mike Bostock.
MM: Where do you get ideas and inspiration for your work?
JD: I roam the dark corners of Wikipedia late into the night.
MM: Your Rhodonea Curves, Combinatorial Necklaces, and Complete Graphs all depict a sort of complete space of possibilities. Do you look for that sort of thing? Are there any other kinds of mathematical themes that you think a lot about?
JD: Yes, I try and make it possible to explore as many combinations as possible. Geometry is usually a good candidate for visualisation.
MM: What was a challenge — big or small — that you ran into as you were learning how to create and program your visualizations? How did you overcome it?
JD: I think I come across new challenges almost daily when programming, but I enjoy solving challenges as this is what makes it interesting.
For example, when creating my recent visualisation of set partitions – I wanted an efficient way to generate the set partitions for an arbitrary set, so I had to look up an algorithm from the “bible” of computer algorithms, The Art of Computer Programming by Knuth. So now I can efficiently generate set partitions for arbitrary sets, which makes me happy as I can reuse this for other things in future.
MM: How do I know if I’m a mathematician? If I’m in 5th grade, is there any way to tell how mathematical I am?
JD: If you’re reading this, you’re a mathematician! I guess I think everyone can (and should be) a mathematician in some sense. Personally, it seems like a fundamental skill that is useful no matter what you end up doing.
I think mathematics is a much broader and varied subject that people might realise at first. So you might find certain aspects boring simply because it’s not interesting to you personally, for example calculating things just for the sake of getting good at calculating things might seem pointless. But calculating is so useful when you need to solve interesting problems, that it’s well worth practising. If something seems boring, then maybe finding an interesting related problem is what you need to do.
MM: What’s the most important trait for a mathematician to have? Is there one?
JD: Persistance is always useful in maths! I think the stereotype is to be analytical and logical, but in fact there are many other traits that are highly important, for instance communication skills. Mathematics is passed on from person to person, after all, so being able to communicate ideas effectively is dynamite.
MM: Do you have a message you’d like to give to young mathematicians?
JD: The world needs you!
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Are you planning on working on other more complicated diagrams for older students? Is math taught differently in the UK?
Do you every do any visualizations based on origami?