2016 Fields Medal Symposium Lecture

2016 Fields Medal Symposium

I finally had a chance to sit down and watch the Fields Medal Symposium opening lecture. The main speaker for the evening was 2014 Fields Medallist - Manjul Bhargava. Bhargava (born in Hamilton!) is an accomplished number theorist and professor at Princeton University. Initially I thought the lecture was going to be an exploration of obscure number theory (maybe this is why I delayed the viewing) and chuckles at inside jokes about rings and the Farnsworth Parabox. I was so pleasantly surprised by the accessibility of the content (even I could follow it!) and the wonderful connections that Professor Bhargava made to art and the natural world.

After viewing it I decided it would be a great item to share with my students in class and those who show a particular love for number theory. What I thought I would do with this post is breakdown the talk for those who haven't viewed it just in case you want to jump to the bits of particular interest in the event that you want share with your students. The lecture starts at about the 32 minute mark.

For the early going, Professor Bhargava shares his introduction to mathematics as nurtured by his mother and his grandfather, a Sanskrit scholar. In particular he talks about the role that number theory plays in mathematics. He introduces sequences of numbers. Some of these may be familiar to you and to your students. In particular he looks at the visual or geometric proofs for the sums of these sequences. This seems to be  very timely with the current focus on visuo-spatial reasoning. Jump to the 44 minute mark to see a great visual proof of the sum of the first n odd numbers. Here's some more highlights I noted in the talk.

47 min mark - Sum of ascending and descending whole numbers (e.g. 1 + 2 + 3 + 4 + 3 + 2 + 1)

48 min mark - Hex numbers - Connecting them to a visual arrangement. So cool!!!

52 min mark - Exporing the "atoms of our universe of whole numbers" - PRIMES!

57 min mark - Primes in Nature - Why do cicadas have a 17 year gestation period?

1 hour 1 min mark - The role primes play in encryption.

1 hour 6 min mark - What is special about honeycombs?

1 hour 11 min mark - Professor Bhargava shares his favourite problem as a child - Stacking Oranges

1 hour 16 min mark - The Fibonacci Sequence - Professor Bhargava illustrates an amazing connection to Sanskrit poetry and lots of connections to the natural world.

1 hour 40 min mark - What's so special about the number 142 857?

1 hour 44 min mark - Fractals!

As you can see there is so much here to explore and share with your students. Each and every topic is explained in very accessible language and presented with such clarity it is hard not to be excited by the connections that number theory has to the world around us.