The Heisenberg and Witt algebras

Here - a nice introduction by Akhil Mathew @ Climbing Mount Burbaki

The attractiveness of primes for experimental mathematics...

'Although the prime numbers are rigidly determined, they somehow feel like experimental data'

Timothy Gowers. Mathematics: A Very Short Introduction (Oxford Univ. Press, 2002) p.118; as cited in "surprising connections between number theory and physics"