The exhibtion, of material from the man's notebooks isn't primarily an aesthetic experience (although there are some beautiful things there). What it's about is giving you an insight into Leonardo's thinking, and the full range of his preoccupations.
Nowadays, the term 'Renaissance man' is applied to any science PhD who's read a novel and got grade 3 clarinet (women tend to do lots of different things without running around giving themselves grand names). This exhibition shows you better than anything I've ever seen what being a Renaissance man really meant. Leonardo treated the artistic, scientific, mathematical, biological, architectural, mechanical, you name it, as all one and the same - often on the same sheet of paper. Designs for musical instruments are alongside those for palaces, and stage sets, which are alongside plans for epic murals, or engines of war, or anatomical drawings, or clouds. Astonishing.
On the science side, it looks very much as if he was thinking about problems, such as finding a shape's centre of gravity, or a volume's solid, that were solved by Newton/Leibniz's invention of calculus. He also seems to have pondered other Newtonian stuff, such as gravity and mechanics. (And he tried to square the circle, and build a perpetual motion machine. Nothing I could see on thurning base metals into gold, though.)
He also did some drawings on the form of trees, river networks, and blood vessels that (looking at things with a biased eye, I admit) intriguingly prefigures the network models of metabolic rate, river networks, and other stuff by West et al. and Banavar et al.
And here's a quote, presented in the exhibition, which could have come straight out of D'Arcy Wentworth Thompson's mouth, and which sums up world view (one of them, anyway) I write about in ITBOAH:
"A bird is an instrument working according to mathematical law."
Pegged to this exhibtion, there's an interesting piece by Guardian art critic Jonathan Jones on how the notebooks ended up in the hands of the British royal family.