There are plenty of formulas in the new maths. Littlewood is right that the great "heyday" of certain types of formulas is over. But what this really means that mathematical taste has both changed and have widened.

One formula that I like is Stoke's theorem. It's a formula of vector analysis. By finding the right context for it, that is on manifolds, the formula is now valid for any curved space (the original formulas was only valid in flat 3d space), and for curved spaces in higher dimensions as well as lower. In fact, in 1d the formula becomes the fundamental theorem of calculus first shown by Newton. Moreover, the formula is systematic.

What's not to like about this?

One aim of the new maths is to make sure that all the formulas's found by Euler, Littlewood et al find similar contexts that explain why they take the form they do and relate them.

Another aim, is that proofs become mathematised into formulae. This is one of the great successes of category theory and why it's talked about as a 'language' of mathematics. It helps discern proof strategies in theories amd makes formulae out of them.

For example, Emily Riehl in one her books on category theory showed that singular homology is the composition of five functors. This is as much of a formula as the identities beloved by Euler or Littlewood.

What's not to like about that either?

There are plenty of formulas in the new maths. Littlewood is right that the great "heyday" of certain types of formulas is over. But what this really means that mathematical taste has both changed and have widened.

One formula that I like is Stokes' theorem. It's a formula of vector analysis. By finding the right context for it, that is on manifolds, the formula is now valid for any curved space (the original formulas was only valid in flat 3d space), and for curved spaces in higher dimensions as well as lower. In fact, in 1d the formula becomes the fundamental theorem of calculus first shown by Newton. Moreover, the formula is systematic.

What's not to like about this?

One aim of the new maths is to make sure that all the formulas found by Euler, Littlewood et al. find similar contexts that explain why they take the form they do and relate them.

Another aim is that proofs become mathematised into formulae. This is one of the great successes of category theory and why it's talked about as a 'language' of mathematics. It helps discern proof strategies in theories and makes formulae out of them.

For example, Emily Riehl, in one of her books on category theory, showed that singular homology is the composition of five functors. This is as much of a formula as the identities beloved by Euler or Littlewood.

What's not to like about that either?