Borrowing techniques from other disciplines is another kind of abracadabra [algebracadabra]. Many mathematicians borrow techniques from physics, including quantum gravity, to prove theorems in geometry or topology by eliminating all physical notions and boiling them down to their essential mathematical arguments. It is surprising because not many can spot a complicated argument in physics, fully understand it, see through it, cut away the extra branches, and find the essence.

These tricks elicit a moment of awe because, essentially, they go beyond expectations. It needs an ‘eye’. But not every eye can capture that; experience can play a role, but it’s not enough. For that, I argue, one needs ‘vitality’, as in poetry.

Day-Lewis proposed that the object is not merely poetic per se; the object becomes poetic because of the poet. Good poets have high vitality; they live in the present, or, as the literature scholar John Livingston Lowes said, they don’t ‘ensconce themselves like hermit-crabs, generation after generation, in the cast-off shells of their predecessors’. They observe with a fresh eye to pin down an original thought. In fact, the originality of the image they see is directly linked to their vitality and to how connected they are to the present moment. The object becomes distinctly poetic as a result of their presence in the moment.

Mathematical objects, techniques and all the lemmas are the same. Sometimes, the experienced technical mathematician even knows them by heart and teaches them every year. They generously introduce open problems to novice mathematicians and patiently share every single detail about their progress. However, it takes a fresh PhD student just out of college to see the original image or a proof from THE BOOK. That, I argue, is because of their high vitality. This further results in vitality of the mathematical structure; the structure doesn’t die or become isolated. It moves, excites, and creates – in essence, it’s alive.