The announcement of the 2018 Fields Medal winners, made last month at the opening of the International Congress of Mathematicians held in Rio de Janeiro, Brazil, was greeted with widespread acclaim well beyond the mathematics community.

Of the four winners, the work of Alessio Figalli on optimal transport, which seeks the most efficient way to distribute goods on a network, is probably the most straightforward to connect to the real world. The recognized contributions of the other three awardees, Caucher Birkar, Peter Scholze and Akshay Venkatesh, are on more abstract topics concerning algebraic varieties, p-adic fields and number theory, respectively — humbling subjects even for the most theoretically inclined of physicists.

Although often referred to as the Nobel Prize of mathematics, the Fields Medal is in fact very different in terms of its procedures, criteria, remuneration and much else. Notably, the Nobel is typically given to senior figures, often decades after the contribution being honoured. By contrast, Fields medallists must all be under 40, an age at which, in most sciences, a promising career would just be taking off.

Indeed, the most famous instruction left by the prize’s main proponent, John Charles Fields, was that the awards should be both “in recognition of work already done” and “an encouragement for further achievement”.

So let us celebrate the work of these brilliant young mathematicians. And let us encourage them to further achievements that will doubtless spill into physics as well.