The French mathematician Cédric Villani won the Fields Medal (maths equivalent of the Nobel Prize) in 2010 for work with Clément Mouhot on the subject of “Landau damping” in mathematical physics.
Villani has written a book about that research. Oddly, it makes no attempt to explain the maths of the research. One appreciative reviewer, Hannah Fry, writes (click here for review) that she could not follow the maths despite having a Ph D in a closely related field of mathematical physics. But the book tells us vividly about the “partnership, courage, doubt and anxiety, elation and despair” involved in mathematical research.
Clément Mouhot described it like this in an email to me: “a fun book, and giving an idea of mathematical enthusiasm”.
Look at the paper in which Villani and Mouhot reported their research, and you find again that they are concerned to use words and diagrams to explain concepts and convince the reader, not just to give long calculations.