Lulu Miller’s book arrives in the UK four years late, already an international bestseller. Fittingly for a story about the limits of categorisation, it defies literary taxonomy. The frame is a biography of David Starr Jordan, the founding president of Stanford University and tireless ichthyologist whose team catalogued one-fifth of all the fish we can identify today. But that frame contains a memoir, a love story, philosophy, psychology, true crime, some powerful reportage and a decent stab at the meaning of life, all in about 200 pages. File under sui generis.

Miller, an American science journalist, first latched on to Jordan’s story while in the throes of heartbreak, shame and annihilating depression, seeing him as an exemplar of perseverance against the odds. In 1883, a few years into his fish-collecting career, a bolt of lightning set fire to Jordan’s laboratory, incinerating every specimen and document. Undeterred, he began all over again, only for the San Francisco earthquake of 1906 to reduce his life’s work to a ruin of broken glass, spilt ethanol, rotting flesh and suddenly useless name tags. Jordan pressed on. Whenever he could identify a fish from memory, he sewed a tag into its flesh, insisting that no matter how great the visiting catastrophe, “it is the will of man that shapes the facts”. He epitomised what HG Wells at the time identified as America’s invincible, “ultra-human” faith in its own resilience. Raised by an atheist biochemist who told her life was chaos without purpose, Miller was entranced by this “wonderful bastard” who believed he could catch the world in a net and force it to make sense.

Jordan’s biographer Edward McNall Burns hailed him as “one of the most versatile men America has produced”: a scientist, educator, explorer and peace campaigner in the mould of Thomas Jefferson or Benjamin Franklin. He was also possibly a murderer and definitely a champion of eugenics. The title of 1902’s The Blood of the Nation: A Study of the Decay of Races Through the Survival of the Unfit says it all. Miller initially thought he was teaching her “how to have hope in a world of no promises”, but the more she learns, the more she sees the folly of turning a dead naturalist into a self-help guru.

Now, a cynical reader might wonder whether Miller was really unaware of Jordan’s dark side when she began researching his life. It also seems implausible that a Peabody award-winning science writer would have been oblivious to the history of American eugenics, which involved tens of thousands of forced sterilisations under laws that inspired Nazi Germany’s programme of “race hygiene”. Some of Jordan’s peers didn’t think Hitler went far enough. There’s surely a bit of sleight of hand here. Miller hosts the WNYC show Radiolab and she has that familiar NPR-style tone of calculated informality (taxonomists “get a little woo-woo about the whole naming thing”) and faux-naif storytelling, gobsmacked by each new discovery. Of course, she knows exactly what she’s doing. The book is a marvel of narrative construction – fast-moving, deftly balanced, full of surprises and shimmering prose. Dazed students spill from the rubble of Stanford “like ants from a picnic basket”; a school of fish swims past Miller “like a catchable train”.

Among other things, Why Fish Don’t Exist speaks to our current ambivalence about scientific genius (Christopher Nolan’s Oppenheimer, Benjamin Labatut’s novels) and statue-toppling scrutiny of great men who did terrible things. Miller’s Jordan is neither hero nor villain but a bullish giant whose vices were inseparable from his virtues. His refusal to admit defeat made him ruthless while his determination to name and order the underwater world led him to impose sinister hierarchies on human beings. Ironically, his own name has recently been erased from Stanford campus buildings, but Miller aims to understand rather than cancel.

I won’t ruin the final twist (unless you’re an ichthyologist, I suppose) that explains the book’s title. Let’s just say that it leads Miller to the transformative conclusion that she should see the uncontrollable, unnameable elements of life as a source of wonder rather than terror. She winds up on the side of the earthquake: smash the jars and scatter the labels.