Early on in this darkly fascinating novel based on real people and events, the Austrian physicist Paul Ehrenfest speaks of a “strange new rationality” that’s taking shape as the old certainties of classical physics crumble around him. He describes it as “a spectre haunting the soul of science… both logic-driven and utterly irrational… preparing to thrust itself into our lives through technology by enrapturing the cleverest men and women with whispered promises of superhuman power and godlike control”.

Ehrenfest is speaking from the depths of a breakdown but his warning sets the tone for the rest of Benjamín Labatut’s book, which explores how these clever men and women (though mostly men) set about unleashing that spectre with dazzling and devastating consequences. After a short, riveting account of Ehrenfest’s demise – he killed himself and his son in 1933 as the Nazis rose to power – we meet John von Neumann, the formidably intelligent Hungarian mathematician, physicist and computer scientist who contributed to the Manhattan Project, laid the foundations of modern computing (Maniac is the name of a computer he developed) and foresaw the possibilities of artificial intelligence. Then we flash forward to the rise of AI, whose promises enrapture its developers even as they fret over its apocalyptic potential.

This isn’t particularly new territory for Labatut. His previous book, When We Cease to Understand the World – his first to be translated into English – traced the intellectual struggles of prominent 20th-century scientists and mathematicians, one of whom, Fritz Haber, was instrumental in the creation of chlorine gas and artificial fertiliser. Written with extraordinary lucidity and an eye for macabre detail, it was, the Chilean author explained in the acknowledgments, “a work of fiction based on real events”, with “the quantity of fiction” growing as the book went on.

The Maniac, too, is presented as fiction based on fact. The details largely conform to what you’ll read in the history books, but Labatut affords himself considerable latitude to imagine real lives from the inside. He taps into Ehrenfest’s feverish mind as he awaits the train that will convey him to his terrible final act. Later, we’re plunged into an epiphany that the British programmer Demis Hassabis, now head of AI at Google, experienced in a field in Liechtenstein, with chess moves and church bells whirling through his consciousness.

In the case of Von Neumann, introduced as “the smartest human being of the 20th century”, Labatut takes a step back, as if daunted by the prospect of giving voice to his monstrous intelligence. Instead, he ventriloquises the people in Von Neumann’s orbit, the colleagues he wowed and alienated, the family members he drove to distraction, building a more nuanced picture than a single perspective would allow. We follow him to the US, where his coldly logical view was put to the service of state power. It was Von Neumann who influenced the US army to detonate the atomic bomb higher above its Japanese targets, knowing it would inflict vastly more damage.

Examining the minds of these architects of the nuclear age sheds some light on today’s scramble towards artificial general intelligence. In the competitiveness, hubris and ravenous curiosity of Von Neumann and others, we might find explanations for why today’s AI pioneers are so eager to push forward despite the risks. But in Hassabis, we also see the appeal of harnessing the power of machines to solve the world’s problems, even if his opening gambit is to crush human opponents at the boardgame Go.

Labatut handles all of this with impressive dexterity, unpicking complex ideas in long, elegant sentences that propel us forward at speed (this is his first book written in English). Even in the more feverish passages, when yet another great mind succumbs to madness, haunted by the spectres they’ve helped unleash on the world, he feels in full control of his material.

• The Maniac by Benjamín Labatut is published by Pushkin Press (£20). To support the Guardian and Observer order your copy at guardianbookshop.com. Delivery charges may apply