What would you prefer: to be forgotten altogether or to be remembered only because you had been wickedly parodied, skewered, by a famous writer? Saul Bellow, for example, filled his novels with richly realised but cruel renditions of people close to him and lost many friends as a result. In Humboldt’s Gift he reinvented the poet Delmore Schwartz as the dissolute and volatile Von Humboldt Fleisher – but the novel is more widely read and admired than Schwartz’s poems. A posthumous insult or a helping hand out of oblivion?

The philosopher Gottfried Wilhelm Leibniz is at no risk of being forgotten – he routinely appears on lists of the greatest philosophers of his or any age – but he is unusual in that the most famous summary of his thought is taken not from his own work but from the best-known parody of him: the figure of Pangloss in Voltaire’s Candide, who proclaims, in the face of a relentless series of indignities pointlessly suffered, that “all is for the best in the best of all possible worlds”. If this kind of sunny metaphysical optimism was proving difficult to sustain when Voltaire wrote his 1759 novel, thanks not least to disasters such as the Lisbon earthquake of 1755, it may seem to have even less to offer our own moment, when every news cycle brings catastrophes and atrocities of which Candide’s author could scarcely have dreamed.

Michael Kempe’s biography, published in German in 2022 and now translated into English, sets out to complicate this sense of Leibniz as a cheery but deluded soul out of step with melancholy modernity. If there is a reason why Leibniz has been at particular risk of being outshone by the parodies of his philosophy, this may be because – unlike, say, Descartes Spinoza, Kant or Wittgenstein – there is not a small subset of obviously pivotal works for an interested reader to make a start on his philosophy. His writing, in several languages and on a head-spinning array of topics, sprawls into dozens of volumes within which a reader may easily feel disoriented and intimidated. Kempe’s response to this challenge is ingenious and twofold. First, rather than downplaying the scale and eccentricity of Leibniz’s achievement, he celebrates it as the feature that paradoxically speaks to the modern moment the most clearly. Second, even as he relishes Leibniz’s insatiable curiosity and prolixity, the form of the biography is designed to make it manageable in scale. Rather than seeking to cover the whole of a complex and restless life, Kempe gives us “seven pivotal days” when Leibniz’s movements and his acts of writing can be pinned down with some precision, and where we can see some of his key insights – such as the formulation of differential calculus, credit for which he disputed throughout his life with Newton and his followers – begin to crystallise.

The virtue of this approach lies in the fact that it is not arbitrary: the form of the biography is part of the argument that Kempe wants to make about its subject. Leibniz is presented as a figure especially compelling for the way he requires us to rethink the nature of particular phenomena and their often imperceptible, tiny components. This is the basis of Leibniz’s other famous philosophical contribution, the concept of the “monad”, the internally complex unit from which larger and more complex entities are formed. Leibniz loved concocting beautiful metaphors to explain this idea, such as the bruit de la mer, the roar of the sea, in which the loud crashing of a wave is made up of many small waves producing sounds too tiny to be audible to human ears. Likewise, every flash of inspiration “would be made up of an infinite number of tiny ‘flickers’ of inspiration”, the texture of which this book seeks to convey.

Leibniz as Kempe presents him is not, as Voltaire would have it, the philosopher of dopey acquiescence in the face of reality’s horrors. He is, instead, the great philosopher of the possible; the thinker who sees the surface of reality as rippling with possibilities, not all of which will achieve the privilege of being realised. This was true for Leibniz himself, who left an abundance of unfinished projects, and many of whose schemes for personal advancement and attempts to effect practical and political change came to nought. Kempe’s affinity and admiration for his subject, his determination to celebrate his restless effusiveness, is winning, even if the enthusiasm can become, at times, rather too breathless: descriptions such as “words and ideas just poured out him” recur more often than necessary, giving the book its own tendency to gush. This is, however, a symptom of an approach striving to be as humane and capacious as Kempe’s presentation of Leibniz himself. Above all, the Leibniz who emerges here wants to expand our sense of what is possible: the alternative to vacuous Panglossian optimism is not curmudgeonliness or despair but a view of the world as “always already the best because it carries within itself the possibility of its optimisation”. What is required is not acceptance, whether cheerful or resigned, but “an ongoing labour on the possible”.

• The Best of All Possible Worlds: A Life of Leibniz in Seven Pivotal Days by Michael Kempe is published by Pushkin Press (£20). To support the Guardian and Observer order your copy at guardianbookshop.com. Delivery charges may apply