Gottfried Wilhelm Leibniz
Based on Wikipedia: Gottfried Wilhelm Leibniz
At seven years old, Gottfried Wilhelm Leibniz inherited a library. His father, a professor of moral philosophy at the University of Leipzig, had just died, leaving behind shelves packed with Latin texts on philosophy and theology. Most children would have ignored such a gift. Leibniz devoured it.
By twelve, he had taught himself Latin well enough to read these advanced works fluently. At thirteen, he composed three hundred lines of Latin verse in a single morning for a school event—not stumbling through a homework assignment, but producing polished hexameter poetry before lunch. By nineteen, he had written his first book.
This was just the beginning.
The Last Universal Genius
Leibniz has been called "the last universal genius," and the title isn't hyperbole. He made foundational contributions to mathematics, philosophy, physics, logic, theology, law, history, and linguistics. He designed mechanical calculators. He developed a cataloguing system for libraries that became a model across Europe. He anticipated ideas in probability theory, biology, medicine, geology, psychology, and computer science—fields that wouldn't fully emerge for centuries.
What makes this particularly remarkable is what came after him. The Industrial Revolution brought specialization. Experts narrowed their focus. A physicist today might spend an entire career studying one particular type of subatomic particle. The idea of a single person making major contributions across a dozen unrelated fields became, essentially, impossible.
Leibniz was the last person to do it. He stood at the end of an era when one exceptional mind could still hold much of human knowledge.
The Calculus Wars
Ask a mathematician what Leibniz is famous for, and they'll likely mention calculus—though with a complicated addendum.
Leibniz developed differential and integral calculus in the 1670s. So did Isaac Newton, working independently in England. What followed was one of the ugliest priority disputes in the history of science.
Newton accused Leibniz of stealing his ideas. When Leibniz visited London in 1676, Newton later claimed, he must have somehow seen Newton's unpublished manuscripts. The Royal Society, which Newton effectively controlled, launched an investigation. It concluded—unsurprisingly—that Newton deserved all the credit.
Modern historians see it differently. Both men genuinely developed calculus independently. Their approaches were distinct. Newton thought in terms of velocities and flowing quantities, influenced by his work on physics and motion. Leibniz approached it more abstractly, focusing on the formal manipulation of infinitely small quantities.
Here's the telling detail: we use Leibniz's notation today, not Newton's. When you see dy/dx in a calculus textbook, that's Leibniz. His symbols were clearer, more flexible, and better suited to the generalizations mathematicians would need to make in later centuries. Newton may have gotten there first—or maybe not—but Leibniz created the language we still speak.
Binary and the Distant Future
In an age before electricity, before transistors, before anyone could imagine a computer, Leibniz worked out the modern binary number system.
Binary is how computers think. Every piece of data in every digital device—every photograph, every email, every video—is ultimately stored as ones and zeros. This isn't an accident of engineering convenience. It's mathematically fundamental. Binary is the simplest possible number system: just two digits, on and off, true and false.
Leibniz saw the elegance in this. He documented the system carefully, noting how any number could be expressed using only ones and zeros. He didn't have a practical application in mind—how could he? But he recognized something profound about the nature of information.
A footnote for the historically meticulous: the English astronomer Thomas Harriot actually devised the same system decades earlier. But Harriot's work remained obscure, while Leibniz published and promoted his ideas. In science and mathematics, being first matters less than being heard.
Mechanical Minds
Leibniz didn't just think about computation abstractly. He tried to build it.
He spent years developing a mechanical calculator, building on earlier work by Blaise Pascal. Pascal's machine could add and subtract. Leibniz wanted one that could also multiply and divide automatically. He designed the "Leibniz wheel," a stepped drum mechanism that would later become the core of the arithmometer—the first mass-produced mechanical calculator, though that came long after his death.
When Leibniz demonstrated a prototype to the Royal Society in London in 1673, they were impressed enough to make him an external member on the spot. The machine could execute all four basic arithmetic operations. It was temperamental and never fully reliable, but it worked.
Think about what this meant. In an era of quill pens and candlelight, Leibniz was trying to mechanize thought itself. He believed human reasoning could be reduced to precise rules, that logic could be captured in symbols and manipulated by machinery. He was, in essence, dreaming of artificial intelligence three centuries before the term existed.
The Best of All Possible Worlds
Leibniz's philosophy is often reduced to a joke. Voltaire's satirical novel Candide features a character named Dr. Pangloss who insists, amid catastrophe after catastrophe, that we live in "the best of all possible worlds." Pangloss is a parody of Leibniz, and not a particularly fair one.
The actual argument is more subtle. Leibniz believed in a God who was both all-powerful and perfectly rational. Such a God, when creating a universe, would naturally choose the best possible option among all logically coherent alternatives. Therefore, our world must be the best that could exist.
This doesn't mean suffering isn't real or that everything happens for easily apparent reasons. Leibniz acknowledged evil and pain. His argument was about logical necessity: if God is both able and willing to create the best world, and God exists, then this must be it. Any apparent imperfection reflects our limited perspective, not a flaw in the cosmic design.
You can see why this irritated Voltaire, writing in the aftermath of the Lisbon earthquake of 1755, which killed tens of thousands of people. But you can also see what Leibniz was attempting: a systematic answer to the problem of evil that had troubled theologians for millennia.
The Monads
Leibniz's metaphysics gets strange. At its center are "monads"—indivisible, immaterial units that constitute all reality.
Physical matter, in Leibniz's view, isn't fundamental. What exists, ultimately, are these monads: simple substances without parts, each one reflecting the entire universe from its own unique perspective. They don't interact with each other directly. Instead, God has arranged them in "pre-established harmony," like clocks synchronized at creation to forever keep the same time without ever touching.
This sounds bizarre to modern ears, but Leibniz was grappling with real philosophical puzzles. How do mind and body interact? If matter is infinitely divisible, what are its ultimate constituents? How can there be genuine unity in a world of scattered parts? His answers were unusual, but the questions were serious.
The monad theory also connects to his mathematics. Leibniz was fascinated by continuity—the idea that nature makes no jumps. His "law of continuity" stated that whatever holds for the finite should hold in the limit for the infinite, and vice versa. This intuition, though imprecise by modern standards, anticipated important developments in mathematical analysis.
A Life in Courts
For all his intellectual range, Leibniz never held a university position. He spent most of his career as a courtier—a librarian, historian, and political advisor to German nobility.
After completing his doctorate at age twenty, he entered the service of the Elector of Mainz. He drafted legal codes. He wrote diplomatic memoranda. He hatched a scheme to distract the French King Louis XIV by encouraging France to invade Egypt, thereby protecting German-speaking Europe from French aggression. The plan never materialized, though Napoleon's Egyptian expedition over a century later would follow a curiously similar logic.
In 1676, Leibniz took a position with the House of Brunswick in Hanover. He would remain in their service for forty years, until his death. The job was theoretically about managing the ducal library, but Leibniz's actual duties ranged across everything from diplomatic negotiations to writing the Brunswick family history to advising on mining operations in the Harz mountains.
The court at Hanover was provincial. The city had only about ten thousand inhabitants. Leibniz chafed at the limitations, but he also built genuine friendships, particularly with the women of the Brunswick family: Electress Sophia, her daughter Sophia Charlotte (who became Queen of Prussia), and Caroline of Ansbach (who would eventually be Queen of England). These were intellectual companions who appreciated Leibniz more than their husbands did.
A Visit to Spinoza
On his way from London to Hanover in 1676, Leibniz made a detour to The Hague. He had several reasons. One was to meet Antonie van Leeuwenhoek, the Dutch lens-grinder who had discovered microorganisms—an achievement that fascinated Leibniz.
But the more significant visit was to Baruch Spinoza.
Spinoza was the most radical philosopher of the age. He had been excommunicated from the Jewish community of Amsterdam for his heterodox views. His magnum opus, the Ethics, argued that God and Nature were identical, that everything followed from divine necessity, and that free will was an illusion. The book was so controversial that Spinoza refused to publish it during his lifetime.
Leibniz spent several days in intense conversation with him. We don't know the details of what they discussed, but we can guess: the nature of substance, the reality of God, the structure of the universe. Two of the greatest philosophical minds of the seventeenth century, face to face.
Spinoza died shortly afterward. The Ethics was published posthumously, and Leibniz would spend years developing his own philosophy partly in response to Spinoza's—keeping what he found valuable while rejecting what he considered dangerous materialism.
The Correspondence
Leibniz wrote letters. Thousands upon thousands of letters.
His surviving correspondence includes exchanges with more than a thousand different people across Europe. He wrote to scientists, philosophers, theologians, diplomats, and aristocrats. He wrote in Latin, French, and German, depending on the recipient and the subject matter. He wrote about mathematics one day and theology the next, about legal theory in the morning and mining technology in the afternoon.
Much of his philosophical work exists only in these letters and in manuscripts he never published. Unlike Newton, who jealously guarded his ideas, Leibniz scattered his thoughts across every available medium. This generosity meant his influence spread widely during his lifetime. It also meant that sorting out his intellectual legacy would take centuries.
Even now, not all of Leibniz's papers have been published. Scholars are still editing and analyzing manuscripts he left behind three hundred years ago.
A Death Without Mourning
Leibniz died on November 14, 1716, in Hanover. He was seventy years old.
His later years had been difficult. The British Act of Settlement in 1701 had designated the Brunswick family as heirs to the English throne, and when Queen Anne died in 1714, Elector George of Hanover became King George I of Great Britain. Leibniz had played a role in the negotiations that led to this outcome, but he was not invited to accompany the court to London. George I disliked him.
Left behind in Hanover, Leibniz was increasingly isolated. The Brunswick family wanted him to finish the history of their house that he had been working on for decades, but he kept getting distracted by other intellectual projects. His health declined. The calculus dispute with Newton had damaged his reputation in England.
When he died, no member of the court attended his funeral. His grave went unmarked for fifty years.
But ideas don't depend on funerals. Leibniz's notation became standard in calculus. His logic anticipated developments that wouldn't fully emerge until the twentieth century. His concept of "possible worlds"—different ways the universe could have been—became a standard tool in modern philosophy. His binary arithmetic became the foundation of digital computing.
The last universal genius left a legacy too large for any one field to contain.
The Mind That Contained Multitudes
How do we explain someone like Leibniz? Partly through circumstance: he came of age before specialization, when a single person could still reasonably hope to master multiple disciplines. Partly through opportunity: his father's library, his access to European intellectual networks, his position at a court that tolerated (if didn't always appreciate) his wide-ranging interests.
But mostly through sheer, relentless intellectual hunger. Leibniz read everything. He thought about everything. He wrote about everything. He corresponded with everyone who might have something interesting to say.
He was not, by all accounts, particularly easy to work with. He promised more than he delivered. He started projects he didn't finish. The Brunswick family history was supposed to take a few years; Leibniz spent decades on it and never completed the task. He could be vain about his achievements and thin-skinned about criticism.
But he was also generous with ideas, eager to share insights, genuinely excited by other people's discoveries. When he met Christiaan Huygens in Paris and realized how much he still had to learn about mathematics, he didn't sulk—he studied. He pushed himself to master what he had missed and then pushed beyond it to make original contributions.
That might be the most instructive thing about Leibniz: his willingness to be a beginner again and again, to acknowledge gaps in his knowledge and fill them, to treat the whole of human understanding as a territory to be explored rather than a fixed possession to be defended.
He wasn't just the last universal genius. He was a model for how to think across boundaries, how to connect ideas that others kept separate, how to see the unity beneath diversity.
We can't be Leibniz. The world has grown too complex, too specialized, too vast for any single mind to encompass. But we can remember what he demonstrated: that the walls between disciplines are conventions, not laws of nature, and that the most interesting ideas often live in the spaces between.