Gottfried Wilhelm Leibniz (1646–1716) is arguably the most centrifugal polymath in Western history — the figure who made genuine, lasting contributions across the widest range of genuinely distinct fields. His output spans: mathematics (co-inventor of calculus, inventor of binary arithmetic and much of early symbolic logic), philosophy (Monadology, theodicy, pre-established harmony), physics (vis viva, the debate with Newton over absolute vs. relational space), history (court historian for the House of Hanover, archival projects), law (jurisprudence, natural law theory), linguistics (early comparative philology), engineering (mine-drainage pump designs), and diplomacy (plans for European peace).
Unlike Leonardo, Leibniz did finish things — he published the calculus, he produced his philosophical system, he completed historical manuscripts. But like every polymath of ambition, he left more unfinished than he completed. His lifelong project — the characteristica universalis, a symbolic language for all knowledge — was never completed and never could have been. The ambition was structurally outrunning the available time and corpus.
Burke identifies Leibniz as the pinnacle of the 17th-century pansophia movement. His encyclopedic ambitions were not eccentric hobby-horse thinking; they were the mainstream intellectual program of his era, shared (if less systematically pursued) by Mersenne, Comenius, and Bacon. Leibniz just had the broadest skills to attempt it.
He is also the figure who demonstrates why the "monster of erudition" epithet stuck: his breadth was so extreme that contemporaries found it difficult to trust. If a man claimed expertise in mathematics, philosophy, law, history, and engineering, surely he could not be taken seriously in all of them? The answer, in Leibniz's case, was that he could — but the suspicion is a permanent cost of centrifugal polymathy.