What did Dirac do with the equation's 'nonsense' solutions?

Took them seriously. His 1928 equation combining quantum mechanics with special relativity produced solutions with negative energy, which every convention said should be discarded as unphysical - and rather than throw them out he proposed they described a real particle, identical to the electron but positively charged. Carl Anderson photographed one four years later.

That is a specific intellectual move worth naming: trusting the mathematics further than the intuition. Dirac made a career of it, and said explicitly that it is more important for an equation to have beauty than to fit experiment, on the grounds that a discrepancy might be a bad measurement while ugliness is usually a sign of being wrong. It is a dangerous principle that worked spectacularly for him.

He was also famously literal and near-silent - colleagues at Cambridge defined a unit called the dirac, one word per hour. Asked after a lecture by an audience member who said he did not understand an equation, Dirac said nothing at all; pressed by the chairman, he explained that it had not been a question. His Nobel lecture predicted that the universe might contain stars made entirely of antimatter, which remains an open question.