To play this extraordinary chap, Goyer chose English-born actor Tom Riley.
The 31-year-old starred in the British TV medical drama "Monroe," and in 2011 performed on Broadway in the revival of Tom Stoppard's "Arcadia" alongside Billy Crudup and Raul Esparza.
Riley's da Vinci is sexy, mercurial and irrepressible.
He savors life in his native Florence: "Chaos and culture are celebrated within these walls," he says lustily. "Florence only demands one thing of its people -- to be truly awake!"
But da Vinci suffers from being too awake. He is too driven, too full of ideas, too haunted by doubts about his life's intended mission.
He is no stranger to opium, which he uses, he explains, because "I think too much. I need to dull my thoughts or I will be eviscerated by them."
At times he overreaches, stumbles and falls (though ever so dashingly). And he has an eye for a pretty face, including -- at high risk -- comely Lucrezia Donati (Laura Haddock), the mistress of Lorenzo di Medici (Elliot Cowan), da Vinci's benefactor and one of the city's most powerful figures.
He has an answer for everything, including an accuser who brands him "arrogant."
"Arrogance implies that I exaggerate my own worth," da Vinci fires back. "I don't."
Goyer says he hit upon doing a show about da Vinci only by chance. He had never done anything historical before, and when asked by Starz to create a drama focused on some towering figure from the past, he first demurred.
"I said, `I'm not -- no offense -- interested in doing a kind of dry, BBC historical drama.' And they said, `No, no, no. We don't want THAT!"'
A number of possible candidates were considered for what was now envisioned as a "reinvention-of-history show." There was Cleopatra and Genghis Kahn, "and also on that short list, da Vinci came up," recalls Goyer.
"Then I realized, no one's ever done a show about da Vinci! That's crazy! People say he's the most recognized figure in history other than Jesus Christ!"
To prepare for the series, Goyer says he read dozens of biographies, da Vinci's journal pages and many of his letters.
He has written or co-written all eight episodes of season one (with work well under way on a second season's scripts), and directed the first two episodes of the show, which shoots in Wales.
Recapturing 15th-century Florence, not to mention the highfalutin exploits of da Vinci, demands impressive visual effects, and Goyer set the bar high: "My goal was to be at least on par with the production values of `Game of Thrones,"' he says.
But even as it recaptures the past, the show, like da Vinci, is forward-looking.
"The central conflict is about who controls information," Goyer says. "On the one hand, you've got the Vatican Secret Archives.
The Church wants to control the information. On the other hand, shortly before our show starts, Gutenberg invented the printing press.
"This is a modern-day touchstone that viewers can identify with. If da Vinci were alive today, his slogan would be, `Information wants to be free."'
