The majority of the internet thinks that Leonardo da Vinci said:
"Nothing strengthens authority so much as silence."
Of all the things Leonardo da Vinci might have said, that seems to be about the least probable. Da Vinci lived from 1452 to 1519, a time when power was held absolutely, whether by the Borgias, the de Medicis, or the Popes (who were a bit of both). The Enlightenment and ideas of individual rights like free speech were still centuries away. People who spoke out against authority didn't live long. In fact, if you had asked Leonardo the question "what strengthens authority?," he might have responded "loyal troops," "firm alliances," "talented ministers," or perhaps (foreshadowing the "reveal" below), the "splendor of the strong," or "shelter of the weak."
"Silence" would not have occurred to him.
Turns out the quote is from Charles de Gaulle, who comes in a distant second as far as the internet is concerned. To its credit (perhaps) brainyquote lists it under both da Vinci and de Gaulle.
Interestingly, ChatGPT recognizes that there is a dispute of sorts on attribution:
who said "Nothing strengthens authority so much as silence."
The quote "Nothing strengthens authority so much as silence" is attributed to Leonardo da Vinci, a famous artist, inventor, and scientist who lived during the Renaissance period. However, it is important to note that the attribution of this quote to da Vinci is sometimes disputed and its origins are not entirely clear.
But ChatGPT doesn't provide the de Gaulle suggestion, even as a hypothesis.
Interestingly, it's not really correctly attributed to de Gaulle either. In his book Le Fil de l'épée, de Gaulle actually said:
"Rien ne rehausse l'autorité mieux que le silence, splendeur des forts et refuge des faibles"
That translates to:
"Nothing builds authority up like silence, splendor of the strong and shelter of the weak."
See Vacapinta's contribution here: https://ask.metafilter.com/243455/Primary-Source-for-Leonardo-da-Vinci-Qoute
So rather than the notion that silence alone is the greatest strengthener of authority, de Gaulle's point was that the top three things that strengthen authority also include the splendor of the strong and shelter of the weak.
I should admit that I have not read through Leonardo's thousands of pages of notebook entries to confirm that he never said this. While it's clear that in those notebooks he occasionally made some quoteable remarks about the nature of life, including human life, I'm not aware of any other quote by him that ventures so far into the domain of Englightenment political philosophy.