Speak softly and carry a big stick
A proverb advising the tactic of caution and non-aggression, backed up by the ability to do violence if required.
The notion being expressed here is the opposite of the tactics employed by every temporary schoolteacher - who begin stern and tough and, when discipline allows it, become more easy-going. The 'speak softly...' doctrine, like the earlier phrase 'the iron fist in the velvet glove', was to begin gently, but hold a decisive weapon in reserve.
The widespread use of 'speak softly and carry a big stick' began with American president Theodore Roosevelt. In a letter to Henry L. Sprague, on January 26th 1900, he wrote:
"Speak softly and carry a big stick; you will go far."
Roosevelt claims the phrase to be of West African origin, but I can find no corroborative evidence for that assertion. If it truly was proverbial in 1900 it ought to be easy to find earlier citations of it, but I can find none. Nor is there any record of the phrase actually being used in West Africa before Roosevelt's time. Whether Roosevelt actually believed, for whatever reason, that the expression was West African, or whether he knew that it wasn't and was indulging in a form of 'Confucious he say' hokum in order to impart a degree of distinction to it, we don't know. It is certainly possible that he coined the phrase himself.
See also: the List of Proverbs.