Combine sugar, corn syrup, and water in a heavy saucepan. Cook over medium heat, stirring until sugar dissolves. Stop stirring and continue cooking until the mixture reaches 260°F (hard ball stage) on a candy thermometer.
While the syrup cooks, beat egg whites in a large bowl with an electric mixer on high speed until stiff peaks form.
With the mixer running on high, slowly pour the hot syrup in a thin, steady stream into the beaten egg whites. Do not scrape the saucepan.
Continue beating on high for 8-10 minutes until the mixture becomes thick, holds its shape, and starts to lose its glossy sheen. Stir in vanilla and pecans.
Quickly drop rounded spoonfuls onto wax paper or parchment paper. Let set at room temperature for 2-3 hours until firm.
Notes
Humidity is the enemy of divinity. Make this on a dry day for best results. If the mixture is too sticky, beat it a bit longer.