In a large saucepan over medium-high heat, combine the sugar, corn syrup, and water. Cook and stir constantly until boiling. Clip a candy thermometer to the pan and without stirring, bring the temperature up to 260°F (hard ball stage) over medium heat. This will take approximately ten minutes.
When the candy mixture is nearly at the hard ball stage, begin to beat the egg whites. In a large mixing bowl, attached to an electric freestanding mixer, beat the egg whites until stiff peaks form.
Gradually, in a slow steady stream, pour the hot sugar mixture into the beaten egg whites, beating on high speed the entire time. This should take about 3 minutes. Scrape the sides of the bowl and add in your vanilla extract (or almond extract).
Continue to beat on high speed for approximately 6-10 minutes, until the candy starts to lose its glossy finish. When the beaters are lifted, the mixture should mound on itself and not flatten. You can test it by dropping a spoonful onto a parchment paper-lined baking sheet; if it stays mounded, the mixture has been beaten sufficiently. If it begins to flatten, continue beating and check again after a minute or so.
Once properly beaten, fold in the chopped pecans. Spoon (using a heaping tablespoon) the divinity onto parchment paper-lined baking sheets. Allow about an hour or two to set. Store in a tightly covered container at room temperature. Enjoy!
Notes
Store divinity candy in an airtight container at room temperature. Using parchment paper between layers can prevent sticking.