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cut (one's) eyeteeth
To gain experience with something, especially at a young age (when one's teeth would be coming in). One's "eyeteeth" are the canines. Oh, I cut my eyeteeth on those kinds of equations! Give me a challenging problem for a change! Jen may be young, but she cut her eyeteeth at a prestigious journal, so her perspective and expertise will be invaluable to us.
cut one's eyeteeth on something
Fig. to grow up experiencing something; to have had the experience of dealing with something [successfully] at a very early age. My grandfather taught me how to fish, so I cut my eyeteeth on fishing. Fred cut his eyeteeth on writing; both his parents were authors.
give one's eyeteeth
(for someone or something) Go to give one's right arm (for someone or something).
give one's right arm (for someone or something)and give one's eyeteeth (for someone or something)
Fig. to be willing to give something of great value for someone or something. I'd give my right arm for a nice cool drink. I'd give my eyeteeth to be there.
give your eyeteeth for something(spoken)
to want to have or do something very much Right now I'd give my eyeteeth for a chocolate ice cream soda!
cut one's teeth on
Also, cut one's eyeteeth on. Get one's first experience by doing, or learn early in life, as in I cut my teeth on this kind of layout or He cut his eyeteeth on magazine editing. This term alludes to the literal verb to cut teeth, meaning "to have teeth first emerge through a baby's gums," a usage dating from the late 1600s.
give one's eyeteeth
Also, give one's right arm. Go to any lengths to obtain, as in She'd give her eyeteeth for a mink coat, or He'd give his right arm for a new car. These hyperbolic expressions both allude to something precious, the eyeteeth (or canines) being useful for both biting and chewing and the right arm a virtual necessity for the 90 percent of the population who are right-handed. Both date from the first half of the 1900s, when the first replaced give one's eyes, from the mid-1800s.
cut one's eyeteeth
To have knowledge or skill gained through long experience. “Eyeteeth” are the canines, which lie directly under our eyes. They cut through the gums when we were very young, so we've had them for almost as long as we've been alive. To ask a pianist how long she played ragtime might be answered with “Oh, I cut my eyeteeth on that kind of music” In other words, for a very long time. Like many other childhood possessions, eyeteeth are so prized that “I'd give my eyeteeth” means to exchange a valuable asset for something that's highly desirable.