During the early Renaissance, artists were inspired by the discovery and collection of numerous works of classical art. Greek and Roman sculpture, in particular, were so revered that artists verged on idolatry as they slavishly sought to imitate the classical forms. However, the greatest of what we currently refer to as Renaissance art, the work of Raphael, Leonardo da Vinci, and Michelangelo, is notable primarily for the way it breaks out of mere emulation into seeking the highest possible achievements in the creation of character and the expression of emotion in a movement sometimes known as "Mannerism."
In a similar fashion, cosmetic surgery used to adhere to a strictly classical notion of what made a nose attractive. Rhinoplasty was governed by angles and proportions that were considered absolute as Plato's forms. The bridge of the nose was supposed to have an angle of 115-130 degrees from the vertical, and the nose itself should be the 3-4-5 right triangle we all remember from high school trigonometry.
Nowadays, though, cosmetic surgery recognizes that all faces are not identical, and that the best results for your rhinoplasty are determined by the way that the appearance of your nose interacts with the rest of your face. Following a rhinoplasty, the proportions of your nose should not be governed by mathematical ratios that came to a long-dead philosopher after days of involuntary fasting or a night of heavy drinking.
Although this development is generally positive and will lead to better results for the majority of people, it does have one major caveat. Without the governance of pure mathematics, a rhinoplasty is governed only by the innate sense of aesthetics of the plastic surgeon. This means that you have to be careful in your selection of a plastic surgeon and choose one with a demonstrated record of successfully judging what makes a nose harmonize properly with the rest of the face.