Wiles was born in Utica, New York, and educated at the Sedgwick Institute in Great Barrington, Massachusetts. As a young man he studied art with his father Lemuel Maynard Wiles and from 1879-1881 attended the Art Students League in New York City. At the League he was a student of Thomas Wilmer Dewing, William Merritt Chase and James Carroll Beckwith. He became close friends with Chase and Beckwith and their art had a long lasting influence on his work. After studying from 1882-1884 in Paris at the Académie Julian and in the private atelier of Carolus-Duran, Wiles returned to New York and established his reputation as a figure and portrait painter. He also worked as an illustrator for Century, Harpers and Scribners from about 1884-1894.
During the course of Wiles career he exhibited widely and received several coveted awards, including the Shaw Prize for the best figure painting at the 1900 annual exhibition of the Society of American Artists and a gold medal in 1915 at the Panama Pacific Exposition. From the mid 1880s through 1907 he taught at the Art Students League. He also assisted at his father Lemuel's art school in upstate New York at Silver Lake where regular classes were held each summer through 1894. Four years later Wiles bought a tract of woodland bordering the north shore of Little Peconic Bay in Peconic, Long Island, and built a cottage and studio on the edge of the high bank above the beach. While residing in Peconic, first for several months a year and then permanently, Wiles became active as a marine and landscape painter and occasionally depicted his large garden with its many varieties of flowering plants.
"Ideal Head" dates from the early years of the twentieth century. Wiles' figure paintings of young attractive women from this period were admired for their charm, elegance, refined treatment of character, and masterful paint handling. Wiles partially wraps his model in loose fitting white drapery, which he renders with vivid, flowing brushwork while emphasizing the softness and transparency of the material. The drapery has fallen exposing her left shoulder, and Wiles emphasizes the beauty and shimmering sensuality of her skin. In 1909, Wiles explained his artistic approach: "Always the difference between a good and a bad thing in art lies not in the subject represented, but in the way the subject is seen, and the way it is done. The ability to see beauty of a distinguished kind in a subject, whether that subject be a beautiful woman, or a bit of still life. . . depends upon the personality of the artist. To be able to so make his picture that others will also see [its] beauty . . . depends upon . . . technical ability. . . . Paint as simply as possible. Try for the largeness of things (Irving R. Wiles, "Portrait Painting," Palette and Bench 1 [January 1909]: 84-85).