Hinton taught at Cheltenham Ladies College while he studied at Oxford, where he obtained his B.A. in 1877. From 1880 to 1886, he taught at Uppingham School in Rutland, where Howard Candler, a friend of Edwin Abbott Abbott's, also taught. Hinton also received his M.A. from Oxford in 1886.

In an 1880 article entitled "What is the Fourth Dimension?", Hinton suggested that points moving around in three dimensions might be imagined as successive cross-sections of a static four-dimensional arrangement of lines passing through a three-dimensional plane, an idea that anticipated the notion of world lines, and of time as a fourth dimension (although Hinton did not propose this explicitly, and the article was mainly concerned with the possibility of a fourth spatial dimension), in Einstein's theory of relativity. Hinton later introduced a system of coloured cubes by the study of which, he claimed, it was possible to learn to visualise four-dimensional space (Casting out the Self, 1904). Rumours subsequently arose that these cubes had driven more than one hopeful person insane.

Hinton created several new words to describe elements in the fourth dimension. According to OED, he first used the word tesseract in 1888 in his book A New Era of Thought. He also invented the words "kata" (from the Greek "down from") and "ana" (from the Greek "up toward") to describe the two opposing fourth-dimensional directions...the 4-D equivalents of left and right, forwards and backwards, and up and down.

Hinton's Scientific romances, including "What is the Fourth Dimension?" and "A Plane World" were published as a series of nine pamphlets by Swan Sonnenschein & Co. during 1884–1886. In the introduction to "A Plane World", Hinton referred to Abbott's recent Flatland as having similar design but different intent. Abbott used the stories as "a setting wherein to place his satire and his lessons. But we wish in the first place to know the physical facts." Hinton's world existed on the surface of a sphere rather than a flat plane. He extended the connection to Abbott's work with An Episode on Flatland: Or How a Plain Folk Discovered the Third Dimension (1907).

Hinton was convicted of bigamy for marrying both Mary Ellen (daughter of Mary Everest Boole and George Boole, the founder of mathematical logic) and Maud Wheldon. He served a single day in prison sentence, then moved with Mary Ellen first to Japan (1886) and later to Princeton University in 1893 as an instructor in mathematics.

In 1897, he designed a gunpowder-powered baseball pitching machine for the Princeton baseball team's batting practice. According to one source it caused several injuries, and may have been in part responsible for Hinton's dismissal from Princeton that year. However, the machine was versatile, capable of variable speeds with an adjustable breech size, and firing curve balls by the use of two rubber-coated steel fingers at the muzzle of the pitcher. He successfully introduced the machine to the University of Minnesota where Hinton worked as an assistant professor until 1900, when he resigned to move to the U.S. Naval Observatory in Washington, DC.

At the end of his life, Hinton worked as an examiner of chemical patents for the United States Patent Office. He died unexpectedly of a cerebral hemorrhage on April 30, 1907.

Hinton was one of the many abstruse thinkers who circulated in Jorge Luis Borges's pantheon of writers. Hinton is mentioned in Borges's short story, “El milagro secreto” (“The secret miracle”):

Hinton is mentioned several times in Alan Moore's celebrated graphic novel From Hell & his theories regarding the fourth dimension form the basis of the book's final chapter. His father, James Hinton appears in the 4th and 10th chapters.