Stealth refers to the act of trying to hide or evade detection. It is not so much a technology as a concept that incorporates a broad series of technologies and design features. As a concept, stealth is nothing new, having been invented by the first caveman to cover himself with leaves so that he could sneak up on a dim-witted antelope. Soldiers hid behind trees. Submarines hid under the waves to sneak up on ships, and it was submarines that first used special coatings on their periscopes to avoid radar detection during World War II.
For airplanes, stealth first meant hiding from radar. After World War II, various aircraft designers and strategists recognized the need to design planes that did not have large radar signatures (a radar signature is how big the airplane appears on radar from a specific angle and distance; it is often referred to as the "radar cross section"). But their ability to hide from radar was limited for many years for several reasons. One major limitation was aircraft designers' inability to determine exactly how radar reflected off an airplane.
In the nineteenth century, Scottish physicist James Clerk Maxwell developed a series of mathematical formulas to predict how electromagnetic radiation would scatter when reflected from a specific geometric shape. His equations were later refined by the German scientist, Arnold Johannes Sommerfield. But for a long time, even after aircraft designers attempted to reduce radar signatures for aircraft like the U-2 and A-12 OXCART in the late 1950s, the biggest obstacle to success was the lack of theoretical models of how radar reflected off a surface. In the 1960s, Russian scientist Pyotr Ufimtsev began developing equations for predicting the reflection of electromagnetic waves from simple two-dimensional shapes. His work was regularly collected and translated into English and provided to U.S. scientists. By the early 1970s, a few U.S. scientists, mathematicians, and aircraft designers began to realize that it was possible to use these theories to design aircraft with substantially reduced radar signatures. Lockheed Aircraft, working under a contract to the Defense Advanced Research Projects Agency, soon began development of the F-117 stealth fighter.