Born in 1813 in Madison, New York, Maynard became a renowned dentist in Washington, D.C. While he is known for developing surgical procedures and inventing many dental instruments still in use today, Maynard is best known for his contributions to the firearms and munitions industries. In 1845, he patented a percussion priming system (a priming system ignites a charge to propel a bullet or ball from a rifle), which was later used to convert flintlock firearms. Maynard's invention consisted of a coiled, tape-like paper strip containing fifty fulminate caps spaced at regular intervals. When the hammer was cocked, one charge was automatically projected over a metal nipple. When the hammer descended, it cut off and fired the charge. The United States government bought Maynard's patent, called the Maynard tape primer, and equipped its military with new percussion priming pistols and rifles.

Maynard is also credited with making improvements to existing firearms. In 1851, he invented a percussion breech-loading rifle, the Maynard rifle, in which the ammunition was loaded at the rear rather than from the muzzle, and improved metallic cartridges, resulting in finer precision and ruggedness. Maynard also came up with a method of converting muzzle-loading arms into breechloaders in 1860. Later, he created a device that allowed two rifle or shotgun barrels to expand or contract endwise independently of each other to prevent warping of the barrels. In 1866, Maynard patented an invention for indicating at any time the number of cartridges in the magazine of a repeating firearm.

Maynard was considered one of the leading scientists in the world during his lifetime, and was awarded many honors. While the King of Prussia awarded him a top military honor and the King of Sweden gave him a Great Medal of Merit, Tsar Nicholas I of Russia attempted to persuade Maynard to become his Court Dentist. Maynard died in Washington D.C. on May 4, 1891.