He started with a number of designs in the medical world, including a remote-control pacemaker, but started working at Atari in the late 1970s. There he managed to combine an entire breadboard of components into a single chip, known as the TIA. The TIA was the display hardware for the Atari 2600, which would go on to sell millions. After working on the TIA he headed up the design of the follow-on chip set that would go on to be the basis of the Atari 8-bit family of home computers, known as ANTIC and GTIA.
In the early 1980s Jay, along with other Atari staffers, had become fed up with management and decamped. They set up another chip-set project under a new company in Santa Clara, called Hi-Toro (later renamed to Amiga), where they could have some creative freedom. There, they started to create a new 68000-based games console, codenamed Lorraine, that could be upgraded to a full-fledged computer. To raise money for the Lorraine project, Amiga designed and sold joysticks and game cartridges for popular game consoles such as the Atari 2600 and ColecoVision, as well as an odd input device called the Joyboard, essentially a joystick the player stood on.
Tramiel invested $500,000 in the Lorraine project, hoping to use the results in an upcoming series of 32-bit machines that would replace Atari's existing home computer line. When Amiga was going to run out of money, Commodore bought the entire Amiga staff and Lorraine project, just before Tramiel could take the company over. He sued Amiga for that $500,000 never returned, but Commodore gave them $1M to pay their debts.
Jay worked at Commodore-Amiga for several years, at Los Gatos facilities (CA). They had a brilliant time at the beginning, but as Commodore management changed, they became marginalised and the original Amiga staff was fired or left out on a one-by-one basis, until the day the entire Los Gatos office was closed. After that, Jay worked as a consultant for Commodore until it went bankrupt.
He was known as the 'Padre' (father) of the Amiga among Amiga users.
Jay always took his dog "Mitchy" (a cockapoo) with him wherever he went. While he worked at Atari, Mitchy even had her own ID-badge, and Mitchy's paw print is visible on the inside of the first few Amiga 1000 cases alongside the signatures of the engineers who worked on it.
He lived with "faulty kidneys" for most of his life, according to his wife, and relied on dialysis. His sister donated one of her own. Four years later, Miner died due to complications from kidney failure at the age of 62.