A sweater by definition is a knitted top, and knitted garments have been around a very long time. So the real answer to who invented the sweater is the same answer to "who invented knitting?"
Knitting by definition is the process of using at least one, and usually two needles to loop or knot yarn together to create a garment or piece of fabric. It is believed that the oldest knitted garments were socks, however, since knitting did not require a large piece of equipment like a loom, it has been hard to trace the exact history of knitted garments. Historians have had to rely on the remnants of knitted garments that have remained and given the fragile nature of fabrics, few have.
Nailbindning & Dura-Europos Fragment
A precursor to knitting, was a craft called "nalbindning', a one needle form of knitting that was much more difficult to execute. In fact, nailbindning did not become a commonplace craft because it was so difficult. The first example of a knitted garment, a fragment of stocking, was made by this method and dates back thousands of years, found by archeologists, in the Indus River Valley. Called the Dura-Europos fragment, it is considered by many to be the oldest fragment of knitting in existence.
The Coptic Socks
The first example of a garment made by the two needle form of knitting, that we are familiar with today, are the fragments and whole Egyptian "coptic socks" that date back to 1000 CE. Many examples have been found by archeologists. The socks were made from white and blue dyed cotton, and had symbolic patterns woven into them called Khufic, that were intended to protect the wearer.
The Cardigan Sweater
The cardigan sweater was named after the seventh Earl of Cardigan, James Thomas Brudenell. Brudenell was a military captain who led his troops at The Charge of the Light Brigade into the Valley of Death. Brudenell's troops were outfitted in knitted military jackets nicknamed cardigans.
