In 1798 Jacob Mather paid rent at Breightmet. This may have been his father.
Jacob was born about 1802 in Bolton, possibly the son of Jacob. There is no baptism for Jacob, and likewise Jacob Snr was widowed, and also no first marriage or baptism records.
In 1841, Jacob was 35, a cotton washer at Crook Street, E Bolton with Sarah (30) and John (15). Also present were William and Alice Taylor (both 25), possibly related. Neighbours were John and Mary Buckley (65 & 60), the Oil Sheet Maker.
In 1843, Jacob's wife Sarah died in 1843, so in 1851 he was a widower (49), living in lodgings at 22 Moor Lane, Western Bolton.
By 1861, Jacob (58, born Bolton) was a Cotton Hand, working and lodging at Mayfield Terrace, Mayfield, Staffordshire with Joseph Dagnall (23 a cotton hand) and wife Betsey (23, born Bolton), not Jacob's daughter, as Joseph Dagnall married Elizabeth Pollitt Q1/1859 in Ashborne.
There are so few records for Jacob, it seem likely he went by another name, probably James, a common alternative.