When Mary and Isaac had the twins, they were named after Isaac's parents, Alice and Samuel.
In 1851, Samuel (7) was living at 1 Simpson Street, Little Bolton, Lancashire with parents and sisters Eliza (13) and Jane (4).
In 1861, Samule (17) was living at 2 Nuttall Square (off Blackburn Rd), Little Bolton (Halliwell) with parents Isaac and Mary (51 & 49) and siblings Jane (15) and Wiliam (9).
In 1871, Samuel (29, Head) and William (19) were spinners living at 51 Halliwell Road (with Martha Murry, aged 60, a housekeeper).
4 May 1872, Samuel Mather, Spinner, son of Isaac Mather a weaver married Sarah Booth, a widow, daughter of Thomas Birchall, a forgeman at St George's, Little Bolton.
The 1877 the marriage of Samuel Mather to Selina J Cooper may be another (a wealthy family with large monument for Selina in Southport), although this is probably another from Manchester. However, Samuel does appear to have left Sarah.
In 1881, Samuel Mather was married (38), lodger with Pennington family at Westhoughton and still in Westhoughton in 1891, near brother and family.
In 1881, after Martha's second husband James France had died, Samuel Mather (38, mar) was lodging with Martha Pennington. He is probably the father of Mary Ellen Pennington (as her death record records her father as Samuel Pennington). Mary Ellen recorded her MMN as Pennington on the first three UK births of her children, but Mather for Cecil, also hinting as Samuel being her father.
Samuel was recorded as Married in 1881, but single again in 1891, so did he marry? Well YES, as in 1901 he's recorded as a widower, so 1891 is probably an error.
In 1883, Samuel Mather Patterson married Catherine Sharp at Bolton Holy Trinity. This is another person, the widowed son of John Patterson.
In 1891 Isaac’s daughter Eliza Pendlebury (52, Wid) had moved into 4 Simpson Street. With her were two sons John and Israel (24 & 21) and her brother Samuel Mather (47, Single) was visiting.
Was living alone in 1901 at 19 Simpson St, still a cotton spinner.