Thomas was born in 1829 in Breightmet and his baptism took place on March 15th, 1829.1
Birth Notes
1829 is too late for Hannah giving birth to Thomas. His mother would have been about 49. Later his father left him with his brother James to go and live in the USA. Perhaps Thomas was the illigetimate son of Thomas's oldest daughter Ann. There is a baptism for Thomas son of Anne from Breightmet, Spinster,
Name: Thomas Mather Baptism Date: 15 Mar 1829 Parish: Bolton-le-Moors, Lancashire, England Father: Mather - Anne is a spinster ! Mother: Anne Register Type: Bishop's Transcripts Reference Number: Drm/2/23a Abode: Breightmet
Breightmet is an area between Bolton and Bury, East of Bolton and only just South of Harwood, so this baptism could be Ann (single) the (possibly adopted) daughter of Richard and Hannah. It makes good sense. Hannah would surely have been too old, whereas Ann was just 17 when Thomas was conceived. Her parents then brought baby Thomas up.
In 1939 baptism shows Thomas is the son of Ann Mather (spinster) of Breightmet.
If Thomas was the son of Richard and Hannah (as 1841 and 1851 census suggests), then they were about 50 when Thomas was born. Maybe an illegitimate son of one of their children, most likely Ann, or a nephew.
In 1841, Thomas (18) was at Dandy Row, Sharples with his (assumed) brothers John and James (20 & 15) and father Richard (60). Because he appears after James he is not in birth order, so may not be Richard's son.
In 1851, Thomas (21, Un) was living with his brother James.
Thomas was a cotton spinner like his other male siblings. However, the marriage in Bolton to Mary Ann Beswick 14 July 1850 must be another, as Thomas was with his "brother" James in 1851, unmarried.