Thomas in 1841, but would have been 11 if the 1851 census is correct. There is a Thomas listed on the 1841 census with Richard Mather (head, 60). Thomas (18 or maybe 8) is listed after James (15), so either not a son of Richard or actually age 8.
Thomas was 21, unmarried in 1851, living with "brother" James. Recorded as Sharples, so probably born Harwood as the other family.
Name: Thomas Mather Baptism Date: 21 Feb 1830 Baptism Place: Bolton-le-Moors, St Peter, Lancashire, England Mother: Rachel Mather Reference Number: GB127.L243/1/3/9
Thomas son of Rachel Mather, spinster. Abode: Great Bolton
Thomas Mather, baptised 1830, was the illegitimate son of Rachel Mather before she married William Rostrom in 1832. In 1833 Rachel and Thomas had William Rostrom, and then her husband died the same year. There was another illegitimate Thomas, son of Anne of Breightmet baptised in 1829.
Rachel's parents, Richard and Hannah adopted both children (Thomas Mather and William Rostron) as their own.
In 1841, Thomas Mather (18) and William Rostron (8) were living with Richard Mather (60) brothers John and James (20 & 15) at Dandy Row, Sharples. Thomas's age was about 12, but the census appears to have altered to 18 (with the 8 in a darker ink)
In 1851, Thomas (21, Unmarried) was living with "brother" James & Susan Mather (both 29) and family at Blackburn Road, Sharples.
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.
Marriages 1851 - 1861 THOMAS MATHER (DOB etc) MATHER Thomas BOLTON Mary Ann Jane 1852 Bury, St.Mary CE7/13/296 1832 from Tottington, MAJ Bolton from Blackborn MATHER Thomas HORROCKS Harriet 1855 Bolton RO RO/14/49 1833 DNA match between JMG & Rachel Copeland MATHER Thomas WALKDEN Ellen 1857 Bolton, St Peter 18/20/20 1834 Illegitimate. Collier from Blackrod so unlikely. MATHER Thomas DOBSON Jane 1858 Bolton RO RO/15/119 1832 Thomas an Iron Moulder from L.B. MATHER Thomas ABBOTT Mary 1859 Horwich, Holy Triny 38/1/59 1834 Son of John & Jenny MATHER Thomas RATHBONE Violet 1860 Prestwich, St.Mary CE18/21/204 1838 From Oldham, son of John.