According to "New England Families, Genealogical and Memorial: ..., Volume 3" edited by William Richard Cutter, page 1301  this Thomas Mann was an immigrant and not the son of Richard and Rebecca Mann of Hanover.
Thomas Mann, the immigrant ancestor, settled in Rehoboth, Massachusetts, and in Providence, Rhode Island. On March 26, 1676, during King Philip’s War, the battle at Rehoboth called “Pierce’s Fight” occurred. Fifty-two English and eleven friendly Indians were killed, and one hundred forty of the opposing Indians lost their lives. The affair was very desperate, as shown by the fact that the English fought in a ring back to back for two hours against overwhelming odds, having only eleven surviving white men, among them Thomas Mann, who received a severe wound. [note: some sources say the only survivors were Thomas Mann and a few friendly Indians] On March 7, 1682, he was fined ten shillings for Sabbath breaking. He was surveyor of highways June 9 1683, and on February 7 1689 his name was on the list of inhabitants of Rehoboth. On January 20, 1693, he bought a farm in Providence of Ephraim Pierce of Rehoboth and soon after settled on it. Another Thomas abt 1650 of Rehoboth, married a Rachel Bliss who died at the same time as their daughter. There is a story that she had assisted an injured or destitute Indian, who, when he recovered murdered both mother and child. Another record says she was killed in an Indian attack on the entire town, with many persons killed. This same Thomas then married a daughter (Mary?) of the Wheaton family. [note: this is actually our Thomas]
Mary and Thomas Man's children, born Rehoboth, Massachusetts:
Two separate men named Thomas Mann seem to have been given the birth date August 15 1650. Four wives keep appearing in many genealogies, with two completely separate lists of children. Both children's lists include a Thomas Mann.
The Thomas Mann born in 1681 was the son of Thomas Mann (1650) and Sarah Woodworth or Sarah Ensign. This family lived in Scituate MA, where Richard Mann (1611) lived. Thomas (1650) also had a son named Josiah; so did Richard. Some make Thomas (1681) to be the son of Richard Mann. This Richard Mann would not have been Richard Mann (1652), son of Richard Mann (1611). This would be the correct Thomas Mann born in 1650 to Richard Mann.
The Thomas Mann born in 1685 was the son of the other Thomas Mann (1650) and Mary Wheaton (he also married Rachel Bliss). He seems to have lived in Rehoboth MA, and then his entire family moved to Smithfield RI. This is our Thomas Mann, therefore most likely not the son of Richard Mann (1611). Some records for the other Thomas Mann (1650) give his father as James Mann, died 1693 in Rehoboth (this death isn't listed there). A few call his father Thomas Mann instead, and one William Mann and Frances Hopkins. Most of these can be discounted because of names, and William's son Thomas lived in Virginia and North Carolina.
2019: Family Search has sourced the birth of 7 children in Rehoboth, Mass, and both parents are named.
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