There are possibly several children who were adopted by Mary and John Mather but this needs more research when time allows. Collaboration appreciated!
Sources
"United States Census, 1850," database with images, FamilySearch (https://www.familysearch.org/ark:/61903/1:1:MCT3-D6Y : 23 December 2020), Mary Mather in household of John Mather, Middlesex, Yates, New York, United States; citing family , NARA microfilm publication (Washington, D.C.: National Archives and Records Administration, n.d.).
"New York State Census, 1855," database with images, FamilySearch (https://familysearch.org/ark:/61903/1:1:K6QW-P24 : 3 March 2021), Mary Mather in household of John Mather, Middlesex, Yates, New York, United States; citing p. , line #44, family #26, county clerk offices, New York; FHL microfilm 838,913.
"Adopted daughter " Francis M Mather is 4 years old.
"New York State Census, 1865," database with images, FamilySearch (https://familysearch.org/ark:/61903/1:1:QVNJ-SNVZ : 8 March 2021), Mary Mather in household of John Mather, , Middlesex, Yates, New York, United States; citing Census, p. 14, citing multiple county Clerks; Warren and Lewis County Board of Supervisors; multiple counties in New York; Utica and East Hampton Public Libraries, New York.
"United States Census, 1870", database with images, FamilySearch (https://www.familysearch.org/ark:/61903/1:2:M4Y1-5BT : 29 May 2021), Household of Mary Mather, 1870. (Sons Francis and Willie are 19 and 16 respectively. I think we can remove "childless", there are definitely at least two, possibly three children in the family)
"New York, Yates County, Swann Vital Records Collection, 1723-2009," database with images, FamilySearch (https://familysearch.org/ark:/61903/1:1:QJ8B-DG5F : 1 March 2021), Polly Sleighton in entry for John Mather, 02 Aug 1865; citing Death, Middlesex, Yates, New York, United States, Yates County Genealogical and Historical Society and Oliver Museum and Underwood Museum, Yates.
"New York, Yates County, Swann Vital Records Collection, 1723-2009," database with images, FamilySearch (https://familysearch.org/ark:/61903/1:1:QJ8B-DY4L : 1 March 2021), Polly Mather in entry for David S Morehouse, 04 Jan 1894; citing Death, Middlesex, Yates, New York, United States, Yates County Genealogical and Historical Society and Oliver Museum and Underwood Museum, Yates.
"New York, Yates County, Swann Vital Records Collection, 1723-2009," database with images, FamilySearch (https://www.familysearch.org/ark:/61903/1:2:QKS8-48VT : 1 March 2021), Entry for Polly Moorehouse, 06 Mar 1895; citing Death, Middlesex, Yates, New York, United States, Yates County Genealogical and Historical Society and Oliver Museum and Underwood Museum, Yates.
There should only be one Memorial per person at Find A Grave... but because while we are certain this is the same lady, "the cemeteries are different". So unfortunately, Mary has two, the first listed is the first one created:
Find a Grave, database and images (https://www.findagrave.com/memorial/86499300/mary-polly-mather: accessed 26 July 2022), memorial page for Mary Polly Slayton Mather (8 Jan 1820–6 Mar 1895), Find a Grave Memorial ID 86499300, citing Overackers Cemetery, Middlesex, Yates County, New York, USA; Maintained by Butterfly~Kisses (contributor 46994799).
Find a Grave, database and images (https://www.findagrave.com/memorial/135811529/mary-morehouse: accessed 26 July 2022), memorial page for Mary Slayton Morehouse (6 Jan 1820–6 Mar 1895), Find a Grave Memorial ID 135811529, citing Middlesex Cemetery, Middlesex, Yates County, New York, USA; Maintained by Kathleen Oster (contributor 47973435).
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DNA Connections
It may be possible to confirm family relationships with Mary by comparing test results with other carriers of her ancestors' mitochondrial DNA.
However, there are no known mtDNA test-takers in her direct maternal line.
It is likely that these autosomal DNA test-takers will share some percentage of DNA with Mary: