The title character of this short story, which appeared in the September 1885 issue of Harper's Weekly, is an old, uneducated woman who loves computing (with chalk and slate):
(quoted from An Old Arithmetician)
You have always been very fond of mathematics, haven't you, Mrs. Torry?" said the minister, in his slow retreat.
"Lor', yes. I can't remember the time when I wa'n't crazy to cipher."
"Arithmetic is a very fascinating study, I think," remarked the minister, trying to slide easily off the subject and down the porch steps.
"'Tis to me. An' there's somethin' I was thinkin' about this very forenoon  seein' all them leaves on the ground made me, I s'pose. It's always been a sight of comfort to me to count. When I was a little girl I'd 'most rather count than play. I used to sit down an' count by the hour together. I remember a little pewter porringer I had, that I used to fill up with beans an' count 'em. Well, it come into my head this forenoon what a blessed privilege it would be to count up all the beautiful things in this creation. Just think of countin' all them red an' goldcolored leaves, an' all the grapes an' apples in the fall; an' when it come to the winter, all the flakes of snow, an' the sparkles of frost; an' when it come to the spring, all the flowers, and blades of grass, an' the little new light green leaves. I don' know but you'll think it ain't exactly reverent, but it does seem to me that I'd rather do that than sing in the other world. Mebbe somebody does have to do the countin'; mebbe it's singin' for some."

In the story, the minister and the math teacher, Mr. Plainfield, give her a challenging mathematical problem to work on.
Mrs. Torry lives with her granddaughter, who complains to her about the math teacher, saying that he can't even do sums as well as an old woman. Mrs. Torry defends the teacher, saying:
(quoted from An Old Arithmetician)
"Sometimes it don't make any difference if anybody's ignorant, an' 'ain't got any booklearnin'; air old, an' had a hardworkin' life. There'll be somethin' in 'em that everybody else 'ain't got; somethin' that growed, an' didn't have to be learned. I've got this faculty; I can cipher. It ain't nothin' agin Mr. Plainfield if he 'ain't got it; it's a gift."

In the end, however, she seems to conclude that her gift is more of a curse. The woman becomes angry with herself when her granddaughter goes missing as she is lost in thought, working on the problem.
I'm not exactly sure what kind of problem it is that she is supposed to be working on. At several points, it is referred to as a "sum". However, it is difficult for me to think of a sum that would be so difficult to compute and engrossing. Certainly, there are mathematical problems that capture the attention of people who love mathematics and can keep them occupied for hours, days...even years, but I would not describe any of them as a "sum". Contributed by
John C. Konrath
This is an interesting tale worth the short time that it takes to read. The plot is one that most people can associate with (a loved one is not at an anticipated place at an anticipated time and the protagonist worries.) While a mathematical problem is the tool the author uses to advance the tale, it might just as well have been any distracting undertaking. The story says more about obsessive behavior that any clear aspect of mathematics.

