# Help me track down this mathematician **URL:** \ **Category:** Factual Questions\ **Tags:** science-math\ **Created:** [March 21, 2024, 10:00pm UTC](https://boards.straightdope.com/t/help-me-track-down-this-mathematician/999166 "2024-03-21T22:00:38Z")\ **Posts on this page:** 14\ **Page:** 1
**Author:** ![Chronos](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/chronos/32/134_2.png) [@Chronos](https://boards.straightdope.com/u/Chronos)\ **Post date:** [March 21, 2024, 10:00pm UTC](https://boards.straightdope.com/t/help-me-track-down-this-mathematician/999166/1 "2024-03-21T22:00:38Z")
Or rather, her work. What I know: - Her name was Sr. Mary Ferdinand Torline, CSJ. She might also be referred to as M. Ferdinand Torline, and the “Sr.” and “CSJ” might be omitted. - She wrote a master’s thesis on “The Practical Solution of the Cubic Binomial Congruence” at St. Louis University, in 1949. - She wrote her PhD thesis on “Waring’s Problem, Modulo P” at the same university, in 1955, with her advisor being John Dyer Elder. - She also wrote punch-card programs (I haven’t yet tracked down which language), which suggests that she remained active in her field after her PhD, since computers would have been quite rare in 1955. - More information is certainly available on the master’s thesis and the punch-card programs, as those are physically kept nearby. I was prompted onto this subject by the archivist in custody of said items being curious about them. My first thought was to check Web of Science, but the last time I used that, I still had an institutional affiliation, and didn’t realize that it was subscription-only. My second thought was Google Scholar, but I couldn’t find much there. In addition to knowing what other publications she wrote and who she was cited by, I’m also curious about what the implications of her work would be. On the introductory page of her master’s thesis, she acknowledged that the work had very little practical application, but much has changed in number theory, and in particular modular number theory, since 1949. Would that work be relevant to cryptographic hashes, for instance? ---
**Author:** ![Crafter\_Man](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/crafter_man/32/458_2.png) [@Crafter\_Man](https://boards.straightdope.com/u/Crafter_Man)\ **Post date:** [March 21, 2024, 11:01pm UTC](https://boards.straightdope.com/t/help-me-track-down-this-mathematician/999166/2 "2024-03-21T23:01:59Z")
Not sure if this helps, but I found a 1981 article about her, along with her obit: [![](https://live.staticflickr.com/65535/53602875974_563a243ed2_n.jpg) ](https://live.staticflickr.com/65535/53602875974_563a243ed2_n.jpg) [![](https://live.staticflickr.com/65535/53602535371_3c032b05d4_n.jpg) ](https://live.staticflickr.com/65535/53602535371_3c032b05d4_n.jpg) ---
**Author:** ![Dr.Strangelove](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/dr.strangelove/32/6613_2.png) [@Dr.Strangelove](https://boards.straightdope.com/u/Dr.Strangelove)\ **Post date:** [March 21, 2024, 11:28pm UTC](https://boards.straightdope.com/t/help-me-track-down-this-mathematician/999166/3 "2024-03-21T23:28:35Z")
One cite: > **["Waring's Problem, Modulo p, and the Representation Symbol" by M. Anne...](https://scholarworks.uni.edu/pias/vol66/iss1/49/)** > > The representation symbol \[a,b,c\] is the statement that an integer of n-ic type a is congruent to the sum of an integer of n-ic type b and an integer of n-ic type c. The symbol is extended to include any definite number of elements. New properties,... Similar title as Torline’s, and cites her: > Torline, Sister Mary Ferdinand, C.S.J. “Waring’s Problem, Modulo p,” > Unpublished Ph.D. dissertation, Department of Mathematics, Saint Louis > University, 1955 The “unpublished” suggests that it might be hard to dig up more. ---
**Author:** ![OldGuy](https://avatars.discourse-cdn.com/v4/letter/o/3bc359/32.png) [@OldGuy](https://boards.straightdope.com/u/OldGuy)\ **Post date:** [March 22, 2024, 12:02am UTC](https://boards.straightdope.com/t/help-me-track-down-this-mathematician/999166/4 "2024-03-22T00:02:04Z")
> [@Dr.Strangelove](#): > > Waring’s Problem, Modulo p, According to ProQuest, the dissertation is not available online. ---
**Author:** ![Dr.Strangelove](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/dr.strangelove/32/6613_2.png) [@Dr.Strangelove](https://boards.straightdope.com/u/Dr.Strangelove)\ **Post date:** [March 22, 2024, 12:07am UTC](https://boards.straightdope.com/t/help-me-track-down-this-mathematician/999166/5 "2024-03-22T00:07:18Z")
I didn’t notice this at first, but the author of the other paper is also a nun: Sister M. Anne Cathleen Real, CHM. Didn’t know they were so into math… ---
**Author:** ![Chronos](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/chronos/32/134_2.png) [@Chronos](https://boards.straightdope.com/u/Chronos)\ **Post date:** [March 22, 2024, 12:27am UTC](https://boards.straightdope.com/t/help-me-track-down-this-mathematician/999166/6 "2024-03-22T00:27:17Z")
One other tidbit I found while researching her: In the entire decade 1950-1959, only 104 American women got PhDs in math… and of those 104, 12 were nuns. I guess nuns don’t have much patience with people telling them what women ought and ought not to do. ---
**Author:** ![PastTense](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/pasttense/32/14550_2.png) [@PastTense](https://boards.straightdope.com/u/PastTense)\ **Post date:** [March 22, 2024, 12:55am UTC](https://boards.straightdope.com/t/help-me-track-down-this-mathematician/999166/7 "2024-03-22T00:55:41Z")
> [@Dr.Strangelove](#): > > I didn’t notice this at first, but the author of the other paper is also a nun: Sister M. Anne Cathleen Real, CHM. Anyone look into where M. Anne Real went to college? The thought which comes to mind that she was a Master’s degree student of John Dyer Elder at Saint Louis University who was also the PhD advisor of Sr. Mary Ferdinand Torline–and M. Anne Real’s publication was a condensation of her master’s thesis. [https://www.genealogy.math.ndsu.nodak.edu/id.php?id=7644](https://www.genealogy.math.ndsu.nodak.edu/id.php?id=7644) Note Marycrest College where M. Anne Read taught is only about 250 miles from St. Louis. ---
**Author:** ![gnoitall](https://avatars.discourse-cdn.com/v4/letter/g/bb73d2/32.png) [@gnoitall](https://boards.straightdope.com/u/gnoitall)\ **Post date:** [March 22, 2024, 2:53am UTC](https://boards.straightdope.com/t/help-me-track-down-this-mathematician/999166/8 "2024-03-22T02:53:50Z")
> [@Chronos](#): > > (I haven’t yet tracked down which language) Do the cards not have a printed topline displaying what’s punched on the card? You may have to read the deck to determine that. ---
**Author:** ![Chronos](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/chronos/32/134_2.png) [@Chronos](https://boards.straightdope.com/u/Chronos)\ **Post date:** [March 22, 2024, 10:41am UTC](https://boards.straightdope.com/t/help-me-track-down-this-mathematician/999166/9 "2024-03-22T10:41:03Z")
> [@gnoitall](#): > > Do the cards not have a printed topline displaying what’s punched on the card? Probably. I didn’t have much time to look at them before, and didn’t get past “these are punchcards for a computer program”. ---
**Author:** ![Ruken](https://avatars.discourse-cdn.com/v4/letter/r/f475e1/32.png) [@Ruken](https://boards.straightdope.com/u/Ruken)\ **Post date:** [March 22, 2024, 5:35pm UTC](https://boards.straightdope.com/t/help-me-track-down-this-mathematician/999166/10 "2024-03-22T17:35:21Z")
> [@Chronos](#): > > My first thought was to check Web of Science, but the last time I used that, I still had an institutional affiliation, and didn’t realize that it was subscription-only. And either my subscription doesn’t go back that early, or she doesn’t have anything that they’ve indexed. ---
**Author:** ![Hari\_Seldon](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/hari_seldon/32/5173_2.png) [@Hari\_Seldon](https://boards.straightdope.com/u/Hari_Seldon)\ **Post date:** [March 22, 2024, 11:14pm UTC](https://boards.straightdope.com/t/help-me-track-down-this-mathematician/999166/11 "2024-03-22T23:14:16Z")
Very curious. The mathematical genealogy search does not find her. I have searched for many on that site and never failed before. Edited to add: Then I searched for John Dyer Elder and she came right up as one of his students with her full name and thesis title. She had no known students is all I can add. ---
**Author:** ![Chronos](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/chronos/32/134_2.png) [@Chronos](https://boards.straightdope.com/u/Chronos)\ **Post date:** [March 23, 2024, 12:57pm UTC](https://boards.straightdope.com/t/help-me-track-down-this-mathematician/999166/12 "2024-03-23T12:57:48Z")
I do intend to take a closer look at those punchcards, to see if I can figure out what the program was for (since it was probably something after her PhD). It can’t be more than a few hundred lines; I can suffer through that much Fortran. Meanwhile, if we can’t find the publications or citations themselves, how about the other part, what her work might have been relevant for (even if it went unnoticed)? IIRC, raising numbers to some power, modulo some number, is one of the key operations in cryptography. Would cubic binomials be part of that? ---
**Author:** ![PastTense](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/pasttense/32/14550_2.png) [@PastTense](https://boards.straightdope.com/u/PastTense)\ **Post date:** [March 23, 2024, 1:32pm UTC](https://boards.straightdope.com/t/help-me-track-down-this-mathematician/999166/13 "2024-03-23T13:32:01Z")
Well the subject matter is Waring’s Problem, which @Hari_Seldon can perhaps comment on concerning its importance: > **[Waring's problem](https://en.wikipedia.org/wiki/Waring%27s_problem)** > > In number theory, Waring's problem asks whether each natural number k has an associated positive integer s such that every natural number is the sum of at most s natural numbers raised to the power k. For example, every natural number is the sum of at most 4 squares, 9 cubes, or 19 fourth powers. Waring's problem was proposed in 1770 by Edward Waring, after whom it is named. Its affirmative answer, known as the Hilbert–Waring theorem, was provided by Hilbert in 1909. Waring's problem has its o Lo... And it looks like there are a lot of articles about Waring’s Problem and cryptography: [https://www.google.com/search?q="Waring’s+Problem"+"cryptography"&client=firefox-b-1-d&sca\_esv=18fae8d458e6cfdd&biw=1280&bih=586&ei=w9r-ZfukEaXh0PEP9q2n-AQ&ved=0ahUKEwi7krmswIqFAxWlMDQIHfbWCU8Q4dUDCBA&oq="Waring’s+Problem"+"cryptography"&gs\_lp=Egxnd3Mtd2l6LXNlcnAiIyJXYXJpbmfigJlzIFByb2JsZW0iICJjcnlwdG9ncmFwaHkiMggQABiABBiiBDIIEAAYgAQYogQyCBAAGIAEGKIESMRNUJ8WWPUzcAF4AJABAJgBhgGgAZgCqgEDMi4xuAEMyAEA-AEBmAIDoAKqApgDAIgGAZIHAzIuMaAHmAc&sclient=gws-wiz-serp](https://www.google.com/search?q=%22Waring%E2%80%99s+Problem%22+%22cryptography%22&client=firefox-b-1-d&sca_esv=18fae8d458e6cfdd&biw=1280&bih=586&ei=w9r-ZfukEaXh0PEP9q2n-AQ&ved=0ahUKEwi7krmswIqFAxWlMDQIHfbWCU8Q4dUDCBA&oq=%22Waring%E2%80%99s+Problem%22+%22cryptography%22&gs_lp=Egxnd3Mtd2l6LXNlcnAiIyJXYXJpbmfigJlzIFByb2JsZW0iICJjcnlwdG9ncmFwaHkiMggQABiABBiiBDIIEAAYgAQYogQyCBAAGIAEGKIESMRNUJ8WWPUzcAF4AJABAJgBhgGgAZgCqgEDMi4xuAEMyAEA-AEBmAIDoAKqApgDAIgGAZIHAzIuMaAHmAc&sclient=gws-wiz-serp) ---
**Author:** ![Hari\_Seldon](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/hari_seldon/32/5173_2.png) [@Hari\_Seldon](https://boards.straightdope.com/u/Hari_Seldon)\ **Post date:** [March 23, 2024, 3:33pm UTC](https://boards.straightdope.com/t/help-me-track-down-this-mathematician/999166/14 "2024-03-23T15:33:15Z")
Number theory is not my bag and there is not a lot I can add to the wiki article. Once you know that every number is the sum of 4 squares (not obvious, although I do know an elementary\* proof) and every number is the sum of 9 cubes (I haven’t the faintest idea how to prove it), it seems natural to conjecture that every number is the sum of 16 4th powers. Until you run into the fact that 79 is not the sum of fewer than 19 4th powers (4 16s and 15 1s). I still think that there are only finitely many exceptions and that every sufficiently large number is the sum of 16 4th powers, but I could be wrong. At any rate, Waring conjectured and Hilbert proved that for each natural number n, there is a number G(n) such that every number is the sum of G(n) nth powers. When n \> 3, there is also a number g(n) \< G(n) such that every sufficiently large number is the sum of g(n) nth powers. \*elementary does not always mean easy, only that no advanced concepts are used. In this case the most advanced idea used is modular arithmetic (arithmetic mod n).