# Best way of mentioning specific non-famous/named theorems in my Statement of Purpose (SOP) for PhD math

In my SOP for PhD math in US grad schools, I am mentioning a specific instance where I came up with an easier solution to a problem using elementary theorems, instead of using more complex theorems. Here I'm trying to mention the names of theorems that I could have used and one of them is a non-famous/named theorem (Theorem 16.4c in Willard's General Topology) from a famous Topology text. What is the best way to mention this result? Even though there is no word limit, I don't think quoting the entire thing would be wise. I could just mention its number and mention the book in the references or I could try to summarize it as a "Separability criteria for the product space of non singleton hausdorff spaces". Or should I avoid mentioning any theorems at all?

• What is an SOP? It might be obvious to someone from the US but to anyone here, it is/would-be meaningless? Dec 26, 2022 at 10:47
• I may not advise on SoP for US PhD applications (so not a full answer), but a proposed scenario where the committee has to look up a somewhat obscure reference can not be good. Summarizing seems like a much better choice here, but even then stating the problem you were able to solve and not going into great detail about the solution might be preferable. Unless it was a particularly elegant/strong result, in which case you should be able to summarize it well ;) Dec 26, 2022 at 10:56
• @CrimsonDark My bad, SOP=Statement of Purpose. I've edited it in the title.
– ZSMJ
Dec 26, 2022 at 11:13
• Was any of this published? If not, what assurance do you have that it is correct? Dec 26, 2022 at 13:34
• @Buffy Oh, this wasn't an open problem, just a tough exercise that I wanted to mention since having multiple ways of solving problems is one of the things that attracted me to topology. I read in SOP guides that one should mention specific events from one's past that made them interested in their field, instead of generic sentences that could apply to anyone so I thought including specific names would be helpful. My professor and posts on Math Stack Exchange confirmed that its correct.
– ZSMJ
Dec 26, 2022 at 16:04