Out of curiosity, I was wondering if anyone, historically, has ever been awarded a degree that was a level higher than the one they were enrolled in and studying for, simply because their performance warranted a higher award? For example, somebody could have been awarded a MPhil instead of an MSc or a PhD instead of an MSc?
Although a bit old, there's the case of Luzin's Master's thesis: . . . he completed his thesis The integral and trigonometric series which he submitted in 1915. After his oral examination he was awarded a doctorate, despite having submitted his thesis for the Master's Degree. In fact, even for a Ph.D. thesis, Luzin's is one of the strongest ever written in mathematics --- in my opinion easily in the top 20 (and probably in the top 10) of all-time Ph.D. theses in mathematics for its influence on later developments.
This appears to be the published version of Luzin's thesis, which is 242 pages and in Russian, with the table of contents on pp. 241-242. For references to it, this search and this other search seem to work the best. I didn't get many hits for the title's French translation, by the way.
When Donald Ervin Knuth was a college student at Case Institute of Technology in Cleveland, Ohio, in the 1950s he showed such intelligence and talent that the faculty voted to award him a master’s degree in mathematics simultaneously with his bachelor’s degree.
Knuth himself explained:
At Case I put a lot of time into stuff out of class, but in class, I found a really clever way to, right now, let me brag this way to say, to avoid having to study too hard, for my classes. In the first place, I noticed though, that when I was a sophomore, my grades started to go down, in the first part of my sophomore year. And I ascribed it to too much ping-pong playing and playing cards too much in the dorm, and so; no, I’m sorry; this was the second half of my freshman year. I started having a little problem with my grades, and so I had to give up ping-pong.
But starting in my sophomore — junior year, I found out that you could take graduate courses at Case, and they were easier than the undergraduate courses. The reason is that Case had really strict admissions requirements for undergrads, but they were fairly loose about admitting graduate students. I think they wanted to build up, you know, admit graduate students, so when you had graduate students, in a class, they usually didn’t know as much as the undergrads did, so if you would take a graduate course, you didn’t have as much competition, you know, and the teacher would recycle stuff, and all this. So I started taking graduate classes, and you know, and all these hotshot undergrads would be taking the other classes.
And as a result, I had accumulated also, by the time I was a senior, I had accumulated lots and lots of graduate credits. Now, as a result then, Case did, on Graduation Day, Case did an unprecedented thing that had never been done before, they awarded me a Master’s Degree, simultaneously with my Bachelor’s Degree. And this, the faculty had gotten together and made a, and voted unanimously that this should happen, and I remember, you know, that was another thing that got into the newspapers at the time, that they were awarding a Master’s Degree at the same time as a Bachelor’s Degree. So, but the reason was that I had taken these graduate courses because they were easier. I didn’t, I don’t know if I’ve ever told anybody else this before today, but that was one of the reasons I could do so many other things.
The famous Polish mathematician, Stefan Banach, famously received his PhD in 1920 without having had a college degree. In fact, its a pretty famous story, he did not want to get any sort of degree as he claimed he can still come up with ideas that are better and more deserving of a degree. He was actually tricked into defending a PhD thesis as he was asked to "explain some mathematical problems to people who struggle with understanding them", which later turned out to be members of his PhD defense committee.
You could find interesting details here.
Not quite the same, but George Dantzig famously solved two previously unsolved problems in statistical theory as a graduate student, after showing up late for class and mistaking them for homework assignments. When he decided to start his PhD, his professor told him to "wrap the two problems in a binder, and I'll accept them as your thesis."
Ludwig Wittgenstein was famously awarded his PhD in Philosophy by his advisor, Bertrand Russell, entirely on the basis of classwork completed for his prior degree, plus the addition of a book he had written outside school (The Tractatus) standing in for a thesis.
I had a professor in University whose advisor recommended he switch from a Master's Program to a PhD Program, based on the research he was doing (he never received a Master's).
I realize this may not be in the spirit of your question, but it fits the criteria (awarded a degree higher than they were enrolled in). Apparently transfers like this are common enough to have a process for it at some universities:
Students may be eligible to transfer from a master’s program into a related doctoral program ("fast track") if they have completed the following requirements:
◾Hold a bachelor's degree, and have completed a minimum of one year of study in a master's program with 9 credits at the 500-level or above and of first class standing (80% or better).
◾(for Ph.D.) clear evidence of research ability or potential;
◾(for Ed.D.) first class standing and first class standing in such prerequisite work as may have been required, and five years professional experience; or
◾(for D.M.A.) outstanding ability in performance or composition.
My point is, this may not come up very often, as their performance should be recognized prior to the completion of their program, leading to a transfer to the higher degree program.
In Russia there are two graduate degrees: Candidate of Sciences (an equivalent of PhD) and Doctor of Sciences (a higher degree). It is very rare but not exceptional to be awarded the Doctor degree if the committee recognizes one's Candidate thesis worthy. The most famous cases is Yuri Knozorov, who deciphered the Maya script (his defence was three and a half minutes long).
Such possibility is present in the rules, otherwise, there is no skip over a degree (say, getting Master's degree without Bachelor or Specialist), one can not even enroll.
I expect this isn't what you mean, but everyone who applies for and is awarded a Bachelor's degree (this may only be honours degrees, but even if so that's by far the majority) from Oxford or Cambridge University, is also eligible for a Master's degree 4 years after graduation. Or 7 years after they started studying, I forget the exact rule.
Examples of eligible students would include 3 of the last 4 (and 4 of the last 6) British Prime Ministers. One of the two people with me in the room as I type was awarded the MA, the other has never bothered taking it but is entitled.
Historically, this is because Oxford and Cambridge claimed that the performance of all their graduates merited the higher award. Now they just claim it's "because tradition, alright?!". So to anyone who knows the system, the bonus MA is of course completely worthless as a CV point. But it entitles you to wear a nicer gown, and to vote in elections for Chancellor.
Strictly speaking you do have to apply for the master's separately, but only in the sense of "this is which date I want to attend the ceremony", not in the sense of "enrolling and studying", or submitting any work for consideration.
I say this with no bitterness at all, as someone who studied for an undergraduate master's degree at Oxford and therefore never held a bachelor's degree and don't qualify for the additional master's. One of my mates from school did the same subject at the same time, but an undergraduate bachelor's and separate master's. Same number of years study (4) and he came out of it with a BA, an MSc, and an MA he could claim later, instead of my solitary MMath :-)
Nicolas Demorand, a french journalist, passed a contest for a preparatory class in order to integrate an university of political science, and was immediately proposed a teaching job instead :
sa copie de philo impressionne tant... qu'on l'embauche comme prof. (his philosophy paper impress so much... that he's hired as a professor)
Srinivasa Ramanujan (wiki) was an Indian mathematician notable for influential theories and proofs (…) and for being largely self-taught.
"Though he had almost no formal training in pure mathematics, he made substantial contributions to mathematical analysis, number theory, infinite series, and continued fractions, including solutions to mathematical problems considered to be unsolvable."
Early academic pursuits were not fruitful:
[…] [While enrolled at Pachaiyappa's College, Madras] he passed in mathematics, choosing only to attempt questions that appealed to him and leaving the rest unanswered, but performed poorly in other subjects […] Ramanujan failed his Fellow of Arts exam in December 1906 and again a year later. Without a FA degree, he left college and continued to pursue independent research in mathematics, living in extreme poverty and often on the brink of starvation.
His independent research continued until:
"In 1913 he began a postal partnership with the English mathematician G. H. Hardy at the University of Cambridge, England. Recognizing the extraordinary work sent to him as samples, Hardy arranged travel for Ramanujan to Cambridge…"
[In March 1916] Ramanujan was awarded a Bachelor of Science degree by research (this degree was later renamed PhD) for his work on highly composite numbers, the first part of which was published as a paper in the Proceedings of the London Mathematical Society.
On 6 December 1917, he was elected to the London Mathematical Society.
In 1918 he was elected a Fellow of the Royal Society, the second Indian admitted to the Royal Society, following Ardaseer Cursetjee in 1841.
On 13 October 1918, he was the first Indian to be elected a Fellow of Trinity College, Cambridge.
According to the Ramanujan Institute website:
On 16 March 1916 Ramanujan graduated from Cambridge with a Bachelor of Science by Research (the degree was called a Ph.D. from 1920). He had been allowed to enrol in June 1914 despite not having the proper qualifications. Ramanujan's dissertation was on Highly composite numbers and consisted of seven of his papers published in England.
The takeaway is this: Bachelor of Science by Research is a doctoral degree, which post-1920 at Cambridge was renamed to Ph.D; albeit nuanced a difference that Bachelor's degree is not analogue to what our current idea of a BA is; that is why I've included all the other qualifications and elections he earned prior to 1920.
Aubrey de Grey:
More recently (2000), Aubrey de Grey was awarded a Ph.D. for a book he published although he was not enrolled in a doctoral program or had worked towards a Ph.D. This is not an honorary degree. This is known as a Ph.D. by Special Regulations. According to Cambridge University: "available only to Cambridge degree holders (of whatever discipline) permit the submission of "...a significant contribution to scholarship" instead. Though the awardee has not been registered as a Ph.D. student, the degree is not honorary; applicants are evaluated by the usual methods, with examiners appointed and an oral defense of the submitted work."
It depends on the academic regulations of the respective institutions. I don't think this is generally possible these days. However, if you check this academic CV, you'll notice a conspicuous absence of a diploma which I know (due to personal knowledge) to be no accident. This was in Germany in 1962, considerably later than some other examples here. I should be surprised if this was a singular (even though rare) occurence to happen at that time even though I don't know personally of other examples.