If a teenager using the words ‘like’ and ‘you know’ makes you a little nuts, this (Hannah’s presentation below) will make you a lot nuts. But it’s still a fun viewing if you have any math background (to be clear, I’m familiar with Fourier transforms, but was quickly lost here).
Well, if there’s no standardized testing for homeschoolers, then the only other standard for when a student finishes high school would be “when her parents say she’s finished”, and by that standard, it’d be even more surprising for her not to be finished.
I’m not sure how you landed on that either/or, but in California - much like Massachusetts - you are expected to cover a bunch of subjects to a specified level, and declare that you have done so…we, for example, filed progress reports every year (but I can’t describe the California specifics, other than what the law states).
Yes they are real students. You may not learn the types of things an undergrad learns, having done that already, but you learn important things about a career like how to write a paper, how to research, and how to construct an argument at a high level.
Other stuff. Ed Fredkin, who was head of Project MAC at MIT when I was there, never seems to have finished any academic college degrees. It does happen. A friend of mine at MIT didn’t have a high school degree, officially, since she went to the High School of Music and Art in NY and didn’t jump through some hoop or other. Didn’t hurt her.
Advisors range from really cool people to monsters. Never had the latter. Did have the former.And to tie stuff to the IAS discussion, he worked for the only person I’m aware of who had appointments at both Princeton and IAS. My advisor got his PhD from Princeton but worked on the IAS machine. When I lived in Princeton I knew a topologist at IAS pretty well, but I don’t know if they stuff they were honoring him for was done before or after he got there.
As for her math knowledge, I suppose she’ll be taking quals, so it won’t be an issue. I assume Math departments have quals, right?
There are two sides to every story, and I wouldn’t weigh too heavily the article’s take on the admissions decisions. The real aspects of the decisions will not be visible, and they will certainly be complicated. “You don’t have a degree” may be just what a sheet of paper says at the end of a much more involved process.
There’s the obvious real-world-readiness question, i.e. whether a home-schooled math savant is a good match to that school’s particular grad school environment. From our peanut gallery, we do not know if parents will be involved or if they need to be. Will the student suddenly have to deal with rent and food and car insurance for the first time without any structure? Grad school is not the ivory tower idealization and students are not robots, and it’s not fair to put someone in a situation they aren’t going to thrive in. (Not saying she is or isn’t; just putting this forward as one aspect of many.) There’s the teaching side: grad students in math departments typically do a lot of teaching, and a university might pause to ask whether a student that hasn’t been through the college experience is adequately prepared to teach college students (and if it is fair to those students, for whom quality of teaching will be a big factor in their educational experience.) On the raw research side, excellent students are rejected at a high rate at top schools even in routine situations for reasons of limited funding, alignment of research interests, and more. On the “no degree” side, there may be real implications with university accreditation and legal aspects of university charters or by-laws or union contracts, and these will vary university to university. If a school is part of a state system, the very legislature of the state might have written something down that precludes admission. Anyway, I would not have expected a particularly high success rate on her grad school applications, and I see no reason for outrage or finger wagging.
On the question of “why grad school?”: the stat block or skill tree of a researcher has many facets. Grad school (and also postdoctoral positions) is where those get fleshed out. Weak points are improved upon; strong points are utilized. We don’t know how her research has operated up to now. Maybe she did the whole thing in her bedroom (unlikely) or maybe she was bouncing ideas off experienced mentors every day (also unlikely; the truth will be somewhere in between.) But regardless, every academic researcher has plenty of soft and hard skills they will develop further through the grad school experience. Grad school is where the training wheels can be slowly removed, and by the time of the thesis defense, it’ll be clear (to the student and the advisor(s)) whether the student is biking on their own and whether they like biking at all.
I know this is somewhat tangential to the main topic but I just want to make one more point about why Feynman’s assertion that the traditional teaching paradigm (meaning, in this context, teaching undergraduate classes) is essential to good research bothers me so much. The basic issue is that thought processes, inspiration, and research methodologies are personal things that very much vary with the individual.
For example, I know of respected and well-regarded researchers who considered it a blessing and a gift of time to their research programs to be exempted from undergraduate teaching. And speaking for myself as a former software designer, I still remember being struck by inspiration about a particularly challenging software design problem, which involved the architecture of a mission-critical system with multiple loosely-coupled computers that had to achieve a high level of availability. The necessary abstractions that led to the design came to me, not in response to student questions, not while talking to a rubber duck, but while pacing my living room in quiet isolation. Exactly the kind of isolation that Feynman declared to be so unproductive.
We’re all different, and we achieve inspiration in different ways.
I feel sorry for any students who unfortunately had these “professors” who thought that teaching was beneath them and ruin the general education that universities are supposed to supply.
If you don’t want to teach, don’t become a tenured professor. Just go stay in a national lab somewhere where you can avoid the students you loathe so much.
You are, again, very much mistaken. There is far more to universities than undergraduate courses, and far more to teaching than undergraduate teaching. As I noted upthread, the graduate students in my experience, far from being “loathed” by the PI, were considered colleagues and friends. What is important is using the limited time of the most talented researchers in the most productive way. For some, it may involve undergraduate teaching; for others, not.
My asshole grad adviser happened to be an outstanding lecturer and I was a very good student. That’s largely why we chose one another. To say it was a bad fit would be an understatement. He was an excellent fundraiser as well. I badly needed mentorship and he was incapable of providing it. He assigned me an experiment that couldn’t be done with the available equipment and he didn’t understand that and I wasn’t capable of proving it. So I was forced into a situation where I had to quit and a year or so later a much better researcher proved that I was correct.
Again, if they don’t want to be part of an academic university they should stay in a national or private lab. If they only want to do research they can do just that there.
I know one other. He was also a HS dropout. Long story.
I was invited to spend a month in Denmark and get a month’s salary. My host asked me when I had gotten my master’s since the salary was determined by how much time had elapsed. When I told him I didn’t actually have a master’s degree, he asked me when I would have gotten a master’s if I had gotten one. I made up a date and that is what he put on the form.
Boy, is this ever true! About 30 years ago, I was halfway through writing a book that summarized my main early work in a field called homological algebra. I decided to teach a course based on the work so far. One of the students asked me two questions. I told him that I didn’t know but would think about them. In the process I wrote down a diagram. Let me see if I can picture it here.
C ←—– B ——→ A
|
|
V
C’ ←—–B’ ——–> A’
(just cannot simulate the vertical arrow from C to C’). Anyway, the key theorem was getting an arrow (arrows represent functions) from A to A’. When I looked at that diagram, which I had never written in that form before, the scales fell from eyes. Because the theorem in question had two principle hypotheses, the first being that the arrow from A to B was quasi-invertible and the second that the arrow from B’ tp C’ was as well. Homologically they were equivalences and provided the desired arrows that answered the student’s questions. It was such a revelation that I threw away the half-written book and started completely over. I now had a new and more elegant take on the whole subject. I gave the student full credit for this in the preface of the book. He is now a well respected professor of mathematics.
It was Dantzig, and it was in his first year as a PhD student at Berkeley. Details and cites here:
I was almost a case of not having a high school diploma. I was admitted to Carnegie-Mellon after my junior year in high school through a program they then had. My high school decided to give me a diploma the following year even though I was missing a phys ed course (they were happy to count my college courses otherwise). But if they hadn’t given me a diploma, it shouldn’t have mattered to my later career (on through getting a PhD in math).
And to @Hari_Seldon, very elegant! (I assume you mean that the map B to A was quasi-invertible.)
I was involved in hiring the GS-15 director of a new office at my Federal lab. Even though we were never going to hire somebody who didn’t have a PhD, HR wouldn’t let us say that in the job posting. They tossed applications from candidates with PhDs who didn’t supply their undergraduate transcript (I am somewhat sympathetic to taking a harsh stand on “can’t follow instructions”). Conversely, they made us consider applications from people who were only a few months out of undergrad, to lead an office of experienced PhD and Masters staff.
Yeah that’s what I meant. The maps were homotopy equivalences. Although it led to a generalization in which they were merely homology equivalences. And these were all (co-)chain complexes.
It is a common misconception that the purpose of any university is teaching students, and that the job of a university professor is essentially the same as that of a high school teacher but at a more advanced level.
This is sort of true of community colleges and at least some teaching-centered colleges and universities, but it is not an accurate description of research universities. And it means that it is a mistake for a high school student who is deciding where to go to college to assume that the most prestigious universities are where they will get the best education as an undergraduate.
My Father In Law (at second) had stage fright. He’d get more and more anxious in the days leading up to his required teaching presentations. AFAIK, he never invented anything original, but his name was on a lot of research papers for the analysis he did for international research projects.
My dad petitioned for his university diploma: they had a requirement that graduation happened at the graduation ceremony, and if you didn’t attend that, you hadn’t graduated. Fortunately, during the war, a lot of people had missed graduation for one reason or another, and they let him through.
It did make a difference to his career: the minimum entry requirements for university professor were expressed in a way that made a documented degree necessary.