# 17-year-old refutes math conjecture, enters PhD program without a degree **URL:** \ **Category:** Miscellaneous and Personal Stuff I Must Share\ **Tags:** science-math\ **Created:** [August 3, 2025, 1:07pm UTC](https://boards.straightdope.com/t/17-year-old-refutes-math-conjecture-enters-phd-program-without-a-degree/1021655 "2025-08-03T13:07:46Z")\ **Posts on this page:** 20\ **Page:** 6
**Author:** ![Zoobi](https://avatars.discourse-cdn.com/v4/letter/z/13edae/32.png) [@Zoobi](https://boards.straightdope.com/u/Zoobi)\ **Post date:** [August 4, 2025, 10:39pm UTC](https://boards.straightdope.com/t/17-year-old-refutes-math-conjecture-enters-phd-program-without-a-degree/1021655/101 "2025-08-04T22:39:59Z")
I have a PhD, in a “hard science “. You aren’t explaining any “misconception” to me. Teaching isn’t _the_ purpose, but it should be _a_ purpose for being at a university. ---
**Author:** ![nearwildheaven](https://avatars.discourse-cdn.com/v4/letter/n/90db22/32.png) [@nearwildheaven](https://boards.straightdope.com/u/nearwildheaven)\ **Post date:** [August 4, 2025, 10:40pm UTC](https://boards.straightdope.com/t/17-year-old-refutes-math-conjecture-enters-phd-program-without-a-degree/1021655/102 "2025-08-04T22:40:19Z")
I can’t be the only person who has a feeling that she will have a nervous breakdown, or its equivalent, before she’s 20 years old. ---
**Author:** ![Melbourne](https://avatars.discourse-cdn.com/v4/letter/m/b5e925/32.png) [@Melbourne](https://boards.straightdope.com/u/Melbourne)\ **Post date:** [August 4, 2025, 10:43pm UTC](https://boards.straightdope.com/t/17-year-old-refutes-math-conjecture-enters-phd-program-without-a-degree/1021655/103 "2025-08-04T22:43:24Z")
I’ve heard it expressed that people who come up through this kind of path do not make good Medical Doctors, and have trouble with staff politics, but perhaps I’m not the only one feeling that “Math PhD” doesn’t have the same personal-interaction requirements as Family Medicine Doctor 🙂 ---
**Author:** ![Wendell\_Wagner](https://avatars.discourse-cdn.com/v4/letter/w/8491ac/32.png) [@Wendell\_Wagner](https://boards.straightdope.com/u/Wendell_Wagner)\ **Post date:** [August 4, 2025, 11:01pm UTC](https://boards.straightdope.com/t/17-year-old-refutes-math-conjecture-enters-phd-program-without-a-degree/1021655/104 "2025-08-04T23:01:11Z")
There’s no evidence that people this intelligent are more likely for nervous breakdowns than any other random group of people. ---
**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:** [August 4, 2025, 11:08pm UTC](https://boards.straightdope.com/t/17-year-old-refutes-math-conjecture-enters-phd-program-without-a-degree/1021655/105 "2025-08-04T23:08:46Z")
But there _is_ evidence that people really like to believe in some kind of “conservation of talent” principle, such that if a person is skilled in one area they must be deficient in another. ---
**Author:** ![Frodo](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/frodo/32/302_2.png) [@Frodo](https://boards.straightdope.com/u/Frodo)\ **Post date:** [August 4, 2025, 11:25pm UTC](https://boards.straightdope.com/t/17-year-old-refutes-math-conjecture-enters-phd-program-without-a-degree/1021655/106 "2025-08-04T23:25:38Z")
Well you only have so many points when you make your character, can’t put the max to everything… ---
**Author:** ![hajario](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/hajario/32/171_2.png) [@hajario](https://boards.straightdope.com/u/hajario)\ **Post date:** [August 4, 2025, 11:31pm UTC](https://boards.straightdope.com/t/17-year-old-refutes-math-conjecture-enters-phd-program-without-a-degree/1021655/107 "2025-08-04T23:31:50Z")
That never occurred to me ---
**Author:** ![wolfpup](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/wolfpup/32/10618_2.png) [@wolfpup](https://boards.straightdope.com/u/wolfpup)\ **Post date:** [August 5, 2025, 4:02am UTC](https://boards.straightdope.com/t/17-year-old-refutes-math-conjecture-enters-phd-program-without-a-degree/1021655/108 "2025-08-05T04:02:46Z")
> [@Thudlow\_Boink](#): > > 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](https://en.wikipedia.org/wiki/Research_university). **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.** Emphasis mine. Oh man, that is so, so true! My first undergraduate year at a very prestigious university, fresh out of high school, was a shocking and miserable experience, especially at an unusually young age. It soon became apparent that their prestigious reputation stemmed from their research and post-graduate programs and that most undergraduates were regarded just as revenue-generating headcount. Things improved dramatically when I switched to an honours track, from engineering to Honours Science. That was really quite enjoyable, though eventually I switched to a different university for unrelated personal reasons. But I cannot emphasize enough my strong agreement with your point. Students applying for undergraduate admission need to carefully evaluate the quality of the **undergraduate** program, not the quality of the university as a whole. A few really top-tier schools like MIT or Cal Tech will have terrific undergraduate programs, but in most cases students might consider smaller, mid-tier schools for their undergraduate degree, and focus a bit more on a school’s research reputation (in their specific field) if and when they move on to post-graduate studies. > [@Zoobi](#): > > I have a PhD, in a “hard science “. You aren’t explaining any “misconception” to me. Teaching isn’t _the_ purpose, but it should be _a_ purpose for being at a university. It seems strangely incongruous for someone with a post-graduate degree to regard a university as a sort of glorified high school, only with harder exam questions. ---
**Author:** ![Voyager](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/voyager/32/133_2.png) [@Voyager](https://boards.straightdope.com/u/Voyager)\ **Post date:** [August 5, 2025, 5:53am UTC](https://boards.straightdope.com/t/17-year-old-refutes-math-conjecture-enters-phd-program-without-a-degree/1021655/109 "2025-08-05T05:53:24Z")
> [@Zoobi](#): > > 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. Do give us some labs where they can do the same kind of research. I worked closely with people from Sandia. They published, really good stuff, but it was directed towards the goals of the place, and was not pure research. A small part of Bell Labs did it 40 years ago. Google is cutting back. A while ago someone who want to leave the IBM Watson Labs said that researchers had to get funding from business units. I’m pretty certain there is no pure research being done at Meta, and if there is some at MIcrosoft it is by top people they attracted. 45 years ago, when I started, your advice kind of made sense. Not today. BTW, though I have heard plenty of professors plotting on how to decrease their teaching of undergrads - especially in big introductory classes - I’ve never heard one say they didn’t want to teach and work with grad students. ---
**Author:** ![Fretful\_Porpentine](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/fretful_porpentine/32/2873_2.png) [@Fretful\_Porpentine](https://boards.straightdope.com/u/Fretful_Porpentine)\ **Post date:** [August 5, 2025, 12:00pm UTC](https://boards.straightdope.com/t/17-year-old-refutes-math-conjecture-enters-phd-program-without-a-degree/1021655/110 "2025-08-05T12:00:52Z")
> [@Voyager](#): > > BTW, though I have heard plenty of professors plotting on how to decrease their teaching of undergrads - especially in big introductory classes - I’ve never heard one say they didn’t want to teach and work with grad students. I have! I even know someone who outright _refused_ to teach grad students, despite considerable pressure from his department chair and the head of the graduate program. Granted, the circumstances were somewhat unusual (brand-new, predominantly-online MFA program that would have entailed a lot of course design work up front; the professor was a fiction writer who really just wanted to concentrate on his own writing, and he was becoming famous enough that he felt like he was kind of being used for his name while still being paid at the same rock-bottom rates as the rest of the younger faculty at our regional state university). Incidentally, I was trying to figure out what the humanities version of Hannah’s story might look like, and I think it would pretty much have to involve a teenager with extraordinary achievement in a creative field. Even if a seventeen-year-old discovered a lost copy of [Love’s Labour’s Won](https://en.wikipedia.org/wiki/Love%2527s_Labour%2527s_Won) and knew enough to recognize its significance (both of which could, conceivably, happen), they _still_ wouldn’t be able to write an article about it that would pass peer review without considerable assistance, nor would anybody even suggest that they should be admitted directly to a PhD program. I’m not sure if this says good or bad things about the state of scholarship in my field! ---
**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:** [August 5, 2025, 12:23pm UTC](https://boards.straightdope.com/t/17-year-old-refutes-math-conjecture-enters-phd-program-without-a-degree/1021655/111 "2025-08-05T12:23:54Z")
> [@Thudlow\_Boink](#): > > 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. Indeed. One of the schools I was looking at for undergrad was MIT (certainly a prestigious research institution). I asked the tour guide how easy it was to talk to a professor. “Oh, very easy. You just make an appointment with their secretary, and you’ll be able to see them within a couple of weeks!” I opted not to apply. > [@nearwildheaven](#): > > I can’t be the only person who has a feeling that she will have a nervous breakdown, or its equivalent, before she’s 20 years old. The most likely outcome is reversion to the mean: After her very bright start, she’ll settle down to become a perfectly competent but basically ordinary mathematician. > [@Fretful\_Porpentine](#): > > Incidentally, I was trying to figure out what the humanities version of Hannah’s story might look like, and I think it would pretty much have to involve a teenager with extraordinary achievement in a creative field. Possibly writing a critically-acclaimed novel while in high school, like S. E. Hinton? Discovering a lost work of Shakespeare isn’t really a personal accomplishment; it just means that you went to the right estate sale. ---
**Author:** ![Fretful\_Porpentine](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/fretful_porpentine/32/2873_2.png) [@Fretful\_Porpentine](https://boards.straightdope.com/u/Fretful_Porpentine)\ **Post date:** [August 5, 2025, 1:19pm UTC](https://boards.straightdope.com/t/17-year-old-refutes-math-conjecture-enters-phd-program-without-a-degree/1021655/112 "2025-08-05T13:19:18Z")
> [@Chronos](#): > > Possibly writing a critically-acclaimed novel while in high school, like S. E. Hinton? Yeah, that was the sort of “extraordinary achievement in a creative field” that I had in mind (although, TBH, I’m not sure why a teenager who had alreadly attained that sort of success would _want_ to bother getting an MFA afterward, even if they let her directly into the program). Fair point that discovering a copy of a previously-thought-to-be-lost work isn’t that much of a scholarly accomplishment! Making a discovery like [this](https://www.ox.ac.uk/news/2025-03-03-oxford-university-researcher-uncovers-hidden-copy-shakespeare-sonnet) might be a better example – it’s conceivable that a gifted teenager might get a chance to do archival research in a location where they might stumble across a seventeenth-century verse miscellany, and that they might recognize the poem as an alternate version of Sonnet 116 and recognize that the discovery was probably important (especially if they were enough of a Shakespeare geek to know how few surviving manuscript versions there are of the sonnets), but they almost certainly _wouldn’t_ have the background knowledge to think “OK, there are also Christmas carols in this manuscript, and it dates from a time and place when the act of copying out a Christmas carol was actually an act of political defiance, so maybe we should see how reading this poem through a political lens changes our understanding of the added lines.” ---
**Author:** ![peccavi](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/peccavi/32/388_2.png) [@peccavi](https://boards.straightdope.com/u/peccavi)\ **Post date:** [August 5, 2025, 1:57pm UTC](https://boards.straightdope.com/t/17-year-old-refutes-math-conjecture-enters-phd-program-without-a-degree/1021655/113 "2025-08-05T13:57:18Z")
Perhaps an analogy would be if Jodie Foster had decided to major in Drama at Yale (instead of African American Literature). At that point she’d been acting for 15 years and been nominated for an Oscar and won a BAFTA award. ---
**Author:** ![Voyager](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/voyager/32/133_2.png) [@Voyager](https://boards.straightdope.com/u/Voyager)\ **Post date:** [August 5, 2025, 3:30pm UTC](https://boards.straightdope.com/t/17-year-old-refutes-math-conjecture-enters-phd-program-without-a-degree/1021655/114 "2025-08-05T15:30:52Z")
> [@Fretful\_Porpentine](#): > > I have! I even know someone who outright _refused_ to teach grad students, despite considerable pressure from his department chair and the head of the graduate program. I was thinking in terms of PhD research students, so I was excessively narrow. I know of a famous university which has a program that pumps out MS students, for large fees I’m sure, in carload lots. Every year I’d get 40 or so mostly identical resumes from these students. Professors not wanting to teach them I can buy. So, I stand corrected. ---
**Author:** ![Voyager](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/voyager/32/133_2.png) [@Voyager](https://boards.straightdope.com/u/Voyager)\ **Post date:** [August 5, 2025, 3:45pm UTC](https://boards.straightdope.com/t/17-year-old-refutes-math-conjecture-enters-phd-program-without-a-degree/1021655/115 "2025-08-05T15:45:39Z")
> [@Chronos](#): > > Indeed. One of the schools I was looking at for undergrad was MIT (certainly a prestigious research institution). I asked the tour guide how easy it was to talk to a professor. “Oh, very easy. You just make an appointment with their secretary, and you’ll be able to see them within a couple of weeks!” I opted not to apply. How odd. When I went there I had no trouble getting an appointment to talk to Marvin Minsky and I talked to lots of other professors, not as many as I should have. Today everyone undergrad gets involved in a research project involving a professor. I had a lot more contact with professors than the undergrads in the large state school I attended for grad school. Of course it depends on the professor. Claude Shannon’s office was across the hall from my lab and I doubt I could have set up an interview with him. It’s not just MIT. My daughter had no problem getting in contact with a famous professor when she was at Chicago. ---
**Author:** ![carrps](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/carrps/32/2957_2.png) [@carrps](https://boards.straightdope.com/u/carrps)\ **Post date:** [August 5, 2025, 5:08pm UTC](https://boards.straightdope.com/t/17-year-old-refutes-math-conjecture-enters-phd-program-without-a-degree/1021655/116 "2025-08-05T17:08:25Z")
> [@Topologist](#): > > 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). LOL. This vaguely reminds me of my high school graduation. I attended UCLA during my senior year of high school , and I’d completed all the classes required for a high school diploma before that year, so I didn’t really need to go. But I wanted to, to be with my friends and for the socialization, and I nearly flunked PE. I _hated_ all the gym teachers, and I was bored and bratty. But she chickened out and gave me a D. I was so proud of my only D! ---
**Author:** ![hajario](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/hajario/32/171_2.png) [@hajario](https://boards.straightdope.com/u/hajario)\ **Post date:** [August 5, 2025, 5:21pm UTC](https://boards.straightdope.com/t/17-year-old-refutes-math-conjecture-enters-phd-program-without-a-degree/1021655/117 "2025-08-05T17:21:43Z")
One of my childhood friends is a surgeon at Cedars Sinai and literally one of the top in his field in the world. He got into Northwestern Medical School out of High School which isn’t particularly crazy because they have a prestigious six year medical program where they do an accelerated two year undergrad and then start med school. After the second year of med school they awarded the six year people a bachelor’s in some kind of general science. What’s interesting is that he never technically graduated High School which is irrelevant but we still keep it a secret. He spent a lot of his senior year flying around the country for interviews with various accelerated programs like that and the Health teacher at our terrible urban High School was a prick and wanted to fail this straight A, perfect SAT kid for poor attendance. He was allowed to take the requirement through some sort of correspondence school. He never bothered to finish it and the High School never checked. ---
**Author:** ![Maserschmidt](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/maserschmidt/32/18829_2.png) [@Maserschmidt](https://boards.straightdope.com/u/Maserschmidt)\ **Post date:** [August 5, 2025, 6:30pm UTC](https://boards.straightdope.com/t/17-year-old-refutes-math-conjecture-enters-phd-program-without-a-degree/1021655/118 "2025-08-05T18:30:09Z")
> [@wolfpup](#): > > My first undergraduate year at a very prestigious university, fresh out of high school, was a shocking and miserable experience, especially at an unusually young age. It soon became apparent that their prestigious reputation stemmed from their research and post-graduate programs and that most undergraduates were regarded just as revenue-generating headcount. I think mine was the same? At the graduate level we had prize-winning teachers/mentors (Steven Weinberg, Ilya Prigogine among others), great facilities (two optics labs, a tokomak reactor, lots of government grants, I forget what else), but undergraduate teachers who were not really teachers, for the most part…some of them were outright awful. That said, unlike a lot of folks posting here, I wasn’t really a good enough student to have taken advantage of a great undergraduate program. ---
**Author:** ![Pasta](https://avatars.discourse-cdn.com/v4/letter/p/ecccb3/32.png) [@Pasta](https://boards.straightdope.com/u/Pasta)\ **Post date:** [August 5, 2025, 6:51pm UTC](https://boards.straightdope.com/t/17-year-old-refutes-math-conjecture-enters-phd-program-without-a-degree/1021655/119 "2025-08-05T18:51:46Z")
> [@Thudlow\_Boink](#): > > 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. Both “prestigious university” and “best education” have such wildly open definitions that this is certainly true in general. But for certain definitions of those phrases, there will be positive correlation. As @wolfpup notes, MIT and Caltech are examples (but far from the only ones) for one set of interpretations of the phrases. > [@Chronos](#): > > Indeed. One of the schools I was looking at for undergrad was MIT (certainly a prestigious research institution). I asked the tour guide how easy it was to talk to a professor. “Oh, very easy. You just make an appointment with their secretary, and you’ll be able to see them within a couple of weeks!” I opted not to apply. This is a very “YMMV” situation, and choosing not to apply to MIT because of a passing comment by a tour guide seems like it can’t be the whole story. At any school, some profs will have very busy periods and be harder to pin down, while others will be able to engage quickly. Also, triaging meetings is a thing in any professional sector, and one student might not get a profs time for a few weeks because the request simply isn’t urgent, versus something time-sensitive that would, say, help keep a student from getting behind on work or the like. Professors also don’t usually have a secretary gatekeeping their schedule. A small fraction will, particularly those with notable administrative roles, but the general system is that students just email professors directly. If you have a class with a certain professor, you have opportunities each class period or during regular office hours (if offered) to directly talk to them. As @Voyager notes upthread, undergraduate research is a key piece of the university experience at A-list STEM schools, and a student can have _lots_ of professorial interaction on the research side if they seek it out. Having crazy low student-faculty ratios to go with the high research rankings helps, of course. ---
**Author:** ![Saint\_Cad](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/saint_cad/32/18907_2.png) [@Saint\_Cad](https://boards.straightdope.com/u/Saint_Cad)\ **Post date:** [August 5, 2025, 6:56pm UTC](https://boards.straightdope.com/t/17-year-old-refutes-math-conjecture-enters-phd-program-without-a-degree/1021655/120 "2025-08-05T18:56:35Z")
> [@Dr.Strangelove](#): > > But there _is_ evidence that people really like to believe in some kind of “conservation of talent” principle, such that if a person is skilled in one area they must be deficient in another. If you watch Sabine Hossenfelder’s videos, there is also “expert in one thing = expert in everything” [Previous page](https://boards.straightdope.com/t/17-year-old-refutes-math-conjecture-enters-phd-program-without-a-degree/1021655.md?page=5) [Next page](https://boards.straightdope.com/t/17-year-old-refutes-math-conjecture-enters-phd-program-without-a-degree/1021655.md?page=7)