<p>I don't know about small study groups, but I know that S has problem sessions in the evening in both math and physics with graduate students.</p>
<p>CountingDown - Princeton very much has a LAC feel. Not only is the student body relatively small (4,600), but each underclassman is assigned to a residential college of about 250 students who live and eat together. Cookieson agrees that DS should visit him.</p>
<p>Cookiemom,
DS agrees! Does anyone hold class on the Friday before Easter? If not, we can always get DS up there another time -- he would like to visit a class or two.</p>
<p>I'm pretty sure they are holding classes that Friday. I'll check with him and let you know. I PM'd you his email address so DS can contact him himself.</p>
<p>Getting back to the main subject...can anybody tell me more about the collaborative atmosphere, or lack thereof, at other schools generally viewed as "competitive"?</p>
<p>arkleseizure -- S's at Columbia which is full of competitive people, yet I don't get any sense they compete against each other. I'd say it's more of an individualistic atmosphere than a competitive atmosphere. He's had no trouble finding informal study groups in math and physics classes when he's sought them out, has shared notes, helped friends with material and been helped by them, gotten lots of info from fellow-students on internships, studied with friends for exams, etc. The problem is that they tend to take so many classes and also be involved with so many activities that it's hard to find time that informal study groups can meet regularly, which is why I'd describe it as more individual than collaborative. As for the departments, they provide help rooms staffed by grad students, as I suspect most universities do. I think it's a rare math or physics prof who doesn't want students to learn. (My favorite story was the physics prof who apologized to the class after they did poorly on the midterm, saying it was his fault and that he'd only give himself a "C" for the way he'd been teaching the course up to that point!)</p>
<p>Chipper -- Relevant to the isolation vs collaboration question, my S had a conversation with a math PhD grad student recently about a math summer research program vs other summer possibilities. The grad student described math research as working on a problem alone, under supervision of a prof, and said that is exactly what he likes about pure math. This confirms my general impression that on an isolation to collaboration scale, pure math would be the most isolated, applied math less so, and physics the most collaborative. This is a generalization about the professions, though, not the undergrad majors.</p>
<p>Sac:</p>
<p>ummmm... it may be true of the professions, I have no idea. But for undergraduate experience, that's not been the case at all. My S loved his three summers at PROMYS, he had a gang of friends who started out as a study group and became close buddies. They groaned and moaned together over problem sets, played board games in the middle of the night, put on skits, etc... I know that people who attended MathCamp had the same experience.
It may be different in grad school, but he is currently in 2 study groups, as I mentioned earlier. He has been, since arriving on campus.</p>
<p>I think how solo a mathematician does research work depends in part, although not exclusively, on whether the mathematician had early experiences that involved group work on math research. It sounds like PROMYS and MathCamp both can get a student used to group work in math. I'm not as sure how characteristic that is of other programs. I know one Ross alumnus who mostly works alone in his current career--which is all applied math. He communicates with colleagues mostly by email, although he does do a bit of business travel.</p>
<p>It is also a function of the personality/temperament of the students/professors/researchers.</p>
<p>Most professors at colleges are introverts. This is especially true in the "pure" sciences - with math the "most pure" - it is not surprising that they are more introverted. </p>
<p>And, what's funny is that an introverted student will believe a program quite social while an extraverted one finds the same program isolating.</p>
<p>Are those involved in "theoretical physics" more or less collaborative. The only extravert in physics of which I am aware is Feynman.</p>
<p>There is a line in James Gleick's biography of Feynman quoting someone who knew him as saying that Feynman depressed looked like anyone else elated.</p>
<p>Good line! </p>
<p>So, could you pick up any "feeling" about what life among physicists is like from that book?</p>
<p>I'm speaking as someone who quit a PhD program due to the isolation. Is there a way to avoid such?</p>
<p>S was an experimental physicist, working in a group. The group had lunch together almost every day. Introverts? Nah...</p>
<p>As for S's study groups, there some real extroverts there.</p>
<p>Interesting discussion. I was talking about the profession and not the undergrad experience. The PhD student who characterized math research as independent is not an introvert and collaborates extensively on musical projects, yet apparently prefers to work on his own in mathematical ones. So I'm not even sure it's a matter of personality.</p>
<p>Perhaps it depends on the nature of the problem people work on? I once spent some time with a mathematician who said what he loved about it was that he could do everything just with a pencil and a piece of paper, and that his favorite way to work was to walk in the woods and think. Then, he delivered his work knowing perhaps six people in the world would really understand it, and that even the majority of mathematicians in the audience when he spoke at conferences would not get every aspect of it. Yet, I wouldn't call him an introvert either. </p>
<p>As for Feynman, if I remember his autobiography, one of his favorite ways to pass the time was with Las Vegas showgirls. Not an introvert.</p>
<p>The whole introvert-extrovert distinction means different things at different times. The conventional distinction is something like withdrawn vs. gregarious. But in some psychological contexts I think it means inner-directed vs. directed by social cues. In the second sense, I am prepared to believe that 100% of mathmaticians are introverted (and Feynman hanging out with showgirls is not evidence to the contrary). It may be relatively unusual for inner-directed people to also be gregarious and social, but that's not impossible at all, and certainly some such people are (and even win Nobel Prizes).</p>
<p>My experiences with math have been extraordinarily social, but I went to HCSSiM, which is....just special.</p>
<p>My dad gave up chemistry as a career because he wanted to spend more time with people than with test tubes, and became an industrial engineer. But I think both my parents are "naturally" introverted enough that they got their social satisfaction at work, and in my childhood we didn't have lots of social interaction with other families, mostly spending time with one another at home. My son, by contrast, spends LOTS of time with neighbors and classmates, and yet likes his math, so he'll doubtless look for work that involves regular daily interaction with other people.</p>
<p>I used introverted and extraverted as implied by Jungian psychology - not as utilized in everyday jargon. As utilized by Jung, extraverts are energized by involvment with people and objects in the environment. Introverts are energized by inner reflection. </p>
<p>To many laypeople, extraverted means sociable and/or gregarious where introverted implies shy or withdrawn. </p>
<p>In actuality, introverts can be internally focused but extremely sociable and extraverts can be externally directed, yet extremely shy. However, introverts absolutely have to separate from the world to reflect and extraverts must interact with the world. </p>
<p>Tokenadult, it is probably more likely that your dad was an extravert - who fulfilled his needs in the workplace. Rarely would an introvert leave chemistry because he preferred to interact with people versus test tubes. Instead, he would more likely join a bowling league, church group, etc. to provide the desired social context. </p>
<p>Many extraverted scientists, mathematicians, engineers, computer analysts as well as economists, lawyers, accountants, and analysts leave their chosen field due to a need for more interactive/collaborative work.</p>
<p>Well, Jungian psychology is pretty roundly criticized. </p>
<p><a href="http://www-personal.usyd.edu.au/%7Eapert/jung.html%5B/url%5D">http://www-personal.usyd.edu.au/~apert/jung.html</a> </p>
<p><a href="http://skepdic.com/jung.html%5B/url%5D">http://skepdic.com/jung.html</a> </p>
<p>More generally, I take people's self-reports that they either like or don't like to be with lots of other people at face value, but I still would like to see more research about how fixed such tendencies are in most human beings. My time living in Taiwan taught me that there are whole cultures of people who think these characteristics can be malleable (and, yes, Chinese as spoken in Taiwan has equivalents to Jung's terms, used in everyday conversation), and I think I have shown some malleability in that regard. </p>
<p>A psychologist whose writings I recommend for a sound research base is Carol Dweck, author of the very readable popular book Mindset[/url</a>]. Another is K. Anders Ericsson, a co-editor of [url=<a href="http://www.amazon.com/Cambridge-Handbook-Expertise-Expert-Performance/dp/0521600812/%5DThe">http://www.amazon.com/Cambridge-Handbook-Expertise-Expert-Performance/dp/0521600812/]The</a> Cambridge Handbook of Expertise and Expert Performance. </p>
<p>I agree that it is difficult for a job-seeker to go against the grain of the predominant characteristics found in people who seek a particular career. I hope my children will have, because I work at developing a broad social network of adults who know my family, more opportunities than I had to meet adults of varied occupations as they grow up, the better to know what occupations might be most personally fitting.</p>
<p>Well, tokenadult, your choice of references and beliefs on this issue pretty quickly define your personality type. <grin> </grin></p>
<p>But, seriously, one's opinion on this topic is directly related to one's personality type. </p>
<p>However, I don't want to hijack this thread into a debate about personality type theories. There is plenty of evidence to support such and the use of MRI and brain imaging is adding to the considerable support. </p>
<p>I'm not disagreeing that one can practice "mind over matter". And, I am well aware of the studies involving various ethnic groups and cultures. However, I have found that if one lives one's life in accordance with their abilities, passions, and interests, one's life is much more enjoyable.</p>
<p>arkleseizure, thanks for posting about your wonderful experience at HCSSiM! My DS went to HCSSiM and it was a wonderful combination of rigorous mathematics and a social life for him! He'd also attended PROMYS which he enjoyed but there was something very special about HCSSiM for him!<br>
I think its also interesting to note that many math competitions like ARML are very collaborative. Teams work together to solve problems and having proctored the competitions as well as having been a team "mom" and attended lots of practices it truly amazed me (a non-mathematician) the amount of collaboration involved in mathematics.</p>