Princeton or Harvard?

Colleges and Universities A-Z Princeton University
101

<p>“I was in the Putnam top 200 in the country and I don’t stand a chance against any of the heavyweight math geniuses at Princeton who have won the Fields medals.”</p>

<p>LOL, of course not! If you are in the top 200, it means that you got something like 2 problems out of 12 correctly (the easiest two by the way). Remember, the median score on the Putnam is a zero. The vast majority of the several thousand test takers, presumably the best math and physics students in North America, fail to got even a single partial credit point on a single problem. There is a HUGE gap between the top 200 and the top 5. Often the highest scorer has gotten close to a perfect score on the test, getting all 12 problems correctly. This is one reason why it’s important to look at the highest scorers, ie. Putnam Fellows, rather than the top 100. While MIT may get many high scorers, because it starts out with a much larger pool of math/physics students, Harvard has almost always gotten the lion’s share of the very highest scorers. And that’s why Harvard has won so frequently. </p>

<p>Based on the naive comment you just made, comparing yourself to the Field medalists, I am rather skeptical that you actually scored in the top 200, but if it’s really true, congratulations. Not every one can do what you did. But try to put things in perspective.</p>

102

<p>“Though I hope I’m wrong, given the general tenor of this poster’s remarks, I don’t think this was intended to be a joke!”</p>

<p>That put-down was a response to razorazor’s snide comment about Harvard and intellectual dishonesty.</p>

103

<p>Ske, I’m afraid you are quite wrong about the Fields Medal and Wolf Prize count. Here, let’s count them again. The Fields Medal credit should be given to the winner who 1) has earned a degree from the University and 2) who was a Professor at the University at the time the medal was awarded. Fair enough? I think so, since, once again, these are LIFETIME achievement awards. And I used that same criteria for all the other awards. If you want to count professors who were at the university before the award as given (but moved on to another university during which he won the award), we can count those too, but that only gives more advantage to Princeton anyway. So I didn’t count that in my criteria. </p>

<p>Here’s the comprehensive list:</p>

<p>A) Fields Medals </p>

<p>PRINCETON UNIVERSITY (9)</p>

<p>Kunihiko Kodaira
John Milnor
Charles Fefferman
William Thurston
Gerd Faltings
Michael Freedman
Edward Witten
Andrei Okounov
Terence Tao</p>

<p>HARVARD UNIVERSITY (6)</p>

<p>Lars Ahlfors
Heisuke Hironaka
David Mumford
Daniel Quillen
Curtis McCullen
Vladimir Voevodsky</p>

<p>[Fields</a> Medal Winners](<a href=“http://www.xmission.com/~mnielson/math/FieldsMedalWinners.html]Fields”>Fields Medal Winners)</p>

<p>B) Wolf Prize</p>

<p>PRINCETON UNIVERSITY (8)</p>

<p>John Milnor
Elias Stein
Andrew Wiles
Yakov Sinai
Robert Langlands
Phillip Griffiths
Hillel Furstenberg
John Tate</p>

<p>HARVARD UNIVERSITY (5)</p>

<p>Lars Ahlfors
Raoul Bott
Oscar Zariski
David Mumford
Hassler Whitney</p>

<p>[Wolf</a> Prize in Mathematics - Wikipedia, the free encyclopedia](<a href=“http://en.wikipedia.org/wiki/Wolf_Prize_in_Mathematics]Wolf”>Wolf Prize in Mathematics - Wikipedia)</p>

<p>C) National Academy of Science Winners for Mathematics</p>

<p>PRINCETON UNIVERSITY (31)</p>

<p>William Browder
Alice Chang
Ingrid Daubechies
Charles Fefferman
Nicholas Katz
Sergiu Klainerman
Joseph Kohn
Janos Kollar
Elliot Lieb
John Mather
John Nash
Edward Nelson
Yakov Sinai
Elias Stein
Andrew Wiles
Michael Freedman
Hillel Furstenberg
Dennis Sullivan
Yum-Tong Siu
Peter Sarnak
Barry Mazur
George Lusztig
Arthur Jaffe
Melvin Hochster
Richard Hamilton
David Gale
William Fulton
Jeff Cheeger
Eugenio Calabi
Felix Browder
Richard Askey</p>

<p>HARVARD UNIVERSITY (20)</p>

<p>Andrew Gleason
Benedict Gross
Shing-Tung Yau
Clifford Taubes
Daniel Stroock
Shlomo Sternberg
Richard Stanley
Yum-Tong Siu
Kenneth Ribet
Daniel Quillen
George Mostow
Barry Mazur
Richard Askey
Robert MacPherson
Arthur Jaffe
Roger Howe
Jeff Cheeger
Persi Diaconis
Melvin Hocster
Victor Guillemin</p>

<p>Some of these people are on both lists, since they were a student at one of the universities and a professor at the other at the time the award was given. And no, I did not count the Institute of Advanced study as part of Princeton University. Though, just to remark, much of the faculty in the IAS are from Princeton University anyway, including actually being first established in the Princeton mathematics department before it moved 3 miles away to its current location.</p>

<p>[Institute</a> for Advanced Study - Wikipedia, the free encyclopedia](<a href=“http://en.wikipedia.org/wiki/Institute_for_Advanced_Study]Institute”>Institute for Advanced Study - Wikipedia)</p>

<p>Also, 3 of the 6 Millenium Problems in mathematics (the hardest, unsolved problems) are presented by Princeton mathematicians.</p>

<p>[Millennium</a> Prize Problems - Wikipedia, the free encyclopedia](<a href=“http://en.wikipedia.org/wiki/Millenium_problems]Millennium”>Millennium Prize Problems - Wikipedia)</p>

<p>Also take a look at the Clay Mathematics Research Institute, another premier research institution in mathematics. You will notice that most of the research fellows are Princeton mathematicians.</p>

<p>[Clay</a> Mathematics Institute](<a href=“http://www.claymath.org/fas/research_fellows/]Clay”>http://www.claymath.org/fas/research_fellows/)</p>

<p>So it is pretty clear to me that the Princeton mathematics department dominates any other university in the world. The fact that Fields Medal is only given every four years, whereas the Nobel Prize is given every year, further highlights the incredible significance of this medal. Enough said.</p>

104

<p>Yeah, if you’re too arrogant to get accepted, you probably wouldn’t know it. Go for the more essays option if you can. Hard work always pays off.</p>

105

<p>So yes, while Harvard has gotten the lion’s share of the top undergraduate college math majors in this country, Princeton has gotten the lion’s share of the brightest, most talented professional mathematicians on this planet. Not to mention Princeton still performs remarkably well on the Putnam at the undergraduate level. And not to mention that the Princeton mathematics department doesn’t even train us for the Putnam, while many other universities including Harvard undergo rigorous training. And it’s your own competition, it’d be silly if you guys didn’t do well =)</p>

<p>NAS Academy Mathematics winners (forgot to provide link)</p>

<p><a href=“http://en.wikipedia.org/wiki/List_of_members_of_the_National_Academy_of_Sciences_(Mathematics[/url])”>http://en.wikipedia.org/wiki/List_of_members_of_the_National_Academy_of_Sciences_(Mathematics)&lt;/a&gt;&lt;/p&gt;

106

<p>I don’t get what the heavy debate is about. Princeton’s math department is the best in the country <– fact. People who think otherwise are simply misinformed.</p>

107

<p>“Ske, I’m afraid you are quite wrong about the Fields Medal and Wolf Prize count.”</p>

<p>The official numbers, which are the numbers I provided, are based on the home institution at the time of the award. If you want to create another counting system to your liking, you can do that so long as you state exactly what you are counting, but contrary to what you claim, it doesn’t make the official counts “wrong” and your count “correct”. If you are a mathematician, you need to be a little more careful about how you define things and label them “true” or “false”.</p>

<p>You must be pretty anal retentive to check the alma maters of each of these people. Assuming that you didn’t make any mistakes or omissions or misrepresentations, your new counting system shows that Princeton “has” 50% more Field Medalists than Harvard (9 to 6), which is exactly the same ratio based on the official counting system (6 to 4). So what’s new here that gets you so excited?</p>

<p>Please review my posts above and observe that I was not arguing that Harvard has a better math department than Princeton. My point was that Princeton does not “literally obliterate all other competition in garnering these Nobel Prizes of math.” , because 9 winners vs. 6 winners, frankly, is not a huge difference. (Never mind that the number of winners of particular prizes is not necessarily proportional to the quality of the department - For example, does the fact that Princeton has never won the Abel Prize mean that the Princeton Math Department sucks?)</p>

<p>On the other hand, I think it’s fair to say that winning the Putnam Competition 27 times vs. just once is a pretty big difference.</p>

<p>So let’s face it, you exaggerated quite a bit here. I would say you were a little frustrated with the Putnam results and trying to compensate.</p>

108

<p>“And not to mention that the Princeton mathematics department doesn’t even train us for the Putnam, while many other universities including Harvard undergo rigorous training. And it’s your own competition, it’d be silly if you guys didn’t do well =)”</p>

<p>And I am further disappointed that you have to resort to lying. Harvard does not provide coaching for the Putnam.</p>

<p>“In keeping with this attitude, most students do not study for the Putnam. Though some universities give course credit for Putnam preparation, Elkies says, “As a matter of policy we don’t coach people for it.” Those who did study for it practiced with old Putnam problems, and you’ll never find “Math 14: Putnam Prep” in the course catalog.”</p>

<p>[The</a> Harvard Crimson :: Magazine :: Add It Up](<a href=“http://www.thecrimson.com/article.aspx?ref=347763]The”>http://www.thecrimson.com/article.aspx?ref=347763)</p>

<p>The MIT team, on the other hand, does receive coaching by faculty:</p>

<p>[MIT</a> Mathematics | Putnam Competition](<a href=“http://www-math.mit.edu/academics/undergrad/general/putnam.html]MIT”>http://www-math.mit.edu/academics/undergrad/general/putnam.html)</p>

109

<p>And exactly what do you mean by:</p>

<p>“And it’s your own competition, it’d be silly if you guys didn’t do well =)”</p>

<p>Are you saying that Harvard professors write the exams and give the answers to the students? That is utter baloney and you know it. The exam questions are made up by mathematicians from all over North America. You should be ashamed of yourself.</p>

110

<p>

</p>

<p>Yep, its very true, although I’d edit your statement to say “any form of arrogant tone.” I can tell the current administration is doing everything to avoid the old Princeton stereotype, including screening essays for any touch of arrogance.</p>

111

<p>“The official numbers, which are the numbers I provided, are based on the home institution at the time of the award. If you want to create another counting system to your liking, you can do that so long as you state exactly what you are counting, but contrary to what you claim, it doesn’t make the official counts “wrong” and your count “correct”. If you are a mathematician, you need to be a little more careful about how you define things and label them “true” or “false”.”</p>

<p>Uhhh…OK? I simply meant to point out that more Princeton graduates have won the Fields medal than the count you gave by taking the alma mater into consideration, which does reflect the quality of the department…I mean, they graduated from there, for christ sakes…I think you’re the one being highly anal here. Your play on semantics still doesn’t change any of the facts I gave. And as to the difference between your 6-4 and 9-6 ratio, 3 Fields medals is greater than 2, smart guy. Are you saying a school that has won 2000 Fields medals to another which has won 1000 Fields medals is the same as one who has won 2 to another which has won 1?</p>

<p>And evidently, I listed out the numbers for the Wolf Prize and National Academy Prize for mathematics you seem to ignore. You can define “obliteration” as you wish, but for a medal such as the Fields given out every 4 years, nine to six is a pretty big deal to me. It’s as if it’s 36 to 24 (had it been awarded every year). Or the Wolf Prize count of 8-5. Or the NAS medal count of 31-20. Obliteration baby.</p>

<p>And lastly, I don’t even know why you’re arguing, coming from someone whom I assume has never even done any competition math? Or have you? I’m too lazy to even search through your profile because you seem like the type who would nitpick every detail to get your way. Spend time studying some more math before you even have the authority to comment on such things as the Putnam, a competition I doubt you can even score a point on.</p>

<p>And like I said, do you realize how insanely difficult it is to even garner one of these awards? The Putnam is an undergraduate math competition that only tests up to MV and Linear Algebra. The Fields, Wolf, and NAS Medals are LIFETIME achievement awards. So you can win the Putnam as many as you like but it makes no difference to me, if I had three extra hours of time I’m quite sure I could get into the Top 50 in the Putnam. Of course, you wouldn’t know that in math competitions, once you’re at a certain level, comes down to repetition, speed, and recognizing the same type of problem over and over. Laypersons like you might think a USAMO qualifier/ Putnam winner is a genius, but having done math competitions all my life, I know otherwise. Peace out, and go study your math before you comment on things you have no idea about.</p>

112

<p>Idk…I am a HS senior who is a premed hopeful. I would pick Princeton (or Stanford for that matter) over Harvard, but I would b thrilled to be accepted into any of these OUTSTANDING schools. I mean when you get into that HYPSM range, academics is so close that it should not b a deciding factor. At that point, it comes down to which school you feel more at home at and that kind of thing. So, this thread is kind of pointless because the answer is different for everyone.</p>

113

<p>LOL, and I just had the urge to look through all your previous posts…Wow, get a life man. All you seem to do is bash other schools on Princeton v Harvard, Duke vs Harvard, Stanford v. Harvard threads…OK, this is discussion is over. My facts stay and Princeton mathematics department destroys Harvard’s, as ANYONE would clearly confirm, based on the facts I’ve given. Peace.</p>

114

<p>“Are you saying a school that has won 2000 Fields medals to another which has won 1000 Fields medals is the same as one who has won 2 to another which has won 1?”</p>

<p>The only difference is the increase in certainty or statistical significance. With just a handful of awards, it’s hard to know if the ratio of 2 to 1 is really what it is or merely due to random fluctuation. With a 2000 to 1000 ratio, you can be very sure that school X has roughly twice as many stars as school Y. </p>

<p>In case of the Field Medals, you are still talking about single digit numbers so I am afraid your certainty is still not great. For practical purposes, there is really no difference between 6 vs. 4 (or 9 vs. 6 for that matter). What do you make of the 0 out of 9 awards for Princeton for the Abel Prize, which you say is a Nobel Prize for mathematics? Is that significant? For someone who has such high opinion of one’s own mathematical talents , you have pretty poor quantitative reasoning skills.</p>

115

<p>“And lastly, I don’t even know why you’re arguing, coming from someone whom I assume has never even done any competition math? Or have you? I’m too lazy to even search through your profile because you seem like the type who would nitpick every detail to get your way. Spend time studying some more math before you even have the authority to comment on such things as the Putnam, a competition I doubt you can even score a point on.”</p>

<p>Careless thinking, exaggerations, outright lies, and now condescension. I have done my share of competitions and have done significantly better than you. If I were a “layperson”, would I really be so familiar with the scoring system of the Putnam and so forth?</p>

116

<p>"And like I said, do you realize how insanely difficult it is to even garner one of these awards? " </p>

<p>And you were the one comparing yourself just a moment ago to the Field Medalists based on your top 200 performance on the Putnam? </p>

<p>“if I had three extra hours of time I’m quite sure I could get into the Top 50 in the Putnam.”</p>

<p>Sure, you might get 3 out of 12 problems correct instead of 1 or 2 out of 12 problems. But don’t you realize that if other people also had 3 extra hours, they might have also solved an additional problem or two? Idiot.</p>

117

<p>UH, Princeton won 0 Abel Prizes. And so did Harvard, soo…??? As for math competitions, would you be so kind to PM me your name so I can look you up on the USAMO lists?</p>

118

<p>Again, you don’t get the point. Your claim is that the number of prizes reflects quality, even when these numbers are in single digits (which is false and I have been trying to tell you). Since there are 9 other schools that have produced Abel Prize winners, by your reasoning, they must be better than Princeton, right? Whether or not Harvard won is irrelevant. Duhhh…</p>

<p>I prefer not to disclose my identity but if you wish, you are more than welcome to publicize your name and your award-winning history here. I will be happy to comment on them extensively.</p>

119

<p>And before you come up with any of your dumbass arguments, would you be so kind to solve this very simple problem?</p>

<p>The sequence X-1, X-2, X-3,…is defined by X-1=2 and X-(k+1) = (X-K)^2 - X-K + 1 for all K>= 1. Find SUM(k=1, infinity)[1/X-k].</p>

<hr>

<p>X-1, X-2, X-3 represents “X-sub-1,” “X-sub-2,” “X-sub-3”
X-1 = 2 represents “X-sub-1 equals 2”
X-(k+1) represents (X-sub- K+1)
X-K represents “X-sub-K”
SUM(k=1, infinity) represents the summation of k=1 to infinity</p>

<h2>1/X-k represents “1 over X-sub-k”</h2>

<p>Ok, if you’re so good at math, this easy problem should only take about 10 minutes, since you are SO much better than me. Good luck.</p>

120

<p>And if you can’t solve this easy ass sub-USAMO level, AIME-level problem, which I highly doubt coming from a ■■■■■ like you, then you’re just one insecure, idiotic guy. And don’t give me any ******** about “I don’t have to prove my worth to you by solving this problem,” or any other of your idiotic attempts to avoid doing it. If you’re really as good as you say you are, this should only take 10 minutes max. Later.</p>