<p>marite, thank you for the link to Mankiw's blog and his comments on why economics programs emphasize math. My H uses Mankiw's text for his intro. economics courses; believe me, plenty of students have not figured out why they need math to study economics.</p>
<p>I loved point #3. I saw this principle in action with my daughter. No question about it.</p>
<p>As for point #4, my husband takes this position, but it has always annoyed me for its narrow definition of intelligence. I guess economists think alike.</p>
<p>Re #4 Math courses are "a big long IQ test" and "take math till it hurts". I certainly never thought of it that way. Of course while I loved math, I quit taking long before it was painful. My husband on the other hand took math up the ladder until the course he took pass/fail and felt lucky to pass. He might well agree with the blogger. I do think math is only one way to be intelligent. I'll add myself to the chorus of those who find the mathematicians they know, to be among the most articulate people they know. Not at all like their stereotypes.</p>
<p>I know of only one student who got a likely letter--from Yale. He was definitely a star and an incredibly desirable admit. He received his likely letter in mid-October, before the deadline for SCEA applications! No one in his class begrudged him the early notification. Instead they had a celebration in class.</p>
<p>Very interesting thread for me, if only to show that mathematicians, especially girls, are something that's sought. My junior D's insanely gifted in math. I, on the other hand, am gifted in English (especially fiction writing). She and I were discussing what it's like to work within the other's "strength" discipline, and she explained to me that when she's doing a math problem, she usually gets it before she's finished reading the problem, and it's as though it streams out of her like a movie scene. She can just see it. I totally got that, as I am the same way when I write. I visualize the movie in my head and am able to put it on paper. However, with all her joy with math, she's not been considering a math major as an option because she doesn't know what she might do with one. As she's always telling me, what's a mathematician? And, me ... shoot, I'm no help. So, we've been looking at other careeer options, i.e. medicine/pharmacy, as she's also extremely strong in chemistry and physics. She swears she doesn't want engineering as her father's an engineer, and she can't see herself doing what he does (of course, not acknowledging there are other options in engineering). For someone so intelligent, sometimes she's a real bubble-head, too. I may have her read this thread just to realize that EVEN Harvard courts gifted math students. Oh .. she was also a competitive dancer for 11 years and dabbled in art. Her left brain/right brain both like to come out and play.</p>
<p>I, too, wonder what S will do with his pure math degree!
For someone not so focused on pure math, there are many interesting careers in biostatistics, bioinformatics, physics, chemistry. I met one math graduate student who was writing her dissertation on something called dynamical systems (don't ask!) and she explained to me that it's very useful in locating movements in the brain. One MIT prof of cryptography gave a lecture once on zero knowledge proof, explaining its usefulness to encoding data such as credit card information without revealing the information itself. </p>
<p>Your D sounds like a great student all around.</p>
<p>Also, I don't think Harvard's interest is limited to math students and musicians. But those happen to be fields (along with athletics) in which it is actually possible to look at an 18-year-old and say, "That is a prodigy. That person has world-class talent." The same may be true with some writers and visual artists, too, and I suspect that Harvard would have the same response to them. It's a little bit harder with fields like economics or history, where teenagers don't do as much of the real work of the profession. A teenage violinist or mathematician or writer can be doing the same thing that a 30-year-old does, and can produce work that bears direct comparison. It would be very rare for a teenage historian to be in that position.</p>
<p>NB: This was a response to a post mammall made pages and pages ago. I didn't realize there were intervening posts.</p>
<p>As most of you already know, academic and athletic likely letters are not new. They were recruiting devices even with early admissions programs. What will be interesting to see is whether they increase the number of likely letters to court the stars.</p>
<p>I don’t know much about Harvard, but I think JHS is correct in his assessment that likely letters are not just for athletes and math prodigies. It’s been a few years now, but I recall the Harvard admission rep discussing “knowns” during the Q & A session at one of those on the road admission events. It was in regards to a parent question about likely letters that he had heard about. The term “world class” seemed to be defining if I recall. I have no idea what would make a student a “known,” but I imagine competitions and world class talent would be a factor. </p>
<p>As to the timing, the trend as posted on CC for likely letters for regular action tend to come in late Dec & Jan. I assume it’s after an application is read. I could be wrong. Stanford’s aren’t even “likely letters.” They have “clear admit letters” complete with a financial aid read around January. Followed up with Professors calling to discuss departments and research opportunities. Dartmouth has several batches in later winter and early spring. Then there are the “early writes” for some of the LACs. Lot’s of early courting going on. Some include travel money. Some are for athletes, some are for academics, some are for diversity.</p>
<p>While it's not new, I do think it could be tough for students currently applying to see a significant up tick in the number of likely letters. It seems to me it would defeat the intention of doing away with early admissions and create needless anxiety.</p>
<p>
[quote]
My children enjoy being around others who have talents that are varied. It makes life interesting and exciting.
[/quote]
</p>
<p>This is precisely what my son values about his current high school, and is a big part of what he is looking for in a college. (For the record, he gets to decide where to apply, and I'm not at all sure that he will apply to Harvard. But Harvard is one of several colleges that have that desirable quality, as best my son can tell from local young people he knows who have recently started studying there.) </p>
<p>In general, I don't see any reason to disparage the accomplishments of young people. Surely there are dozens of areas of accomplishment among young people that my four children have never pursued at all--there are only so many hours in the day. Life is a lot more enjoyable when a person observing the accomplishments of another says, "Congratulations" and savors the achievements along with the achiever.</p>
<p>Here are a couple of HS underclassmen who would be considered as "known" and have NY pro credentials under their belts. They both fit somewhere in or about the "prodigy" category. Gotta figure though that kids like this are filling the top of the conservatory ranks.</p>
<p>In going after kids like that, exploding offers wouldn't really be an issue - Conservatory offers are relatively late in coming - but convincing them to apply in the first place probably would be.</p>
<p>Why do you think math-liking students are ipso facto inarticulate or incapable of straddling disciplines?</p>
<p>As for impact on society, can you say Einstein? Newton?"</p>
<p>I don't think Einstein or Newton would classify themselves as mathematicians. Einstein would classify himself as a tamed-metaphysicist and pseudo-pantheist seeking unity in the universe. Newton would describe himself as a truth-seeker, though I am unfamiliar with his personal beliefs.</p>
<p>In any case, Einstein's and Newton's work primarily NOT in mathematics, but they did heavily use mathematics as the primary tool. Along the way, each made mathematical contributions to pure and applied mathematics but since it was in pursuit of other subject matter it is hard to called them mathematicians.</p>
<p>As far as I know, Einstein's mathematical contributions to the world (besides equations, which are physical contributions!) were application of the Lagrangian to relativist systems and the development of Einstein tensor notation, which is just a symmantic modification of existing mathematics. Einstein was brilliant in regards to many things (especially math and physics) though I would not call him a mathematician. He was a physicist and philosopher. </p>
<p>In an attempt to clarify mechanics (Newtonian mechanics) Newton essentially developed the core of calculus as a tool to bridge the physical gaps. However, it is tough to say that Newton was really the inventor of calculus since several people were publishing on the subject that year. I don't consider newton a mathematician for the reason that his work was merely physical interpretation and equating.</p>
<p>For Feynman, see Einstein.
Euler was a mathematician.
For Stokes, I'd say a pretty important mathematician seeing how he developed much of multivariable calculus which has major application electromagnetism and fluid field theory. He developed new methods for solving/manipulating such systems in certain circumstances.
My roommate is definitely a theoretical mathematician. He hates multiV and DEs and anything that has any physical or directly-applicable significance. As a pure mathematician we may not see his work become practical for some time. I am just telling you this because even though mathematics has been evolving (even in the "pure" sense) I'd say your statements about Einstein and Newton are bullocks.</p>
<p>I was trying to demonstrate the importance of mathematics to the world. Modern physics is impossible to imagine without mathematics.</p>
<p>It's not about who considers himself or herself a mathematician but who does or did mathematics. And Newton, after all, invented calculus, together with Leibniz.
Descartes, Pascal also made contributions to mathematics, though neither would have considered himself a mathematician. While every French student learns about Cartesian equations, Descartes and Pascal figure chiefly in the philosophy section of the curriculum. Both were extremely articulate.</p>
<p>I do not know when mathematics came to assume the meaning it has today. In Ancient Greece, mathema merely meant learning, study, knowledge (not science as we understand it today).</p>
<p>"I was trying to demonstrate the importance of mathematics to the world. Modern physics is impossible to imagine without mathematics."</p>
<p>I'd agree with you 10000% here. The divergence that you speak of is two-fold:
1) Around the time of Copernicus (1500) the application of mathematics to astronomy was realized. Mathematics would start to be used in predicting astronomical phenomena and do geographic surveys. (And a few years later a philosophical divergence with Baruch Spinoza.
2) The european industrialization (1800s) put science/math into the main-stream, though in the form of applied sciences. This is the major fracture with Platonic studies as it was "particular and temporal". Greek study was non-temporal as the Truth is universal and transcendent of physical particulars.</p>
<p>Biologist Eric Lander is a leading figure in the human genome project, who has won many awards for his work there. </p>
<p>
[quote]
Selected Achievements
Leading contributor to the Human Genome Project, (1990-2003)
MacArthur Fellow (1987-1992)
Member, U.S. National Academy of Sciences (1997)
Member, U.S. Institute of Medicine (1998)
Woodrow Wilson Prize from Princeton University (1998)
Baker Memorial Award for Undergraduate Teaching at MIT (1992)
City of Medicine Prize (2001)
Gairdner International Prize (2002)
<p>Interestingly, his intellectual roots are in math. In high school, he won first place in the Westinghouse Science Talent Search with a math research project, and he was also on the first American team to go to the International Math Olympiad, where he won a medal. As an undergrad math major, he was among the top 10 on the Putnam contest. After graduating from Princeton, he got a PhD in math at Oxford as a Rhodes Scholar. </p>
<p>Afterwards, he decided that math was "too monastic." He explored economics for a while and taught at the Harvard Business School, then decided that biology looked like an exciting field to explore.</p>
<p>THIS is the kind of kid Harvard should be sending likely letters to... </p>
<p>
[quote]
GPA: 4.00 unweighted</p>
<p>12th grade classes:
EPGY AP English Language and Composition
AP Spanish Language with a tutor
Self-studied AP Computer Science AB
Plus (all studied at local university UNC-Chapel Hill):
Differential Manifolds
Differential Geometry
Commutative Algebra
Algebraic Geometry
Measure and Integration
Functional Analysis</p>
<p>SATs:
750 (CR), 800 (Math), 800 (Writing), 2350 total
800 Math 2
800 Physics</p>
<p>APs: (All 5s, Physics B, Calculus BC, and World History were self-studied)
Physics B
Physics C (Mechanics and E+M)
World History
US History
Environmental Science
Chemistry
Calculus BC
Statistics</p>
<p>ECs/Awards:
21 on USAMO ----> MOsP Participant
High scoring member of national champion ARML A team
6th place out of all MOsP Participants on Asia-Pacific Math Olympiad
High placing individual on a bunch of smaller math contests (Mandelbrot, HMMT, etc.)
Member of 1st place teams on bunches of smaller math contests (HMMT, Duke Math meet, etc.)
Coach of local middle school MathCounts team
Selected to participate in the Putnam this year for my local university
US National Chemistry Olympiad Participant
National Merit Semifinalist
Currently doing some math research with a professor (I sent a brief description with my application but we don't have enough to publish yet)