<p>quicksilver: a lot of Putnam questions look not too hard, but there’s almost always a “twist” involved (e.g. one fairly obvious solution and then a second one that hardly anyone finds; or a question that could be easily solved with a calculator but requires some creativity to solve without one). Of course you might just be one of the 100 most mathematically gifted college students in this country…</p>
<p>Some other personal and highly subjective experience and by no means general:</p>
<p>Math was considered one of the hardest majors offered at the university I was taking math courses during high school. About 300 students each year started as math majors, and only about 40 of them passed the intro courses (linear algebra and analysis). The other ~260 students changed their majors, mostly to computer science, physics, engineering, econ and business and most of them are quite successful in their second majors. </p>
<p>Maybe most of these students just declared the wrong major to begin with, but I think that math (axiomatic math and not the crap taught at most colleges – yes, I admit that most math major programs are not too challenging) is one of the harder subjects of human inquiry.</p>