<p>To really get the most out of being a math major at Harvard, you need to come in ready to take 23 (at least) or 25 (more common) your freshman year. It is possible to major in math, having started with 21, or even 1a/1b, but you’ll only be able to access a fraction of the course offerings.</p>
<p>Applied math is more forgiving – you could take 23 or 25, but it’s not a proof-based concentration, so 21 or applied 21 is fine. Applied math (and all the stats you take) is also more relevant for students who want to go off and work for a hedge fund or be a quant.</p>
<p>Physics is a bit similar to math – I don’t think you’d want to be a physics concentrator unless you took 15 or 16 your freshman year, and those are pretty beastly classes, as has been mentioned.</p>
<p>There’s this distinction that you realize at Harvard (or earlier!) between being “normal smart” at math and “freaking smart” - and it becomes really evident as the topics become more abstract and more proof based. I was always very good at math (took AP calc in 8th grade + such), but dabbled a bit at Harvard and quickly realized I didn’t have the math brain that I needed to be an awesome math or physics concentrator.</p>