>> Compare this to number theory, where every interesting extant problem appears to require ten years study. I don't often come here to comment but as someone

>> Compare this to number theory, where every interesting extant problem appears to require ten years study. I don't often come here to comment but as someone in progress on an original research masters in number theory I can say this is utter bullshit. I assume your 'interesting' qualification (somehow) excludes obvious candidates like Landau's problems [0]. Some examples. I was taught about the ABC conjecture as an undergrad. You can easily teach the Brun sieve [1] method of working out that the sum of the reciprocal of the twin primes converges. Novel solutions to Diophantine problems are sometimes accessible to undergrads. Richard K. Guy wrote a whole book on unsolved problems in NT, some of which have been solved using undergraduate number theory and someone's upper bound you can just use (as easy as apt-get installing this_dope_bound). You can start reading papers without a PhD, never mind ten years of study. I think it's possible to get an utterly unrepresentative sample of either field by only sticking to "elementary" results. There are some extraordinarily subtle results in graph theory! Conversely, you can find NT problems amenable to elementary techniques [2]. [0] https://en.wikipedia.org/wiki/Landau%27s_problems https://en.wikipedia.org/wiki/Landau%27s_problems [1] https://en.wikipedia.org/wiki/Brun%27s_theorem https://en.wikipedia.org/wiki/Brun%27s_theorem [2] https://en.wikipedia.org/wiki/Quadratic_reciprocity https://en.wikipedia.org/wiki/Quadratic_reciprocity