Earlier quoted context omitted.
Here is a real example. Pretend like you are in a finance class. It's a case study. On Microsoft buying Yahoo! Determine how much Microsoft should be willing to pay for Yahoo! and the assumptions and rationale behind your conclusion. Or how much is AOL worth as a spinout of Time Warner. The core of the answer lies in something called the Capital Asset Pricing Model and it is as every bit as complex as the fixed point…
"The core of the answer lies in something called the Capital Asset Pricing Model and it is as every bit as complex as the fixed point combinator for which YC was named." Well I don't think the y combinator is a particularly complex concept and I did accept finance as hard and explicitly asked for non finance examples, :-) but that said I see your point (upvoted!). "doing real market research for a natural foods store…
One of the more difficult courses I had focused on managing small-to-medium businesses. The issues and cases we discussed tended not to be quantitative in nature, but really honed critical thinking. A particular case I remember dealt with a struggling, family-owned company whose founder/CEO had just died in the midst of an IP lawsuit, etc. (I don't remember all the details). Imagine you are brought in to run the company. What do you do first, second, third, fourth? The challenges are legal, financial, technical, and interpersonal. There are multiple crises: which do you delegate, which have to be dealt with immediately, and which can wait? What information do you need and from where are you going to get it? The answers are not always obvious and don't necessarily fit inside a neat framework. This is "hard" in a different way from advanced quantitative analysis of futures and options.