Ohhhh, lots of brutal exams come to mind. The idea seemed to be that, in physics and mathematics, performance near and below epsilon+2*sigma is inconsequential, so most of the effort goes into characterizing the performance attributes of the top 5% of the incoming freshman class (the attrition rate remained at 50% even up to 4th year). In contrast, most grading schemes look at roughly uniform resolution across the performance spectrum, resulting in no differentiation between students at the top 5% level, for example.
For undergraduate field theory, the last section of the class was quantum field theory. Now, the math covered up until that point in other classes was nowhere near the level necessary to completely understand this material, so the professor, a real communist who joked that to be respectable he said in mixed company he was merely a socialist (great guy otherwise, very quirky), had to quickly cover some new math concepts in addition to the physics. Because of two false fire alarms, there was not enough time to cover the material from the final two lectures, so he assigned reading and included some handouts containing part of the material with the final exam. Those exam questions were at least possible to complete individually, but nobody finished on time because of the math grindwork involved. The original class of 18 had dropped to 10 by the end of term, and all 10 of us in that final room stayed for 5 hours, punctuated with a 30 minute emergency lesson on some arcane aspect of tensor calculus (basically to share an important trick for simplifying calculations that would otherwise require the use of a computer algebra system) at the 3 hour official exam end mark (9 PM).
Even in sophomore year, I had one professor who announced on the first day that he was aiming to fail 1/2 of the class as a weeding exercise out of compassion, so they could pick a major better suited to their talents sooner rather than later. Near the end of the course, he said anyone not receiving an A would not complete senior year - and he was correct.
For undergraduate high energy physics (the highest level senior course offered, with entry requiring the passing of a qualifying examination administered by the professor one week before classes started), we covered a unit on quantum chromodynamics that surpassed in difficulty any graduate material I later took. The professor was convinced of some (dubious) property of Twistor theory as related to quantum gravity. I remember especially one of the four questions on our final dealing with Yang-Mills instantons and what would later be understood as some element of the AdS/CFT correspondence. None of us (4) students then understood what was going on with that question, but I am certain the professor was hoping the next Witten would emerge from that exam. The other three questions were difficult as well. I did OK (all 4 of us passed), but the experience turned me off HEP forever.
Even after undergrad, there was a need to weed. I had an open-book exam in one graduate math class that was deadly. The professor permitted any material to be brought in - any book, any notes, anything on cassette, any food or drink, even toys and pets - and he stated that the time limit was as long as we remained in the room, save bathroom breaks. The only rule was no communication between students. But there was nothing on this planet that one could have brought in which would have helped on that test (for the record, I brought a large coffee, cookies, my notes and a textbook - the latter two items were useless). The class material directly covered 50% of the exam, and the rest of the exam consisted of open research in the field for which correct answers would have resulted in publications. The professor was busy happily giggling away at the front of the room most of the time. No belling of marks occurred, but I got enough part marks on the impossible-to-complete questions to score well (i.e. impose a crude approximation to “solve” one problem, repose another problem in a more compact form from which the existence, as well as other important properties, of the solution can be directly inferred, etc).
I still have nightmares, lol.
What is your current occupation?