The hardest problem on the hardest test

What Hacker News said

Strong rec skadamat · 2017-12 · on “Communicating Advanced Mathematics to Kids”

So many things I could say about this, but I"ll let Alan Kay speak for me - [LINK] Alan talks about how ideas in Calculus could be manifested from an early age and a richness in understanding built up as they aged up: - at very young ages, kids really respond well through "doing" / the enactive channel. When asked to draw a circle, kids in Papert's group would first emulate what a LOGO turtle would do by rotating their body in a circle (making tiny increments in x and y). - as they got a bit older, the visual / iconic channel was more developed and they could understand the abstraction of a circle on pencil/paper and how the concepts carried over there - closer to early teens, symbols were m

Strong rec naturlich · 2019-07 · on “Think in Math, Write in Code”

Indeed, I'd recommend the "interesting proof" vignettes by 3Blue1Brown: [this video] These are my favorite videos of his

Strong rec pjfin123 · 2020-10 · on “A Programmer’s Intuition for Matrix Multiplication”

3Blue1Brown is really great for learning/refreshing math. He has great visualizations. I especially enjoyed this video (not exactly a math tutorial more of a cool explanation): [this video]

Strong rec JackC · 2021-08 · on “How to avoid being hit by a laser in a room of mirrors [video]”

I like the 3blue1brown youtube series for explaining mathematical problem solving, like this example explaining a difficult problem from the Putnam: [this video] "And those of you who follow the channel know that rather than just jumping straight to the solution, which in this case will be surprisingly short, when possible I prefer to take the time to walk through how you might stumble upon the solution yourself. That is, make the video more about the problem-solving process than the particular problem used to exemplify it." I bailed out of math around calculus, and these videos helped me at least appreciate what I was missing.

Strong rec msdrigg · 2021-08 · on “Manim: An animation engine for explanatory math videos”

This is an extension of an animation library used by math YouTuber 3blue1brown [0]. He has an excellent channel that I would recommend anything from. One of my favorite videos of his is where he shows the thought process behind solving a level 6 Putnam competition problem and makes it seem almost doable [1]. [0] [LINK] [1] [this video]

Recommends tromp · 2019-10 · on “The “Windmill” Problem on the 2011 International Mathematical Olympiad [video]”

I enjoyed watching this similarly insightful video [1] on "The hardest problem on the hardest test" of the Putnam Competition. [1] [this video]

Recommends ncallaway · 2019-11 · on “Moving towards a faster web”

I strongly disagree with this comment. I sincerely doubt 100% of the HN audience always considers those things. You might think some of those things are basic, but that doesn't make them useless. This kind of lack of empathy for new learners can make it incredibly difficult to teach concepts to those who don't have as much knowledge as you may have. See [this video] for a great video by 3blue1brown on this topic.

Recommends mauriziocalo · 2025-07 · on “OpenAI claims gold-medal performance at IMO 2025”

Related — these videos give a sense of how someone might actually go about thinking through and solving these kinds of problems: - A 3Blue1Brown video on a particularly nice and unexpectedly difficult IMO problem (2011 IMO, Q2): [LINK] -- And another similar one (though technically Putnam, not IMO): [this video] - Timothy Gowers (Fields Medalist and IMO perfect scorer) solving this year’s IMO problems in “real time”: -- Q1: [LINK] -- Q4: [LINK]