The Uncracked Problem with 33 - Numberphile
Why Hacker News recommends it
Linked in threads on sums of cubes and Diophantine equations as an accessible introduction.
What it is
Numberphile with Tim Browning on the sum-of-three-cubes problem and why 33 was the lowest unsolved case. The description notes a later solution for 33.
Recommended by 1 HN commenters across 1 different months, 2019 to 2023.
What Hacker News said
Recommends db48x · 2023-10 · on “Ask HN: Fermat's Last Theorem with More Terms: Why Does It Stop at 3?”
It's an open question that has been studied for thousands of years. This type of equation (a polynomial with integer coefficients) is called a Diophantine equation; you can look it up on Wikipedia. Or watch videos about it: [this video]
Cites heinrichf · 2019-03 · on “Sum-of-Three-Cubes Problem Solved for ‘Stubborn’ Number 33”
Numberphile video on the topic with Andrew Booker: [LINK] which is a followup from the 2015 episode [this video] when the 33 problem was unsolved. The announcement elicited this Mathoverflow discussion about "mic drop" moments in mathematics: [LINK]
Cites jerf · 2019-09 · on “42 is found to be the sum of three cubes”
I only recently heard what I think is a pretty solid answer to this question [1] that put it this way: We've pretty much got addition nailed down. We're pretty solid on multiplication. However, we are surprisingly weak mathematically when we try to put the two together; you can write down some extremely small math statements that baffled mathematicians for centuries, and for such statements that we have solutions for, they often get into very, very complicated math. So you have things like Fermat's Last Theorum, or if you prefer, the Question: For a^n + b^n = c^n, are there any solutions with n > 2 for integers? Note how it's just multiplication and addition on the integers. There are simple