9th Grade · Ages 14–15
The Contradiction Year
Fourteen is the year to learn the difference between being confident and being certain — and it takes exactly one proof to feel it.
- 1 Hard Thing
- 5 days · 120 minutes
- 3 unmarkable questions
Ready?
9th Grade · Prove That √2 Is Not a Fraction
Fourteen is the year to learn the difference between being confident and being certain — and it takes exactly one proof to feel it.
Full screen — no distractions
Where this goes
The ladder
The same idea, three times, roughly a year apart. This is what depth looks like from the outside.
This year
√2, by contradiction.
Next year
√3 and √5 by the same argument — then the general statement about any number that is not a perfect square.
The year after
Gödel: that there are true statements no proof can reach.
What lives on the desk this year
- Something you actually enjoy writing with
- A proof notebook, separate from everything else
- A wall list of theorems you can prove from memory
- Somebody to be wrong in front of
- One problem you have not solved for six months
The rest of 9th Grade
One hard thing a day is the sharp end. It sits on top of an ordinary year.
Last updated: September 2026