Theorem

Agreement over a lossy channel is impossible. Why exactly-once delivery is a lie and idempotency is the real answer.

Every non-trivial semantic property of programs is undecidable.

No program decides termination for all programs. The ancestor of every other undecidability result.

Some infinities are bigger; there are more problems than programs. The proof technique that The Halting problem and Godel's incompleteness theorems both reuse.

Amdahl's rebuttal, and then the law that adds a negative term for coordination: past a point, more nodes make it slower.

The serial fraction caps your speedup, brutally. Pure algebra, not an observed regularity — the empirical part of the speedup story belongs to Gustafson's law and...

Any algorithm that shrinks some inputs must grow others. Kills every "compresses random data" claim on sight.

n+1 items, n boxes, one collision. The cheapest impossibility argument in existence, and the seed for No universal lossless compressor and The birthday bound.