Contributions To Mathematics
The Motzkin transposition theorem, Motzkin numbers and the Fourier–Motzkin elimination are named after him. Motzkin first developed the "double description" algorithm of polyhedral combinatorics and computational geometry. He was the first to prove the existence of principal ideal domains that are not Euclidean domains, being his first example.
The quote "complete disorder is impossible," describing Ramsey theory is attributed to him.
Read more about this topic: Theodore Motzkin
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