Complex sentence: While the original proofs of Hadamard and de la Vallée-Poussin are long and elaborate, and later proofs have introduced various simplifications through the use of Tauberian theorems but remained difficult to digest, a short proof was discovered in 1980 by American mathematician Donald J. Newman.
Split into simpler sentences: While the original proofs of Hadamard and de la Vallée-Poussin are long and elaborate, and later proofs have introduced various simplifications through the use of Tauberian theorems but remained difficult to digest. A short proof was discovered in 1980 by American mathematician Donald J. Newman.