The Rainich Trick



Zariski's proof1 of the Hilbert Nullstellensatz makes use of the ineffable Rabinowitch Trick2 (check it out, that has got to be the shortest paper ever). But who is that awesome guy Rabinowitsch? I found out today, and the answer is basically in in this MO post: > Rainich was giving a lecture in which he made use of a clever trick which he had discovered. Someone in the audience indignantly interrupted him pointing out that this was the famous Rabinowitsch trick and berating Rainich for claiming to have discovered it. Without a word Rainich turned to the blackboard, picked up the chalk, and wrote RABINOWITSCH. He then put down the chalk, picked up an eraser and began erasing letters. When he was done what remained was RABINOWITSCH. He then went on with his lecture. Apparently, George Yuri Rainich is the mysterious stranger that went by the name of Rabinowitsch, which was his birthname34. I even updated the wikipedia page. Oh right, the reason this even caught my attention: Daniel R. Grayson has a really sweet, short proof of the Nullstellensatz, also using the Rainich Trick.
  1. Oscar Zariski. A new proof of Hilbert's Nullstellensatz, Bulletin of the Ameican Mathematical Society Volume 53, Number 4 (1947), 362-368. []
  2. J. L. Rabinowitsch, Zum Hilbertschen Nullstellensatz, Mathematische Annalen Volume 102, No. 1 (1929), 520. []
  3. Bruce P. Palka, Editor's Endnotes (May 2004), The American Mathematical Monthly 111 (5): 456–460 []
  4. Bruce P. Palka, Editor's Endnotes (December 2004). The American Mathematical Monthly 111 (10): 927–929 []

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