Friday, March 08, 2019


Via Scott, John Horgan wrote a blog post following on his 1993 Scientific American article The Death of Proof. The article talked about computer-generated proofs, experimental mathematics and even mentioned some of our work on transparent proofs (basically time-efficient probabilistically checkable proofs). I got (sarcastically I think) accused of killing mathematics after that article but of course we had traditional proofs about probabilistically check proofs. Andrew Wiles got a sidebar titled "A Splendid Anachronism?" for merely solving the most famous open problem in all of mathematics. Somehow traditional mathematical proofs survived the article.

Meanwhile in CACM, Moshe Vardi writes Lost in Math? 
TCS is surely blessed with mathematical beauty. As a graduate student a long time ago, it was mathematical beauty that attracted me to TCS, and continued to lead my research for many years. I find computational complexity theory (or complexity theory, for short), with its theorems (for example, the time-hierarchy and space-hierarchy theorems) and its open questions (for example, P vs NP), to be hauntingly beautiful. Beauty, yes; but what about truth?
Here here on the beauty of complexity. So what about truth? I cover much of this in my P v NP survey. In short the P v NP captures the most critical aspects of what is efficiently computable but it is not the endpoint. Nevertheless P v NP captures both truth and beauty and that's why the problem has so captivated and guided me throughout my research career.

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