Probably the most famous mathematical work with a New Hampshire connection is the proof of the four-color theorem, done by Wolfgang Haken and Ken Appel in 1976. (Appel later moved to New Hampshire and became head of the mathematics department at UNH, so the Granite State connection is after-the-fact.)
The proof is famous because it was the first major math accomplishment that relied on computers to analyze a huge number of examples – too many for a human being to double-check.
Carbon-based life forms had to accept the conclusions of a silicon-based life form, and a lot of them didn’t like it. As I said in my 2013 obituary of Appel:
That digital intrusion into the most cerebral of human activities generated so much angst and debate in the scientific community that it made the front page of the New York Times, led to an infamous Scientific American cover story titled “The Death of Proof,” and has been the subject of several books.
I mention this because of a fascinating article in Vice today (read it here) which sets off all my irony alarms: Some mathematicians are arguing that computer-aided proofs are now necessary to determine whether lots of modern math is based on flawed premises.
Kevin Buzzard, a number theorist and professor of pure mathematics at Imperial College London, believes that it is time to create a new area of mathematics dedicated to the computerization of proofs. The greatest proofs have become so complex that practically no human on earth can understand all of their details, let alone verify them. He fears that many proofs widely considered to be true are wrong. Help is needed.
In other words, we’ve gone from “using computers means you can’t be sure the proof is right” to “unless we use computers we can’t be sure the proof is right” in one academic generation.
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