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This. Programming is sponsored by the

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Dan L. Duncan Comprehensive Cancer

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Care Center at Baylor St.

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Luke's Medical Center offering comprehensive

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cancer care that is compassionate,

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personalized, and driven by clinical

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research. More it S T.

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Luke's health.org/cancer. This. Is

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the engines of our ingenuity made possible

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by the friends of K U H

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of Houston? Today guest

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scientist Andrew Boy Color is

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maps the University of Houston

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present this series about the

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machine. Is that make our

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civilization run and the people's

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ingenuity created them? And

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eighteen fifty Two, Francis Guthrie found himself

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trying to color a map of the

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county's of England. It's very helpful to

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have a map where every border county

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has a different color and Guthrie wondered

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how few colors he could use in

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still do this. Three colors wouldn't work,

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but he found he could make do

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with for so he wondered. would four

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colors be enough for any map. Little.

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Did he realize that is question?

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Would Lance hold on generations of

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mathematicians? The seeming simplicity

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of the for Color problem lead

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countless people to try their hand

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at it over the years, including

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some of the world's most renowned mathematicians

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herman Men Cask. He once told

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the students the problem remains unsolved because

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third rate mathematicians had worked on

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it, only to admit much later that

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heaven is angered at my arrogance.

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My proof is also defective. The

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first would be proof of the result

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was published in the American Journal of

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Mathematics in Eighteen seventy Nine, almost thirty

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years after Guthrie first post the problem

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when Alfred Break Camp received great acclaim

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for it. He. Was made a

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fellow of the Royal Society in England and

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was ultimately night at. Eleven.

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Years later, per John, Hayward discovered

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an error and camps proof for

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an incorrect result to be published.

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Much less unchallenged for such a

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long time is very rare and

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helps us understand the special difficulties

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associated with the for. Color problem.

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Unlike many mathematical problems that rely

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on weaving together a small number

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of ideas, all the attempted proofs

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of the for Color problem reduced

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to checking many, many specially constructed

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maps, determining which special maps need

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to be checked and then checking

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them leaves enormous room for mistakes.

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Not until Nineteen Seventy Six did

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mathematicians Apple and he develop the

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first proof of the for Color

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problem. That's with stood the test

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of time, but it wasn't met

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with open arms. They were able

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to reduce the number. Of special

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maps to something manageable but still

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required a computer and twelve hundred

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hours of computing time to complete

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it in Nineteen Seventy six. The

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thought of using a computer in

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a proof was considered outrageous. It

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evokes heated debate. Scientific American went

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so far as to publish an

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article entitled the Deaths of Proof.

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As mathematicians had grown more comfortable

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with computers, the concern about their

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use in proofs has subsided. But

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debate about the proof of the

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for Color problem lingers. In.

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Nineteen Ninety Six for researchers set out

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to verify the Apple had can prove

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because in their own words, as far

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as we know, no one has yet

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verified it in it's entirety. We.

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Have been sacked. tried to but soon

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gave up. Instead, they

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develop their own greatly simplified prove. It

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still relies on a computer, it still

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requires a mathematician to understand it, and

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it's certainly possible that the remain even

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simpler ways to prove what has been

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elevated from the for Color problems into

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the four Colors serum. So

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the next time you look at a

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map, ask yourself how you might get

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away with only three colors or how

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you make convolute the map so it

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would require five. I think you'll find

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it really can be hypnotic. I'm Andy

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Boyd as the University of Houston where

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we're interested in the way in this

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is Moons.