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[math-fun] Proof, the movie
by Thane Plambeck 04 Oct '05

04 Oct '05

I went to see the movie "Proof" last night and enjoyed it quite a bit, even if it upholds the long-standing cinematic tradition of finding mathematicians interesting only if they are also insane, or about to be insane, or recovering from having been insane. http://www.miramax.com/proof/ I've read some lukewarm reviews so thought I offer an endorsement up against that. -- Thane Plambeck http://www.plambeck.org/ehome.htm

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[math-fun] Counting problem
by David Wilson 03 Oct '05

03 Oct '05

Suppose we have m numbers a_1 <= a_2 <= ... <= a_m, and n numbers b_1 <= b2 <= ... <= b_n. How many different ways can the a_i and b_i be related with < and = ? For example, if m = 2 and n = 2, two possible arrangements are a1 < a2 = b1 < b2 (considered equivalent to a1 < b1 = a2 < b2) b1 < a1 = a2 = b2 -------------------------------- - David Wilson

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Re: [math-fun] Some say in coal
by Daniel Asimov 03 Oct '05

03 Oct '05

Some say that coal trains' jazz was among the best. --Dan -----Original Message----- From: Hilarie Orman <ho(a)alum.mit.edu> Sent: Oct 3, 2005 12:09 PM To: math-fun(a)mailman.xmission.com Subject: [math-fun] Some say in coal The New Yorker, Oct. 3 2005, page 77, in an otherwise excellent article "Coal Train" by John McPhee, tells about watching videos of trains and states, "A very large percentage were coal trains, half a light-year of coal trains ..." Hilarie _______________________________________________ math-fun mailing list math-fun(a)mailman.xmission.com http://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun

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Re: [math-fun] about time
by MCKAY＠vax2.concordia.ca 03 Oct '05

03 Oct '05

What is your point, Rich? There was no discovery of Helibacter pylori - just recognition that it occurs in the stomach and withstands the acid there. Marshall had one hell of a fight to establish recognition among the medical profession for his results. What analogous mathematical results are you thinking of? John McKay .

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[math-fun] Some say in coal
by Hilarie Orman 03 Oct '05

03 Oct '05

The New Yorker, Oct. 3 2005, page 77, in an otherwise excellent article "Coal Train" by John McPhee, tells about watching videos of trains and states, "A very large percentage were coal trains, half a light-year of coal trains ..." Hilarie

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[math-fun] about time
by Schroeppel, Richard 03 Oct '05

03 Oct '05

I was wondering if the Nobel committee was completely dominated by theoreticians. Two Australian scientists were today awarded this year's Nobel prize for physiology and medicine for their "unexpected" discovery that has saved millions of people from the pain of stomach ulcers. Robin Warren, a pathologist from Perth, and Barry Marshall, a senior research fellow at the University of Western Australia, share the prize for their 1982 discovery of a bacterium, helicobacter pylori, which causes stomach inflammations and ulcers. Rich

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Re: [math-fun] New proof of Four-Color Theorem
by dasimov＠earthlink.net 02 Oct '05

02 Oct '05

Jud writes: << (I wrote): >As is well-known, the four-color theorem was proved about 1977, >making heavy use of computers. Heavy use for that time - about 1200 hours on an IBM 360. I assume that is the total CPU time and not just the time it was in the machine on a time-sharing basis. Interestingly, the equivalent computing on a typical modern desktop computer would be on the order of 10 minutes. Seconds on a modern supercomputer. >> Aha -- thanks for pointing this out. It may, however, still be about as hard as ever for a human to verify that the original computer proof was valid. The more recent (mid '80s ?) improvment on the original proof would, I think, also be deemed hard to verify the correctness of the computer aspect of the proof. (I suspect that the correctness of at least the improved version is generally believed to now be human-verified, but am not sure of this.) --Dan

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[math-fun] New proof of Four-Color Theorem
by dasimov＠earthlink.net 02 Oct '05

02 Oct '05

As is well-known, the four-color theorem was proved about 1977, making heavy use of computers. And since then, minor errors were fixed and the computer part of the proof was simplified -- but the proof still relied heavily on computer verification. Now it appears that a new proof has been found, not relying on computers, that has been fully (human-) verified. This new proof is by a mathematician named Georges Gonthier. Thomas Hales (whose own 1998 proof of the Kepler conjecture relies heavily on computers) will speak on this new proof at Swarthmore College on Wed., Oct. 5, at 4:30 pm. Here is his abstract: << The four-color theorem states that any map can be colored with four colors in such a way that adjacent countries do not receive the same color. This theorem is one of the most famous math problems ever to be solved by computer. Last year, Georges Gonthier gave a completely formal proof of the four-color theorem. This means that every step of the proof has now been carefully checked all the way down to the fundamental axioms of mathematics. I will describe Gonthier's project and explain how it relates to my current work on packing spheres. >> --Dan

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Re: [math-fun] NYTimes: melting ice cubes cause water to rise ?
by dasimov＠earthlink.net 30 Sep '05

30 Sep '05

Henry Baker wrote that an old SAT question goes like this: << A cube of ice is floating in a glass of water that is filled to the top. (No discussion of meniscus.) When the ice melts, the water in the glass: A. overflows B. stays at the same level C. goes down D. none of the above >> (This sounds more like a question from a physics "achievement test" -- but be that as it may.) I would not say ice displaces the same "amount" of water, since "amount" could mean either mass or volume. The floating ice cube has the same weight as a) the water it displaces and b) the water it becomes when it melts. Thus a) and b) have the same volume. So when the cube melts, the water level shouldn't change. (So what's the business about floating ice raising water levels when it melts?) --Dan

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Re: [math-fun] NYTimes: melting ice cubes cause water to rise ?
by Henry Baker 30 Sep '05

30 Sep '05

You're correct about the potato. However, I was referring to the general technique, not the particular object. At 09:52 AM 9/30/2005, Mike Stay wrote: >On 9/30/05, Henry Baker <hbaker1(a)pipeline.com> wrote: >> As an aside, I recently saw a show on Italian cooking on cable TV, and the cook >> used the change in density of salt water to approximate the correct salinity for >> a salt broth. She put a potato into the water, and added enough salt until >> the potato started to float. That was the correct amount for her recipe. >> Something tells me that this technique was probably used for thousands of >> years. >Except that the potato is from the New World. Anyone know if Andean >indians use salt broths in their traditional cooking? >-- >Mike Stay >metaweta(a)gmail.com >http://math.ucr.edu/~mike

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