11232003, 09:10 PM  #1 (permalink) 
Banned

Mathmatitian Rejoice!!
This has been an unusually productive time in recreational mathematics.
1. It appears that the 40th Mersenne Prime has been discovered: http://www.mersenne.org/prime.htm 2. And we now know that there are no magic knight's tours of a chessboard, a 150year old problem: http://mathworld.wolfram.com/news/20...06/magictours/ 3. And the world's oldest math problem,*the Loculus of Archimedes*, has been solved: http://www.maa.org/editorial/mathgam..._11_17_03.html 
11232003, 10:22 PM  #2 (permalink) 
I am Winter Born
Location: Alexandria, VA

Very interesting that within a fairly recent time span three fairly significant discoveries have been made. Just goes to show that the field of mathematics still has lots of life left in it, in terms of discovering new things and proving old theorems.
Also shows how heavily we rely on computers to aid us in mathematics  each of those 3 were solved with computers.
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11232003, 11:45 PM  #3 (permalink) 
Addict

math will never run out of things to study. the only thing that would kill math is if people stopped caring about it.
and the avid recreational math fan shouldn't despair thinking that math is only composed of mammoth old theorems and metasystems that need a PhD to even read about. there's LOTS of small and accessible problems that can be worked on. and if there isn't one you like, make up your own. 
11252003, 08:34 AM  #4 (permalink) 
Psycho
Location: the hills of aquafina.

Wow. I was never good at even intermediate algebra, so I'm impressed.
What amazes me is that someone thought this crap up....a long time ago. I can't even begin to imagine how to solve it, much less able to think the original problem up!
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11262003, 08:56 AM  #5 (permalink) 
WARNING: FLAMMABLE
Location: Ask Acetylene

Well number two isn't really that big a deal is it? Anyone could have enumerated the combinations and checked each one. It didn't even require that much computing power. It could have been done with technology available many years ago.
I would say the same for number 3 also. The only real challenge seems to be number 1.
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"It better be funny" Last edited by kel; 12012003 at 11:55 AM.. 
11292003, 01:57 PM  #6 (permalink) 
Crazy
Location: Near Chicago, IL

This is very interesting, do any of you know of any websites with interesting problems designed for the high school/collegiate level?
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11292003, 08:24 PM  #7 (permalink)  
Banned
Location: 'bout 2 feet from my iMac

Quote:


11302003, 03:38 AM  #9 (permalink)  
Addict
Location: Grey Britain

Quote:
Interesting to see anyways.
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11302003, 11:30 AM  #10 (permalink) 
Banned

ya.. no one has been able to find any formal proves regarding prime and perfect numbers. we are all waiting for it... but a development of a whole new branch/system or langauge of number theory would be neccessary to do it. Since Godel already proved there is not system powerful enough to encompass it all... we need someoen specific enough to prove it... but within the power of discovered systems. i mean, Euclid did prove tehre are infinite primes, but the problem is no one can prove an equation that gives you. Furthermore, no one has yet proved there are infinite perfect numbers or the existance of odd perfect number.... ahhh who needs science when there is so much to explore in math? :P

12012003, 11:54 AM  #11 (permalink)  
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Location: Ask Acetylene

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There is a couple orders of magnitude difference in computing power between the problems. The first one could NOT (unless you have the secret to uber long living) have been solved by the technology available a few decades ago.
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12012003, 01:40 PM  #12 (permalink)  
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Location: Grey Britain

Quote:
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"No one was behaving from very Buddhist motives. Then, thought Pigsy, he was hardly a Buddha, nor was he a monkey. Presently, he was a pig spirit changed into a little girl pretending to be a little boy to be offered to a water monster. It was all very simple to a pig spirit." 

12022003, 01:24 PM  #14 (permalink)  
Addict
Location: Grey Britain

Quote:
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"No one was behaving from very Buddhist motives. Then, thought Pigsy, he was hardly a Buddha, nor was he a monkey. Presently, he was a pig spirit changed into a little girl pretending to be a little boy to be offered to a water monster. It was all very simple to a pig spirit." 

12022003, 06:07 PM  #15 (permalink)  
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Location: Ask Acetylene

Quote:
Any mathemetician or programmer knows how it is improbable (really impossible) to find large prime numbers efficiently. If an algorithm had been developed it would be some big ass news because modern cryptography would be ruined. Number 2:"Bill Cutler used a computer program to enumerate all solutions." Number 3:"This longstanding open problem has now been settled in the negative by an exhaustive computer enumeration of all possibilities." Enumeration isn't an efficient way of doing things and anyone could have done it years ago, they just would have taken forever to get the results. In the case of prime numbers you would have to wait a few hundred (thousand?) years on a 486.
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