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Math News and Dicussion


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#41
Infinite

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What is the natural constant 'e'?

Excellent video.


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#42
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Mathematicians Race to Debunk German Man Who Claimed to Solve One of the Most Important Computer Science Questions of Our Time

 

This article originally appeared on Motherboard Germany. Since its original publication it has been updated with new information by Motherboard US.
 
What do curable cancer, fair capitalism, and the perfect game of Super Mario Bros. all have in common? Per a mathematical theory, the solution to any one of these problems would allow us to quickly solve the others. All that's needed are better algorithms to prove that complicated questions—such as protein folding, efficient marketplaces, and combinatorial analyses—are merely variations of simpler problems that supercomputers are already able to solve. 
 
But how can one algorithm simplify extremely complicated problems? That depends on another question: What if complicated problems are really just simple problems in disguise? This riddle remains one of the biggest unsolved questions of modern mathematics, and is one of the seven Millennium Prize Problems, for which every accepted answer is rewarded with one million dollars.
 
Now, a German man named Norbert Blum has claimed to have solved the above riddle, which is properly known as the P vs NP problem. Unfortunately, his purported solution doesn't bear good news. Blum, who is from the University of Bonn, claims in his recently published 38-page paper that P does not equal NP. In other words, complicated problems are fundamentally different than straightforward problems and it doesn't look like our high-performance computers will be able to crack these most difficult problems anytime in the near future. And in the days since his paper was published, numerous mathematicians have begun to raise questions about whether Blum solved it at all.
 
continued at...
 

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#43
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https://www.quantama...ysics-20171201/

Secret Link Uncovered Between Pure Math and Physics
By
KEVIN HARTNETT
December 1, 2017

An eminent mathematician reveals that his advances in the study of millennia-old mathematical questions owe to concepts derived from physics.

Minhyong Kim, a mathematician at the University of Oxford, has long kept his vision to himself. “Number theorists are a pretty tough-minded group of people,” he said.
Minhyong Kim, a mathematician at the University of Oxford, has long kept his vision to himself. “Number theorists are a pretty tough-minded group of people,” he said.
Tom Medwell for Quanta Magazine
Mathematics is full of weird number systems that most people have never heard of and would have trouble even conceptualizing. But rational numbers are familiar. They’re the counting numbers and the fractions — all the numbers you’ve known since elementary school. But in mathematics, the simplest things are often the hardest to understand. They’re simple like a sheer wall, without crannies or ledges or obvious properties you can grab ahold of.

Minhyong Kim, a mathematician at the University of Oxford, is especially interested in figuring out which rational numbers solve particular kinds of equations. It’s a problem that has provoked number theorists for millennia. They’ve made minimal progress toward solving it. When a question has been studied for that long without resolution, it’s fair to conclude that the only way forward is for someone to come up with a dramatically new idea. Which is what Kim has done.

“There are not many techniques, even though we’ve been working on this for 3,000 years. So whenever anyone comes up with an authentically new way to do things it’s a big deal, and Minhyong did that,” said Jordan Ellenberg, a mathematician at the University of Wisconsin, Madison.

Over the past decade Kim has described a very new way of looking for patterns in the seemingly patternless world of rational numbers. He’s described this method in papers and conference talks and passed it along to students who now carry on the work themselves. Yet he has always held something back. He has a vision that animates his ideas, one based not in the pure world of numbers, but in concepts borrowed from physics. To Kim, rational solutions are somehow like the trajectory of light.

Continued at...

Link above

#44
Jakob

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Mathematicians Race to Debunk German Man Who Claimed to Solve One of the Most Important Computer Science Questions of Our Time

 

This article originally appeared on Motherboard Germany. Since its original publication it has been updated with new information by Motherboard US.
 
What do curable cancer, fair capitalism, and the perfect game of Super Mario Bros. all have in common? Per a mathematical theory, the solution to any one of these problems would allow us to quickly solve the others. All that's needed are better algorithms to prove that complicated questions—such as protein folding, efficient marketplaces, and combinatorial analyses—are merely variations of simpler problems that supercomputers are already able to solve. 
 
But how can one algorithm simplify extremely complicated problems? That depends on another question: What if complicated problems are really just simple problems in disguise? This riddle remains one of the biggest unsolved questions of modern mathematics, and is one of the seven Millennium Prize Problems, for which every accepted answer is rewarded with one million dollars.
 
Now, a German man named Norbert Blum has claimed to have solved the above riddle, which is properly known as the P vs NP problem. Unfortunately, his purported solution doesn't bear good news. Blum, who is from the University of Bonn, claims in his recently published 38-page paper that P does not equal NP. In other words, complicated problems are fundamentally different than straightforward problems and it doesn't look like our high-performance computers will be able to crack these most difficult problems anytime in the near future. And in the days since his paper was published, numerous mathematicians have begun to raise questions about whether Blum solved it at all.
 
continued at...
 

 

What happened with this? Disproving P vs NP would be pretty big (not as big as proving it though).


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#45
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I'm not sure, time for us to do research and look it up :)

#46
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The paper has been withdrawn apparently

http://www.i-program...-that-p-np.html

Guess that leaves us with the 500 page proof of the ABC conjecture to explore
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#47
Yuli Ban

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Math Geeks Must Wait 100 Years for a Day Like This

In certain circles, including some of the ones I travel in, there’s great excitement about today’s date. We won’t see its like again for another century.
 
What makes today so special? The date -- 1/6/18 -- lines up with the first four digits of the golden ratio, a mathematical constant that’s roughly equal to 1.618 and is commonly denoted by the Greek letter phi, which looks a bit like the letter "p" but with an extra loop on the left-hand side of the vertical axis.
 
So let’s celebrate Phi Day by considering some of the wonderful things the golden ratio has to offer.
 
The golden ratio is the proportion that arises when we cut a line into two parts so that the ratio of the whole length to the long part is equal to the ratio of the lengths of the two parts. Many find those sorts of proportions aesthetically pleasing: Le Corbusier, for example, based his system of architecture on them ; they may also have figured into the Parthenon. And mathematically, the golden ratio is cool because it is the only positive number such that you get its square if you add 1 to it. 
But that’s not all! The golden ratio has been found in nature everywhere from nautilus shells to magnetic resonance at the atomic scale. Perhaps prefiguring this, Luca Pacioli -- a Renaissance-era forefather of modern accounting -- ascribed divine significance to the golden ratio. (On a more earthly plane, the golden ratio co-starred alongside Donald Duck in the 1950s.)


And remember my friend, future events such as these will affect you in the future.





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