What is the natural constant 'e'?

Excellent video.

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# Math News and Dicussion

Started by
Unity
, Jun 01 2016 08:07 PM

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#41
Posted 18 September 2017 - 09:19 PM

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#42
Posted 19 September 2017 - 02:03 AM

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...

- Jakob likes this

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#43
Posted 02 December 2017 - 04:51 AM

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

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
Posted 02 December 2017 - 04:55 AM

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).

- Unity likes this

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Spoiler

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#45
Posted 02 December 2017 - 05:43 AM

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

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#46
Posted 02 December 2017 - 05:50 AM

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

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

Guess that leaves us with the 500 page proof of the ABC conjecture to explore

- Jakob likes this

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