**1)**One of several posts where Andrew Gelman mulls over the research of a business school professor:

**2)**RSA-129 from

**:**

*Numberphile***3)**RJ Lipton reports on an impressive 5-man panel discussion (including one fool ;) of P vs. NP:

**4)**If you’re not too tired of hearing problems with p-values, well here’s a litany:

**5)**A John Baez update on science data amidst the world of Trumpian obfuscation:

**6)**

**aired the story of Ramanujan on their podcast this week:**

*Futility Closet***7)**The map of mathematics via

**YouTube**:

**8)**Mircea Pitici’s “

**The Best Writing On Mathematics 2016**” is now available:

The “

*Introduction*” here: http://press.princeton.edu/chapters/i10953.pdf**9)**The foundations of symplectic geometry from

**Quanta**:

https://www.quantamagazine.org/20170209-the-fight-to-fix-symplectic-geometry/

http://mathmisery.com/wp/2017/02/10/carnival-of-mathematics-142/

**10)**The latest "*Carnival of Mathematics*":http://mathmisery.com/wp/2017/02/10/carnival-of-mathematics-142/

**11)**At

**this week I briefly looked at a physics book and yesterday reported the news of Raymond Smullyan’s death.**

*Math-Frolic*
Potpourri

**BONUS!**(extra NON-mathematical links of interest):
1) The fellow behind the @TrumpDraws **Twitter**viral account:

2) And ICYMI, John Cleese’s letter to the U.S. (though I think perhaps he’s overreached his power a wee bit):

Given a number x and a set S of n positive integers, MINIMUM is the problem of deciding whether x is the minimum of S. We can easily obtain an upper bound of n comparisons: find the minimum in the set and check whether the result is equal to x. Is this the best we can do? Yes, since we can obtain a lower bound of (n - 1) comparisons for the problem of determining the minimum and another obligatory comparison for checking whether that minimum is equal to x. A representation of a set S with n positive integers is a Boolean circuit C, such that C accepts the binary representation of a bit integer i if and only if i is in S. Given a positive integer x and a Boolean circuit C, we define SUCCINCT-MINIMUM as the problem of deciding whether x is the minimum bit integer which accepts C as input. For certain kind of SUCCINCT-MINIMUM instances, the input (x, C) is exponentially more succinct than the cardinality of the set S that represents C. Since we prove that SUCCINCT-MINIMUM is at least as hard as MINIMUM in order to the cardinality of S, then we could not decide every instance of SUCCINCT-MINIMUM in polynomial time. If some instance (x, C) is not in SUCCINCT-MINIMUM, then it would exist a positive integer y such that y < x and C accepts the bit integer y. Since we can evaluate whether C accepts the bit integer y in polynomial time and we have that y is polynomially bounded by x, then we can confirm SUCCINCT-MINIMUM is in coNP. If any single coNP problem cannot be solved in polynomial time, then P is not equal to coNP. Certainly, P = NP implies P = coNP because P is closed under complement, and therefore, we can conclude P is not equal to NP.

ReplyDeleteYou could read the details in:

http://vixra.org/pdf/1704.0335v1.pdf

P versus NP is considered one of the great open problems of science. This consists in knowing the answer of the following question: Is P equal to NP? This incognita was first mentioned in a letter written by John Nash to the National Security Agency in 1955. Since that date, all efforts to find a proof for this huge problem have failed.

ReplyDeleteI show a solution to that problem as follows:

Given a number x and a set S of n positive integers, MINIMUM is the problem of deciding whether x is the minimum of S. We can easily obtain an upper bound of n comparisons: find the minimum in the set and check whether the result is equal to x. Is this the best we can do? Yes, since we can obtain a lower bound of (n - 1) comparisons for the problem of determining the minimum and another obligatory comparison for checking whether that minimum is equal to x. A representation of a set S with n positive integers is a Boolean circuit C, such that C accepts the binary representation of a bit integer i if and only if i is in S. Given a positive integer x and a Boolean circuit C, we define SUCCINCT-MINIMUM as the problem of deciding whether x is the minimum bit integer which accepts C as input. For certain kind of SUCCINCT-MINIMUM instances, the input (x, C) is exponentially more succinct than the cardinality of the set S that represents C. Since we prove that SUCCINCT-MINIMUM is at least as hard as MINIMUM in order to the cardinality of S, then we could not decide every instance of SUCCINCT-MINIMUM in polynomial time. If some instance (x, C) is not in SUCCINCT-MINIMUM, then it would exist a positive integer y such that y < x and C accepts the bit integer y. Since we can evaluate whether C accepts the bit integer y in polynomial time and we have that y is polynomially bounded by x, then we can confirm SUCCINCT-MINIMUM is in coNP. If any single coNP problem cannot be solved in polynomial time, then P is not equal to coNP. Certainly, P = NP implies P = coNP because P is closed under complement, and therefore, we can conclude P is not equal to NP.

You could read the details in the link below...

https://hal.archives-ouvertes.fr/hal-01509423/document