Censorship and Facebook

Facebook has just removed almost all my posts those have been posted by me in different groups including those in my profile. why? because they think those posts are spam. without any extra explanation. 
I went to the support box in which is just a name, and tick all those posts as “it’s not spam’. but then I received same message: we have removed because it looks like spam…”.
More Facebook gets experienced, more it becomes a cruel stupid robot. you at Facebook think it is a good idea to design a robot (as you may answer me no!! they are algorithms!) for every simple task? 
If I am not able to present my posts in different groups so tell me what would be the reason I am working here on my network? 

Largest known prime number discovered: Why it matters

This article has been chosen from: https://anthonybonato.com

In the movie Contact based on the novel of the same name by Carl Sagan, Dr. Ellie Arroway searches for intelligent extraterrestrial life by scanning the sky with radio telescopes. When Arroway, played by Jodie Foster, recognizes prime numbers in an interplanetary signal, she believes it’s proof that an alien intelligence has sent the human race a message.
A number is considered prime if it is only divisible by one and itself. For example, two, three, five and seven are prime. The number 15, which is three times five, is not prime. It’s no coincidence that Arroway believes the aliens in Contact use prime numbers as a cosmic “hello” — they are building blocks of other numbers. Every number is a product of primes.
In December 2017, the largest known prime number was discovered using a computer search. The prime was discovered by Jonathan Pace, an electrical engineer who currently works at FedEx. Why is this important? Because without prime numbers your banking information, Paypal transactions or Amazon purchases could be compromised.
Large primes, like the one just discovered, play a critical role in cyber-security. Cryptography is the science of encoding and decoding information, and many of its algorithms, such as RSA, rely heavily on prime numbers.
Mersenne primes
While there are infinitely many primes, there is no known formula to generate them all. A race is ongoing to find larger primes using a mixture of math techniques and computation.
One way to get large primes uses a mathematical concept discovered by the 17th-century French monk and scholar, Marin Mersenne.
Marin Mersenne. H Loeffel, Blaise Pascal,
Basel: Birkhäuser 1987
CC BY-NC
A Mersenne prime is one of the form 2ⁿ – 1, where n is a positive integer. The first four of these are three, seven, 31 and 127.
Not every number of the form 2ⁿ – 1 is prime, however; for example, 2⁴ – 1 = 15. If 2ⁿ – 1 is prime, then it can be shown that n itself must be prime. But even if n is prime, there is no guarantee the number 2ⁿ – 1 is prime: 2¹¹ – 1 = 2,047, which is not prime as it equals 23 times 89.
There are only 50 known Mersenne primes. An unresolved conjecture is that there is an infinite number of them.
The search for new primes
The Great Internet Mersenne Prime Search (or GIMPS) is a collaborative effort of many individuals and teams from around the globe to find new Mersenne primes. George Woltman began GIMPS in 1996, and in 2018 it includes more than 183,000 volunteer users contributing the collective power of over 1.6 million CPUs.
The most recently discovered Mersenne prime is succinctly written as 2⁷⁷²³²⁹¹⁷ – 1; that’s two multiplied by itself 77,232,917 times, minus one. Jonathan Pace’s discovery took six days of computation on a quad-core Intel i5-6600 CPU, and was independently verified by four other groups.
The newly discovered prime has a whopping 23,249,425 digits. To get a sense of how large that is, suppose we filled up a book with digits, each digit counted as a word and each book having a hundred thousand words. Then the digits of 2⁷⁷²³²⁹¹⁷ – 1 would fill up about 232 books!
How does GIMPS find primes?
GIMPS uses the Lucas-Lehmer test for primes. For this, form a sequence of integers starting with four, and whose terms are the previous term squared and minus two. The test says that the number 2ⁿ – 1 is prime if it divides the (n-2)th term in the sequence.
While the Lucas-Lehmer test looks easy enough to check, the computational bottleneck in applying it comes from squaring numbers. Multiplication of integers is something every school-aged kid can do, but for large numbers, it poses problems, even for computers. One way around this is to use Fast Fourier Transforms (FFT), algorithms that speed up computations.
Anyone can get involved with GIMPS — as long as you have a decent computer with an internet connection. Free software to search for Mersenne primes can be found on the GIMPS website.
While the largest known prime is stunningly massive, there are infinitely many more primes beyond it waiting to be discovered. Like Ellie Arroway did in Contact, we only have to look for them.
Anthony Bonato

Math is not Science!

I enjoy reading this article so much. Dan Ashlock is about to show why Math is more similar to humanities rather experimental sciences. I strongly recommend you to read it:
Cartoon from the weblog Occupy the Math
Occupy Math is a member of the College of Physical and Engineering Sciences at the University of Guelph. The fact that the Department of Mathematics and Statistics is in this college makes it seem as if mathematics is one of the sciences — but it is not. Math is often considered to be part of the natural sciences, and it is central to and remarkably useful to the natural sciences, but the techniques, methods, and philosophy of math are different from those of natural science. Technically, based on its techniques, mathematics is the most extreme of the humanities.
The center of the natural sciences is hypothesis-driven research and experimentation. Experiments yield evidence that supports or fails to support a hypothesis. When new information arrives from experiments, a hypothesis may be revised. Math does exactly none of this. In math, a statement is shown to be true or false by logical argumentation. This means that there is no doubt once a proof of the truth or falsity of a mathematical statement is finished. The methods of mathematics are so different from those of the natural sciences that it is clearly a different sort of animal.
Why do people think math is a science?
The short version of the answer is because (i) many scientists use a lot of math and (ii) a whole lot of math was discovered in order to answer a scientific question. Someone once asked Sir Isaac Newton if the mass of a planet could be considered to be concentrated in the center of mass. He answered in the affirmative — and in order to do so, he invented at least part of integral calculus.
Both scientists and mathematicians perform extensive calculations. This makes them seem similar to people. One of the most mathematical fields, however, is economics — one of the humanities. One of the primary tools that mathematicians use in proving things is formal logic. Formal logic is one of the fields within philosophy — another humanity. Alfred North Whitehead and Bertrand Russell tried to prove that all of math could be deduced by first order logic. Gödel’s incompleteness theorem showed this was not possible — but the proof Gödel constructed illustrates that mathematics is more similar to formal linguistics than any of the natural sciences.
The contrast between math and science.
A new piece of mathematics starts with a guess at something that might be true, called a conjecture. Some conjectures are resolved quickly by the person that proposed them, others last for centuries. Fermat’s last theorem, for example, was actually a conjecture for over 350 years, until it was finally proved in 1995. Contrast this with the Law of Universal Gravitation. This law was never proved logically — rather, it agrees very well with numerous observations. It’s also slightly wrong in some odd circumstances.
Proven mathematical theorems are beyond question. The laws discovered by science are really good approximations that are often false in some circumstances or in small ways. The certainty of math arises from its completely abstract nature. A mathematical theorem nevermakes a statement about reality. A theorem connects a statement about what the situation is to a result of that situation. The fundamental theorem of arithmetic says every whole number factors into prime numbers in exactly one way, as long as we ignore the order of those factors. Whole numbers are abstractions. We use them to count things, but we use our own human notion of “thing” to do it.
Except…
…there is such a thing as experimental mathematics. The methods of science are powerful and can reach farther, in some directions, that the methods of mathematics. The first step in making new math is a conjecture and experiments are a good way to find conjectures that are likely to be true. Occupy Math’s own doctoral thesis used a series of experiments — none of which appeared in the final document. The experiments suggested how to build a whole series of secret codes and also what their structure was. This suggestion led to a conjecture — and (nine months later) to a proof about the structure of the codes — that showed all of them were easy to crack. At the time Occupy Math was in graduate school, reporting the experiments would have been socially unacceptable.
Most of the things that science works on are much too hard to figure out using only the techniques of mathematics. Many of the things that mathematics figures out are unrelated to physical reality. The relationship between math and science is symbiotic. Science views math as an important source of tools, math views science as a wonderful source of examples. Beyond this, the needs of science often spark the discovery of new mathematics and, occasionally, math worked out in a completely abstract setting turns out to be useful for science. Some of the topology that describes string theory, for example, is older than the idea of string theory.
Occupy Math has read, listened to, and participated in many discussions about the relationship between math and science. His view, that they are symbiotic but different, is the result of long cogitation on the issue. If you have your own thoughts on this, please comment!
I hope to see you here again,
Daniel Ashlock,
University of Guelph,
Department of Mathematics and Statistics
The link of the article: Math is not science!

Riemann Hypothesis

Riemann Hypothesis is one the most challenging mathematical problems that human have ever faced with, still unsolved and seem to be uncontrollable. So everyone naturally will find it important to study . Here I have collected some links those I find easy quick guide for someone, like me, unaware about the technical aspects of it, I hope you find them useful:

  1. Will Big Data solve the Riemann Hypothesis? (Posted by Eduardo Siman on February 11, 2016 in Data Science Central)
  2. The Riemann Hypothesis Explained (Posted by ToK maths on June 24, 2013 in IB Maths)

History of Women Mathematicians

At this link you will find an Alphabetical Index of Women Mathematicians

As an example of these biography I am about to quote the biography of Maryam Mirzakhani, the first woman who wins the fields medal in mathematics:
Maryam Mirzakhani (May 3, 1977 – July 15, 2017) was the first woman to be awarded the Fields Medal, the highest award given in mathematics (comparable to a Nobel Prize). She was born in Tehran, Iran. During her high school years she won gold medals at the 1994 and 1995 International Mathematical Olympiads (with a perfect score on the 1995 exam), then earned her B.S. degree in mathematics in 1999 from Sharif University of Technology in Tehran. In 2004 she received her Ph.D. in mathematics from Harvard University with a thesis in hyperbolic geometry entitled “Simple Geodesics on Hyperbolic Surfaces and Volume of the Moduli Space of Curves”. Her work solved several deep problems about hyperbolic surfaces and resulted in three papers published in the top journals of mathematics. Her adviser was Curtis McMullen, who won a Fields Medal in 1998.

From 2004 to 2008 Mirzakhani was a Clay Mathematics Institute Research Fellow and assistant professor of mathematics at Princeton University. In 2006 she was recognized as one of Popular Science’s “Brilliant 10” extraordinary scientists. In 2008 she joined the faculty at Stanford University as a full professor of mathematics.
In August 2014, Mirzakhani was awarded the Fields Medal “for her outstanding contributions to the dynamics and geometry of Riemann surfaces and their moduli spaces.” The citation says that she “has made stunning advances in the theory of Riemann surfaces and their moduli spaces, and led the way to new frontiers in the area. Her insights have integrated methods from diverse fields, such as algebraic geometry, topology and probability theory.” Previously she had also won a 2014 Clay Research Award, the 2013 AMS Ruth Lyttle Satter Prize in Mathematics, and the 2009 AMS Blumenthal Award.
References:
  1. A Tribute to Maryam Mirzakhani, American Mathematical Society
  2. Salerno, Adriana. “Remembering Maryam Mirzakhani,” AMS Blogs, posted July 24, 2017.
  3. Wilkinson, Amie. “With Snowflakes and Unicorns, Marina Ratner and Maryam Mirzakhani Explored a Universe in Motion,” New York Times, August 7, 2017.
  4. Lamb, Evelyn. “Mathematics World Mourns Maryam Mirzakhani, Only Woman to Win Fields Medal,”, Scientific American blog, posted July 17, 2017
  5. Myers, Andrew and Bjorn Carey. “Maryam Mirzakhani, Stanford mathematician and Fields Medal winner, dies”, Stanford University News, July 15, 2017.
  6. Klarreich, Erica. A Tenacious Explorer of Abstract Surfaces,, Quanta Magazine (a video produced by the Simons Foundation in which Mirzakhani discusses the mathematics problems she studies).
  7. Carey, Bjorn. “Stanford’s Maryam Mirzakhani wins Fields Medal”, Stanford Report, August 12, 2014.
  8. “The Work of Maryam Mirzakhani”, Notices of the American Mathematical Society, Vol. 61, No. 9 (October 2014), 1079-1081. (Reprint of the IMU article above)
  9. McMullen, Curtis. “The work of Maryam Mirzakhani,” Laudatio delivered during the 2014 International Congress of Mathematicians.
  10. Svoboda, Elizabeth. “Maryam Mirzakhani“, PopSci’s Fourth Annual Brilliant 10, PopSci.com.
  11. MathSciNet [subscription required]
  12. Mathematics Genealogy Project

Well-Ordering Property of N

One of the most challenging theorems in Mathematics, for me, is the well-ordering property of N. You may wonder why, because it is not so hard to understand. Yes you are right, it’s easy! the principle by itself is easy to understand and also you will very soon learn how to apply it. I have this problem with proves which has been presented in different books. As you know it appears, as its nature, in very first pages of any book so called “first course in analysis”, “first course in abstract algebra” and also all books of “first course in set theory”. So any math student faces with this principal almost three times in the first year of licence. And then, as you may have seen, there is always a unique proof in each book. I have always been facing with this situation that they use something to prove a principal in which those facts by themselves more need proofs than the principle. Have you ever thought about it? why everybody insist to prove it in a new way? and why they use unclear thing to prove it? why while proving all other theorems of mathematics, all books follow the same methods?

Talitha M. Washington

This article has been chosen from: Mathematically Gifted and Black

Dr. Talitha M. Washington is an Associate Professor of Mathematics at Howard University in Washington, DC, and is currently on detail as a Program Officer at the National Science Foundation. Prior to coming to Howard, she was an Assistant Professor of Mathematics at the University of Evansville (2005-2011), an Assistant Professor of Mathematics at The College of New Rochelle (2003-2005), and a VIGRE Research Associate at Duke University (2001-2003).  Dr. Washington holds a 2001 Ph.D. in mathematics from the University of Connecticut with specialization in applied mathematics.

Dr. Washington grew up in Evansville, Indiana and appreciates the familial atmosphere of this community.  While growing up, she enjoyed learning about all subjects.  In high school, her favorite classes were AP Chemistry and an English course on classical plays.  She graduated from Bosse High School a semester early and studied abroad in Costa Rica for six months on an exchange program with American Field Service.  She then entered Spelman College as an engineering major simply because engineering is a popular field in Indiana.  However, this major appeared to require too much work.  Thus, she chose to major in math because of its connection to engineering, and it appeared to be the easier major because there was no laboratory component.  Little did she know, she would fall in love with the subject and lead a long, distinguished career in mathematics.

As an undergraduate, she studied abroad at the Universidad Autónoma de Guadalajara in Mexico where she took a proof-based linear algebra course and earned a 0 on her first assignment. Determined to succeed, she rallied her new classmates to study in the library. By the end of the semester, she earned 100’s on her assignments. This experience taught her that obstacles can be overcome by cultivating and building a community of learners. Upon returning from Mexico to Spelman, she researched the Black-Scholes option pricing model under the direction of Dr. Jeffrey Ehme.  After a summer internship at CIGNA in Hartford, Connecticut, she became interested in pursuing a career in actuarial science.  Dr. Ehme encouraged her to apply to graduate school in addition to seeking positions in industry.  From the support and assistance from Dr. Ehme and other members in the Spelman math department, she gained acceptance at the University of Connecticut and funding from the Packard Foundation.  Thus, she declined an actuarial science position from CIGNA and began her graduate studies.  Since she had secured no employment the summer before entering graduate school, she decided to backpack through southern Mexico, Belize, and Guatemala for two months – sola.

Dr. Washington faced many obstacles along the way but she met them with vigor, resilience, and determination. To her surprise, she entered a graduate program with students who already had earned advanced degrees from other universities.  She met this challenge by actively seeking help and guidance from students and professors.  Diligently, she worked night and day to learn the background material necessary for success.  While she was in graduate school, she gave birth to her first child.  She gained assistance with this transitional time in her life by securing a doula, a professional labor support person, and by participating in a network of mothers through La Leche League.  She now has three vivacious STEM teenagers who are in pursuit of computer science, engineering, and biology.

While in graduate school, she enjoyed the vibrant atmosphere of working through mathematical problems and in particular, the many applications of math.  With her advisor, Dr. Yung-Sze Choi, she researched a theoretical protein-protein interaction model.  They also became involved with the National Resource for Cell Analysis and Modeling at University of Connecticut Health Center.  Dr. Choi pushed Dr. Washington to further her work in mathematics by securing a postdoctoral position.  Thus, after graduating, she headed down to Duke University where she researched a hormone secretion model with Dr. Michael Reed and Dr. Joseph Blum, in the mathematics and cell biology departments, respectively.

Recently, she has researched a fellow Evansville native, Dr. Elbert F. Cox, who is the first Black in the world to earn a Ph.D. in mathematics.  She has shared his story on radio and television stations, as well as in the Notices of the American Mathematical Society, easily the most visible journal to all mathematicians.  With her applied background, she led various undergraduate and graduate research projects from modeling the Tacoma Narrows Bridge to modeling calcium homeostasis to the construction of nonstandard finite difference schemes.  With her passion for education, she led a youth conference, Stepping Up, that encouraged youth to pursue viable careers through higher education.  She also led a one-week research-based summer camp for middle schoolers to explore current trends in mathematics and the sciences.

Dr. Washington enjoys her work at Howard University, in the same mathematics department Elbert Cox once led. As a program officer at the National Science Foundation, she is responsible for shaping the nation’s science and engineering enterprise and ensuring that underrepresented groups and diverse institutions across all geographic regions are included in the scientific enterprise of the nation.  In her spare time, she serves on a number of boards and shares motivational speeches on diversity and mathematics to a wide range of audiences. She balances stress by maintaining a rigorous exercise regimen with fitness guru Cathe Friedrich, that includes kickboxing, step aerobics, strength training, and yoga.  During the warm seasons, you may even find her running down the Rock Creek Park trails in Washington, DC.