Headline August 19, 2017/ ''' MATHEMATICS -STUDENTS- *MONUMENTS* '''

''' MATHEMATICS -STUDENTS- 

*MONUMENTS* '''

*EXPLORING THE WORLD STUDENTS SOCIETY IN MOTION*   -to my utter delight,  memory rarely ever  fails me on that  :

In total secrecy, with a sleigh of hand  and with  cunningness  of a master, that would have delighted Houdini. I set up a  regular secret proficiency test-

And  without letting   these  many  great geniuses discern, I began looking for  Mathematical Talent:

Students :  Rabo, Haleema, Saima, Haider,  Mustafa/LUMS, Ahsen/LUMS, Hussain,  Shahzaib,   Reza/Canada, and   little   angels    Maynah,  Maria, Hannyia.

I found most of  them highly gifted in thinking Mathematics :

Rabo, Haleema, Saima,  Hussain, Mustafa, Salar, in particular  I found highly creative.  

*Rabo and Haleema and Salar and Hussain could articulate complex log*.   ''Look for higher learning and practice and  Masters in Mathematics. Technology is a slide, you could most easily spin out of control,'' I urged,  Rabo  and    Haleema   and  Hussain. 

Expectedly, and heartachingly, none complied. In most cases conventions and events overtook them.  With Hussain in all and  every likelihood ending up in a vertigo.

And with that I turn to Dr. Annie Wilkinson, professor of mathematics at the University of Chicago, for some great inspirations:      

The Mathematics section of the  National Academy of  Sciences lists 104 members. Just four, Yes, Just 4 are women. *And as recently as June, that number was six*.

Dr. Scientist Marina Ratner and Dr. Scientist  Maryam Mirzakhani  could not have been more different, in personality and background. 

Dr. Ratner was a Soviet-born Jew    who ended up at the  University of California, Berkeley, by way  of   Israel. She had a heart attack at 78 at her home in early July.

Success came rather later in her career,  in her 50s, when  she produced her most famous results, known as Ratner Theorems. They turned out to be surprisingly and broadly applicable, with many elegant uses.

In the early 1990s, when I was a graduate student at  Berkeley, a professor tried to persuade  Dr. Ratner to be my thesis adviser, She wouldn't consider it : 

She believed that years earlier she had failed her first  and only doctoral student and didn't want another.

Dr. Scientist Mirzakhani  was a  young  super star  from Iran who worked nearby at  Stanford University.  Just 40 when she died of cancer in July, she was the  first woman  to receive the prestigious Field Medal.

I first heard about Dr, Mirzakhani  when, as a graduate student, she proved a new formula describing the curves on a certain  abstract surfaces, an insight that turned out to have profound consequences  -offering, for example:

*A new proof of famous in conjecture  in  physics about quantum gravity*.

I was inspired by both women and their patient assault on  deeply difficult problems. Their work was closely related and is connected to some of the oldest questions in mathematics.

The  ancient Greek  were fascinated  by the  Platonic solid   -a three dimensional shape  that can be constructed by gluing together identical flat pieces in a uniform fashion.

The pieces must be  regular polygons, with all sides the same length and all angles equal. For example, a  a cube in a platonic solid  made of  eix squares.

Early philosophers wondered  how many platonic solids  there were. 

The definition appears to allow for infinite possibilities, yet, remarkably there are only five such solids, a fact whose proof is credited to the early  Greek mathematician Theaetetus .

The pairing of the seemingly limitless to a  finite number  is a case of what mathematicians call rigidity.

Something that is rigid cannot be deformed or bent without destroying its essential nature.

Like Platonic solids, rigid objects are typically rare, and sometimes theoretical  objects  can be so rigid they don't exist   -mathematical unicorns.

In common usage, rigidity connotes inflexibility, usually negatively.

Diamonds, however, owe their strength to the rigidity of their molecular structure, Controlled rigidity, that is, flexing along certain directions  -allows a suspension bridges to survive high winds.

Dr.Scientist Ratner and Dr. Scientist Mirzakhani were experts in this more subtle form of rigidity. They worked to characterize shapes preserved by motions of space.

One example, is a Mathematical Model called the Koch snowflake, which displays a repeating pattern of triangles along its edges.

The edge of this snowflake will look the same at whatever scale it is viewed.    

The  snowflake is fundamentally unchanged by rescaling ;  other mathematical objects remain the same under different types of motions.

The shape of a ball, for example is nor changed when it is spun.

Dr. Scientist Ratner and Dr. Scientist Mirzakhani studied shapes that are preserved under more sophisticated types of motions, and in higher dimensional spaces.  

The Honor and Serving of the  latest  Operational Research  on : Mathematics and Sciences continues.

With respectful dedication to  All the Mathematicians of the World, Students, Professors and Teachers.  See Ya all on !WOW!   -the World Students Society and Twitter-!E-WOW!   -the Ecosystem 2011:

''' Motion & Mystery '''

Good Night and God Bless

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