Perelman - Revision history

Grad at 20:50, 1 May 2015

2015-05-01T20:50:28Z

Grad at 20:45, 1 May 2015

2015-05-01T20:45:48Z

Grad at 20:43, 1 May 2015

2015-05-01T20:43:52Z

Grad at 20:23, 1 May 2015

2015-05-01T20:23:10Z

Grad at 19:47, 1 May 2015

2015-05-01T19:47:24Z

Grad at 19:41, 1 May 2015

2015-05-01T19:41:33Z

Grad at 22:01, 30 April 2015

2015-04-30T22:01:40Z

Grad at 21:59, 30 April 2015

2015-04-30T21:59:59Z

Grad: Created page with "Two dimensional compact orientable surfaces can be characterized by their genus, which is loosely the number of holes. For example, the surface of a doughnut has one hole, bu..."

2015-04-30T21:58:53Z

Created page with "Two dimensional compact orientable surfaces can be characterized by their genus, which is loosely the number of holes. For example, the surface of a doughnut has one hole, bu..."

New page

Two dimensional compact orientable surfaces can be characterized by their genus, which is loosely the number of holes. For example, the surface of a doughnut has one hole, but the surface of a ball has zero holes. One property of a two dimensional sphere, the surface of a ball, is that any loop on the sphere can be continuously shrunk down to a point without leaving or breaking the surface. This property classifies a collection of certain two dimensional surfaces.

In 1904, Henri Poincaré asked a corresponding question in three dimensions. This conjecture went unsolved for almost 100 years. In 2000, the Clay Mathematics Institute posted seven unsolved math problems, each with a one million dollar prize attached. One of which is the Poincaré conjecture. An equivalent version of his question is

If a compact three-dimensional manifold, ''M'', is simply connected, is it then true that ''M'' is homeomorphic to the 3-sphere?

In 2002 and 2003, Grigori Perelman solved the Poincaré conjecture in a series of articles posted on ArXiv.org. However, Perelman did not seem to care about the prize or the recognition. He declined the one million dollar prize. In 2006, he was awarded the Fields medal, which is sometimes described as the Nobel prize for mathematics. He rejected the Fields medal as well. Before Perelman, no other mathematician had ever rejected the Fields medal. Perelman commented, "If the proof was correct then no other recognition was needed."

@@ Line 13: / Line 13: @@
 [References]:<br>
-Pickover, C. A. (2008), ''The Math Book.'', New York, NY: Sterling Publishing Co., Inc.<br>
+Pickover, C. A. (2008), ''The Math Book.'' New York, NY: Sterling Publishing Co., Inc.<br>
 Nasar, S., Gruber, D. (2006), Manifiold Destiny, ''The New Yorker,'' http://www.newyorker.com/magazine/2006/08/28/manifold-destiny

@@ Line 13: / Line 13: @@
 [References]:<br>
-Pickover, C. A.''The Math Book'', New York, NY: Sterling Publishing Co., Inc.<br>
+Pickover, C. A. (2008), ''The Math Book.'', New York, NY: Sterling Publishing Co., Inc.<br>
-Nasar, S., Gruber, D. (2006), Manifiold Destiny, http://www.newyorker.com/magazine/2006/08/28/manifold-destiny
+Nasar, S., Gruber, D. (2006), Manifiold Destiny, ''The New Yorker,'' http://www.newyorker.com/magazine/2006/08/28/manifold-destiny

← Older revision		Revision as of 20:43, 1 May 2015
Line 10:		Line 10:

	Perelman may not have desired an award for his work, but he was willing to discuss it. In 2003, he was invite to give a series of talks on his paper at M.I.T., Princeton, and Stony Brook. He accepted all these invitations. When asked about the invitations, he commented simply, "why not?"		Perelman may not have desired an award for his work, but he was willing to discuss it. In 2003, he was invite to give a series of talks on his paper at M.I.T., Princeton, and Stony Brook. He accepted all these invitations. When asked about the invitations, he commented simply, "why not?"
		+
		+
		+	[References]:<br>
		+	Pickover, C. A.''The Math Book'', New York, NY: Sterling Publishing Co., Inc.<br>
		+	Nasar, S., Gruber, D. (2006), Manifiold Destiny, http://www.newyorker.com/magazine/2006/08/28/manifold-destiny

@@ Line 1: / Line 1: @@
 Two-dimensional compact orientable surfaces can be characterized by their genus, which is loosely the number of holes.  For example, the surface of a doughnut has one hole, but the surface of a ball has zero holes. One property of a two-dimensional sphere, the surface of a ball, is that any loop on the sphere can be continuously shrunk down to a point without leaving or breaking the surface.  This property classifies a collection of certain two-dimensional surfaces.
-In 1904, Henri Poincaré asked a corresponding question in three dimensions.  This conjecture went unsolved for almost 100 years.  In 2000, the Clay Mathematics Institute posted seven unsolved math problems, each with a one million dollar prize attached.  One of which is the Poincaré conjecture.  An equivalent version of his question is as follows.
+In 1904, Henri Poincaré asked a corresponding question in three dimensions.  This conjecture went unsolved for almost 100 years.  In 2000, the Clay Mathematics Institute posted seven unsolved math problems, each with a one million dollar prize attached.  These questions are called the millennium problems.  One of which is the Poincaré conjecture.  An equivalent version of his question is as follows.
 ''If a compact three-dimensional manifold, M, has the property that every simple closed curve can be continuously deformed to a point , is it then true that M is homeomorphic to the 3-sphere?''
@@ Line 7: / Line 7: @@
 Here the 3-sphere is the three-dimensional boundary of a four-dimensional ball, such as the set of points <math style="vertical-align:-25%">(x,y,z,w)</math>, such that <math style="vertical-align:-20%">x^2+y^2+z^2+w^2=1</math>.
-In 2002 and 2003, Grigori Perelman solved the Poincaré conjecture in a series of articles posted on ArXiv.org.  However, Perelman did not seem to care about the prize or the recognition.  He declined the one million dollar prize. In 2006, he was awarded the Fields medal, which is sometimes described as the Nobel prize for mathematics.  He rejected the Fields medal as well.  Perelman commented, "if the proof was correct then no other recognition was needed."
+In 2002 and 2003, Grigori Perelman solved the Poincaré conjecture in a series of articles posted on ArXiv.org.  However, Perelman did not seem to care about the prize or the recognition.  Astonishingly, he declined the one million dollar prize. In 2006, he was awarded the Fields medal, which is sometimes described as the Nobel prize for mathematics.  He rejected the Fields medal as well.  Perelman commented, "if the proof was correct then no other recognition was needed."

@@ Line 5: / Line 5: @@
 ''If a compact three-dimensional manifold, M, has the property that every simple closed curve can be continuously deformed to a point , is it then true that M is homeomorphic to the 3-sphere?''
-Here the 3-sphere is the three-dimensional boundary of a four-dimensional ball, such as the set of points <math>(x,y,z,w)</math>, such that <math>x^2+y^2+z^2+w^2=1</math>.
+Here the 3-sphere is the three-dimensional boundary of a four-dimensional ball, such as the set of points <math style="vertical-align:-25%">(x,y,z,w)</math>, such that <math style="vertical-align:-20%">x^2+y^2+z^2+w^2=1</math>.
 In 2002 and 2003, Grigori Perelman solved the Poincaré conjecture in a series of articles posted on ArXiv.org.  However, Perelman did not seem to care about the prize or the recognition.  He declined the one million dollar prize. In 2006, he was awarded the Fields medal, which is sometimes described as the Nobel prize for mathematics.  He rejected the Fields medal as well.  Perelman commented, "if the proof was correct then no other recognition was needed."

← Older revision		Revision as of 22:01, 30 April 2015
Line 5:		Line 5:
	If a compact three-dimensional manifold, ''M'', is simply connected, is it then true that ''M'' is homeomorphic to the 3-sphere?		If a compact three-dimensional manifold, ''M'', is simply connected, is it then true that ''M'' is homeomorphic to the 3-sphere?

−	In 2002 and 2003, Grigori Perelman solved the Poincaré conjecture in a series of articles posted on ArXiv.org. However, Perelman did not seem to care about the prize or the recognition. He declined the one million dollar prize. In 2006, he was awarded the Fields medal, which is sometimes described as the Nobel prize for mathematics. He rejected the Fields medal as well. ~~Before Perelman, no~~ other mathematician had ever rejected the Fields medal. Perelman commented, "if the proof was correct then no other recognition was needed."	+	In 2002 and 2003, Grigori Perelman solved the Poincaré conjecture in a series of articles posted on ArXiv.org. However, Perelman did not seem to care about the prize or the recognition. He declined the one million dollar prize. In 2006, he was awarded the Fields medal, which is sometimes described as the Nobel prize for mathematics. He rejected the Fields medal as well. No other mathematician had ever rejected the Fields medal nor solved a millennium problem, for that matter. Perelman commented, "if the proof was correct then no other recognition was needed."

@@ Line 1: / Line 1: @@
 Two dimensional compact orientable surfaces can be characterized by their genus, which is loosely the number of holes.  For example, the surface of a doughnut has one hole, but the surface of a ball has zero holes. One property of a two dimensional sphere, the surface of a ball, is that any loop on the sphere can be continuously shrunk down to a point without leaving or breaking the surface.  This property classifies a collection of certain two dimensional surfaces.
-In 1904, Henri Poincaré asked a corresponding question in three dimensions.  This conjecture went unsolved for almost 100 years.  In 2000, the Clay Mathematics Institute posted seven unsolved math problems, each with a one million dollar prize attached.  One of which is the Poincaré conjecture.  An equivalent version of his question is
+In 1904, Henri Poincaré asked a corresponding question in three dimensions.  This conjecture went unsolved for almost 100 years.  In 2000, the Clay Mathematics Institute posted seven unsolved math problems, each with a one million dollar prize attached.  One of which is the Poincaré conjecture.  An equivalent version of his question is below.
   If a compact three-dimensional manifold, ''M'', is simply connected, is it then true that ''M'' is homeomorphic to the 3-sphere?
-In 2002 and 2003, Grigori Perelman solved the Poincaré conjecture in a series of articles posted on ArXiv.org.  However, Perelman did not seem to care about the prize or the recognition.  He declined the one million dollar prize. In 2006, he was awarded the Fields medal, which is sometimes described as the Nobel prize for mathematics.  He rejected the Fields medal as well.  Before Perelman, no other mathematician had ever rejected the Fields medal. Perelman commented, "If the proof was correct then no other recognition was needed."
+In 2002 and 2003, Grigori Perelman solved the Poincaré conjecture in a series of articles posted on ArXiv.org.  However, Perelman did not seem to care about the prize or the recognition.  He declined the one million dollar prize. In 2006, he was awarded the Fields medal, which is sometimes described as the Nobel prize for mathematics.  He rejected the Fields medal as well.  Before Perelman, no other mathematician had ever rejected the Fields medal. Perelman commented, "if the proof was correct then no other recognition was needed."