Poincare Conjecture
http://www.youtube.com/watch?v^ksQs8HWVX10&feature=fvw Pre-listening
1) What do you know about Poincare Conjecture?
2) Who and when solved that problem?
3) What is the Fields Medal?
4) What is a pinnacle?
Listen to and watch the video and answer the questions.
1) What was the question Henri Poincare asked?
2) When was the problem posed?...................................................
3) What is a sphere?...................................................................
4) What is the reason why the presented cannot be inflated to form a sphere?
5) If you inflate an object, which two possible shapes can you get?
6) What happens when you tighten a loop around a ball?
7) What is the difference between a surface of a sphere and of a doughnut?
8) Why is the solution important for scientists?...........
9) What is the so called "blue skies research?.............
10) What does Adam say about Grigori Perelman?
11) What is the thing the presenter will never understand?
m&3 NEWS
Great maths puzzle 'solved1
By Dr David Whitehouse
BBC News Online science editor
Story from BBC NEWS:
http://news.bbc.co.Uk/go/pr/fr/-/2/hi/science/nature/3005875.stm 1) Replace the underlined words with their synonyms.
A Russian mathematician claims to have proved the Poincare Conjecture, one of the most famous problems in mathematics.
Dr Grigori Perelman, of the Steklov Institute of Mathematics of the Russian Academy of Sciences, St Petersburg, has been touring US universities describing his work in a series of papers not yet completed. The Poincare Conjecture, an idea about three-dimensional objects, has haunted mathematicians for nearly a century. If it has been solved, the consequences will reverberate throughout geometry and physics. If his proof is accepted and survives two years of scrutiny. Perelman could also he eligible for a $lm prize sponsored by the Clay Mathematics Institute in Massachusetts for solving what the centre describes as one of the seven most important unsolved mathematics problems of the millennium.
2) Formulate questions so that you can answer with the expressions in italics.
1).................■.....■.................................................................................
2).....................................•....................■...............................................
3) .........................................................................................................
4) .....-....................................................................................................
5) ..........................................................................................................
Spheres and doughnuts
Formulated by the remarkable French mathematician Henri Poincare in 1904, the conjecture is a central question in topology, the study of the geometrical properties of objects that do not change when they are stretched, distorted or shrunk. For example, the hollow shell of the surface of the Earth is what topologists call a two-dimensional sphere. It has the property that every lasso of string encircling it can be pulled tight to a point. On the surface of a doughnut however, a lasso passing through the hole in the centre cannot be shrunk to a point without cutting through the surface meaning that, topologically speaking, spheres and doughnuts are different.
Since the J9th Century, mathematicians have known that the sphere is the only enclosed two-dimensional space with this property. But they were uncertain about objects with more dimensions. The Poincare Conjecture says that a three-dimensional sphere is the only enclosed three-dimensional space with no holes. But the proof of the conjecture has eluded mathematicians. Poincare himself demonstrated that his earliest version of his conjecture was wrong. Since then, dozens of mathematicians have asserted that they had proofs until fatal flaws were found.
3) Fill in the missing prepositions. Internet rumours
Rumours about Perelman's work have been circulating a)......November, when he posted the first of
his papers reporting the result b).....an internet preprint server, c).........then, Perelman has
persistently declined to be interviewed, saying any publicity would be premature.
Dr Tomasz Mrowka, a mathematician d).......the Massachusetts Institute of Technology, said: "It's
not certain, but we're taking it very seriously. "We're desperately trying to understand what he has done here," he adds.
Some are comparing Perelman's work e)......that of Andrew Wiles, who famously solved Fermat's
Last Theorem a decade ago. Indeed, Wiles was f)......the Taplin Auditorium g)........Princeton
University, New Jersey, where he holds a chair h)........mathematics, to hear Perelman describe his
work recently, i).........him sat John Nash, the Nobel Laureate who inspired the film A Beautiful
Mind.
4) Decide whether the statements are true or false.
a) Perelman in fact wanted to prove the Geometrization Conjecture, not Poincare Conjecture.
b) William Thurston's proposal is more complicated than the Poincare's Conjecture.
c) The Poincare result is just a by-product of more complex discoveries.
d) With the Poincare Conjecture solved, we can describe all shapes of the Universe.
Million dollar afterthought
What is all the more remarkable about Perelman's proposal is that he is trying to achieve something far grander than merely solving Poincare's Conjecture. He is trying to prove the Geometrisation Conjecture proposed by the American mathematician William Thurston in the 1970s - a far more ambitious proposal that defines and characterises all three-dimensional surfaces. "He's not facing Poincare directly, he's just trying to do this grander scheme," said Professor Peter Sarnak, of Princeton.
After creating so much new mathematics, the Poincare result is just "a million dollar afterthought," he said. If Perelman has solved Thurston's problem then experts say it would be possible to produce a catalogue of all possible three-dimensional shapes in the Universe, meaning that we could ultimately describe the actual shape of the cosmos itself.
3) HW: Find out who these scholars are:
a) Andrew Wiles.........................
b) William Thurston......................
c) Tomasz Mrowka.......................
d) Peter Sarnak............................
e) John Nash...............................