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The correct answer is option 3. It states that Grigori Perelman works in the area of Cosmology, which is not correct. Grigori Perelman is indeed a genius from Russia, option 1 is correct. He gained recognition for solving the Poincaré conjecture, one of the toughest problems in mathematics. Option 2 is also correct, as he rejected offers of professorship from prestigious universities like Princeton and Stanford. Option 4 is also correct, as Perelman refused to accept the prestigious mathematician awards, the `Fields Medal` and the `Millennium Prize`. However, option 3 is incorrect as Perelman`s work primarily focuses on geometry and topology, not cosmology. His work on the Poincaré conjecture has had significant implications in these areas.