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Preda Milhaescu is a good example http://en.wikipedia.org/wiki/Preda_Mihăilescu.http://en.wikipedia.org/wiki/Preda_Mihăilescu.

He received his PhD with 42, and proved the Catalan conjecture 5 years later.

The Catalan conjecture was open for 160 years.

He proposed in 2009 a proof of the Leopoldt conjecture, but I am not sure about the status of this.

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Preda Milhaescu is a good example http://en.wikipedia.org/wiki/Preda_Mihăilescu.

He received his PhD with 42, and proved the Catalan conjecture 5 years later.

The Catalan conjecture was open for 160 years.

He proposed in 2009 a proof of the Leopoldt conjecture, but I am not sure about the status of this.