23 Hilbert's Problems 

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At the second International Congress of Mathematicians which was held in Paris in 1900, Hilbert posed 23 questions to the world mathematicians to solve in the next century. Some of them were general, such as the axiomatisation of physics (see on Euclid's elements and find out what axioms, and axiomatisation mean), but some were specific and had been solved reasonably quickly. Hilbert's problems were designed to serve as examples for the kinds of problems which lead to mathematical researches that would advance mathematical knowledge and disciplines. Often such work would lead a researcher into something that was not obvious from the start. Quite a few books have been written on these problems, and those mathematicians who managed to solve any of them are considered to be leading mathematicians of their day. Just to get you a taste of the problems, here are the (very) simplified first ten of the total of twentythree. You can also have a look at the original description of problems which are given in the translation of the original paper delivered by Hilbert in 1900.

You can see some other solved and unsolved mathematical problems here, as well as some famous conjectures and theorems. David Hilbert  click on the picture to find more about him. XXV International Congress of Mathematicians was held in Madrid in 2006. You can explore their web site. See the web site of the Clay Mathematical Institute which is offering some large prices to those who can solve some old, and some new problems. 

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