On one occasion, Hilbert squeaked to the assembly: There have been two great crises in the FoundationsofMathematics.
有一天，希尔伯特对它的听众说：数学基础存在两个极大的危机。
2
One may also imagine how distasteful it should be to mathematician to show them that the greatest mathematical conjecture ever, that seems provide the number theoretical foundationsofmathematics.
人们可以想象，向一位数学家出示看来为数学提供数论基础的数学猜想是一件多么令人讨厌的事。
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This is a work of utmost importance in that it lays the foundationsof logic into mathematics and enables us to use this as a tool to explore the unknown.