著名古希腊数学家海帕修斯依靠反证法对的无理性的发现，导致了数学史上第一次数学危机。
Famous ancient Greek mathematician Haipa be required to rely on the irrational Hughes found that the first mathematical crisis led to the history of mathematics.
这些曾经引发数学危机的悖论都是从特定数学共同体公认正确的背景知识中合乎逻辑地推导出来的。
These paradoxes which brought crises to mathematics have been deducted from the acknowledged correct background knowledge of cognitive community in specific scopes.
哥德尔不完备性定理抽走了数学家的逻辑美信仰，数学界出现了信仰危机。
Godel theorem made mathematicians lose their belief of logic beauty, the crisis of belief appeared in mathematical field.
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。
On one occasion, Hilbert squeaked to the assembly: There have been two great crises in the Foundations of Mathematics.
数学史上的三次危机都是由数学悖论引起的。
Three times of crisis in the history of mathematics is caused by mathematical paradox.
现在我们又陷入规模更大的危机，以至于我们要重新认识数学确定性。
Now we were entrapped into a crisis of a larger scale, and the mathematical definiteness was known again.
探讨焦作市解决煤矿衰竭危机实现成功转型的经验，建立了相应的数学模式。
Discussed the experience that Jiaozuo city solved the crisis of coal mine exhausting to realize changing city economic structural type successfully, built relative mathematic mode.
数学的爱好者可以通过对精算学的学习将他们的对数学的热情施展到解决金融危机的方案规划中。
Math lovers can apply that passion to problems of financial risk by entering the field of actuarial science.
这些矛盾中，最深刻的是数学悖论，数学史的三次危机都由悖论而起。
Among these contradictions mathematical paradox is the most profound since the 3 historical mathematical crises were all originated from mathematical paradox.
这些矛盾中，最深刻的是数学悖论，数学史的三次危机都由悖论而起。
Among these contradictions mathematical paradox is the most profound since the 3 historical mathematical crises were all originated from mathematical paradox.
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