Kasner and Newman: New Names for Old




Here is a booby-prize definition of mathematics: Mathematics is the science which uses easy words for hard ideas.


数学中的普通词汇,有着特有的含义。如:Simple curve。

A simple curve is a closed curve which does not cross itself.

A French mathematician, Jordan, gave the fundamental theorem: every simple curve has one inside and one outside. That is, every simple curve divides the plane into two regions, one inside the curve, and one outside.

  This is not a simple curve.

 This is a single curve.

其它几个数学词汇的例子: function, turbine, circle, parhexagon, and radical, etc.


数学概念中天文数字 googol 与 googolplex 的意义。 这些数字 was finite, not infinite.


The name “googol” was invented by a child (Dr. Kasner’s nine-year-old nephew) who was asked to think up a name for a very big number, namely, 1 with a hundred zeros after it.


数学中的新名词, 如 mathescope,

The mathescope is not a physical instrument; it is a purely intellectual instrument, the ever-increasing insight which mathematics gives into the fairyland which lies beyond intuition and beyond imagination.



 (GGB, Vol. 9, pp. 121-136; originally chapter 1 of Mathematics and the Imagination)



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