The longer mathematics lives the more abstract - and therefore, possibly also the more practical - it becomes.

Fashion as King is sometimes a very stupid ruler.

Wherever groups disclosed themselves, or could be introduced, simplicity crystallized out of comparative chaos.

If a lunatic scribbles a jumble of mathematical symbols it does not follow that the writing means anything merely because to the inexpert eye it is indistinguishable from higher mathematics.

In his wretched life of less than twenty-seven years Abel accomplished so much of the highest order that one of the leading mathematicians of the Nineteenth Century could say without exaggeration, "Abel has left mathematicians enough to keep them busy for five hundred years." Asked how he had done all this in the six or seven years of his working life, Abel replied, "By studying the masters, not the pupils."

Pick the assumptions to pieces till the stuff they are made of is exposed to plain view - this is the cardinal rule for understanding the basis of our beliefs.

Science makes no pretension to eternal truth or absolute truth.