The full impact of the Lobachevskian method of challenging axioms has probably yet to be felt. It is no exaggeration to call Lobachevsky the Copernicus of Geometry [as did Clifford], for geometry is only a part of the vaster domain which he renovated; it might even be just to designate him as a Copernicus of all thought.
Interpretation
Lobachevsky's method fundamentally changed our understanding of geometry and thought.
Eric Temple Bell recognizes Lobachevsky's revolutionary impact on geometry, comparing him to Copernicus, who transformed our perception of the universe. Lobachevsky's contributions extend beyond geometry, suggesting that he altered the very foundations of logical reasoning and intellectual discourse in a broader context, indicating the profound reach of his ideas in shaping modern thought.
In practice
In a lecture discussing the evolution of mathematical thought, one might reference Lobachevsky as a pivotal figure.
Guided only by their feeling for symmetry, simplicity, and generality, and an indefinable sense of the fitness of things, creative mathematicians now, as in the past, are inspired by the art of mathematics rather than by any prospect of ultimate usefulness.
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."
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.
Abstractness, sometimes hurled as a reproach at mathematics, is its chief glory and its surest title to practical usefulness. It is also the source of such beauty as may spring from mathematics.
Any impatient student of mathematics or science or engineering who is irked by having algebraic symbolism thrust upon him should try to get along without it for a week.
...It would be more consistent that we call [the Bible] the work of a demon than the word of God. It is a history of wickedness that has served to corrupt and brutalize mankind.
I have here only made a nosegay of culled flowers, and have brought nothing of my own but the thread that tied them together.
No effect of work can be eternal.
No method of procedure has ever been devised by which liberty could be divorced from local self-government. No plan of centralization has ever been adopted which did not result in bureaucracy, tyranny, inflexibility, reaction, and decline.
Unless some other factor is operative, in large, weak and underpopulated states, the luxury of ostentation prevails over that of comfort; but in countries which are more populous than extensive, the luxury of comfort always diminishes ostentation.
Faith is part of who I am, yes. I was raised Christian Scientist. The most important thing I saw every single week on the wall at Sunday school was the Golden Rule: "Do unto others as you would have them do unto you."
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