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.
Such is the condition of life that something is always wanting to happiness. In youth we have warm hopes, which are soon blasted by rashness and negligence, and great designs which are defeated by inexperience. In age, we have knowledge and prudence, without spirit to exert, or motives to prompt them; we are able to plan schemes, and regulate measures, but have not time remaining to bring them to completion.
The central belief of every moron is that he is the victim of a mysterious conspiracy against his common rights and true deserts.
Anybody who is one with what he or she does is building the new earth.
The cross is the surest, truest and deepest window on the very heart and character of the living and loving God.
Blasphemy is an epithet bestowed by superstition upon common sense.
I would rather be a man of paradoxes than a man of prejudices.
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