Talk with M. Hermite. He never evokes a concrete image, yet you soon perceive that the more abstract entities are to him like living creatures.
Interpretation
The quote reflects on the ability of abstract concepts to feel as vibrant and real as living beings.
Henri Poincaré's quote emphasizes the unique perspective of M. Hermite, who engages in discussions that may not conjure specific images but instead illustrate the vitality and existence of abstract ideas. This suggests that while these concepts may lack tangibility, they can evoke deep understanding and appreciation, akin to interacting with living entities.
In practice
In a lecture about the nature of mathematics, one could quote Poincaré to explain the significance of abstract concepts.
When the logician has resolved each demonstration into a host of elementary operations, all of them correct, he will not yet be in possession of the whole reality, that indefinable something that constitutes the unity ... Now pure logic cannot give us this view of the whole; it is to intuition that we must look for it.
It is a misfortune for a science to be born too late when the means of observation have become too perfect. That is what is happening at this moment with respect to physical chemistry; the founders are hampered in their general grasp by third and fourth decimal places.
A scientist worthy of his name, about all a mathematician, experiences in his work the same impression as an artist; his pleasure is as great and of the same nature.
. . . by natural selection our mind has adapted itself to the conditions of the external world. It has adopted the geometry most advantageous to the species or, in other words, the most convenient. Geometry is not true, it is advantageous.
The mathematical facts worthy of being studied are those which, by their analogy with other facts, are capable of leading us to the knowledge of a physical law. They reveal the kinship between other facts, long known, but wrongly believed to be strangers to one another.
What is a good definition? For the philosopher or the scientist, it is a definition which applies to all the objects to be defined, and applies only to them; it is that which satisfies the rules of logic. But in education it is not that; it is one that can be understood by the pupils.
If I didn't care about doing right and didn't feel uncomfortable doing wrong, I should get on capitally.
No matter what part of the world we come from, we are all basically the same human beings. We all seek happiness and try to avoid suffering. We have the same basic human needs and concerns. All of us human beings want freedom and the right to determine our own destiny as individuals and as peoples. That is human nature.
Perjury is the basest and meanest and most cowardly of crimes. What can it do? Perjury can change the common air that we breathe into the axe of an executioner.
God made yeast, as well as dough, and loves fermentation just as dearly as he loves vegetation.
None of us live single-issue lives... That is why intersectionality is a strength, not a weakness.
Both described at the same time how it was always March there and always Monday, and then they understood that José Arcadio Buendía was not as crazy as the family said, but that he was the only one who had enough lucidity to sense the truth of the fact that time also stumbled and had accidents and could therefore splinter and leave an eternalized fragment in a room.
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