I realize that in this undertaking I place myself in a certain opposition to views widely held concerning the mathematical infinite and to opinions frequently defended on the nature of numbers.
Georg CantorRead
The essence of mathematics lies precisely in its freedom.
Interpretation
Mathematics embodies freedom in creativity and thought, allowing for exploration and abstract reasoning.
Georg Cantor's quote emphasizes that the true essence of mathematics is found in the freedom it provides to think, create, and explore ideas without restraint. This freedom not only fosters innovation within the mathematical field but also reflects the limitless possibilities of thought processes and problem-solving inherent in mathematics, highlighting its beauty as a discipline that transcends restrictiveness.
In practice
A professor gave a lecture on how mathematical freedom allows for innovative theories in his classroom.
I realize that in this undertaking I place myself in a certain opposition to views widely held concerning the mathematical infinite and to opinions frequently defended on the nature of numbers.
Mathematics, in the development of its ideas, has only to take account of the immanent reality of its concepts and has absolutely no obligation to examine their transient reality.
A set is a Many that allows itself to be thought of as a One.
The transfinite numbers are in a sense the new irrationalities [ ... they] stand or fall with the finite irrational numbers.
There is no doubt that we cannot do without variable quantities in the sense of the potential infinite. But from this very fact the necessity of the actual infinite can be demonstrated.
The essence of mathematics lies in its freedom.
Electrical science has disclosed to us the more intimate relation existing between widely different forces and phenomena and has thus led us to a more complete comprehension of Nature and its many manifestations to our senses.
Go out and collect data and, instead of having the answer, just look at the data and see if the data tells you anything. When we're allowed to do this with companies, it's almost magical.
I don't walk into the lab in the morning thinking, 'I am a woman, and I will carry out an experiment that will conquer the world.' I am a scientist, not male or female. A scientist.
When the sexes differ in beauty, in the power of singing, or in producing what I have called instrumental music, it is almost invariably the male which excels the female.
The feeling is constantly growing on me that I had been the first to hear the greeting of one planet to another.
It is to them [fossils] alone that we owe the commencement of even a Theory of the Earth ... By them we are enabled to ascertain, with the utmost certainty, that our earth has not always been covered over by the same external crust, because we are thoroughly assured that the organized bodies to which these fossil remains belong must have lived upon the surface before they came to be buried, as they now are, at a great depth.
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