Etymology and definitions by famous mathematicians and philosophers
"Mathematics is the science of structuring a studied reality, it is the whole of its elements, proportions, relationships and patterns of evolution in ideal conditions for a delimited scope."
... In other words, "doing math is to unravel the rhythms of the universe." ....
(I think, ... for my purposes)
... In other words, "doing math is to unravel the rhythms of the universe." ....
(I think, ... for my purposes)
Mathematics comes from the Latin form Mathematica (Cicero), based on the plural in Greek τα μαθηματικά (Ta mathēmatiká), used by Aristotle and which means, in great traits, "all the mathematical things."
The American Mathematical Society distinguishes some 5,000 different branches of mathematics, understood as specific tools for particular areas.
In a large subdivision of mathematics, four basic study objects are distinguished: the quantity, structure, space, and change that correspond to arithmetic, algebra, Geometry, and Calculus. Also, there are branches of mathematics connected to other fields such as logic and ensemble theory, and applied mathematics.
It gives the discussion between neurologists and philosophers as to whether mathematics is strictly a human creation or if it is inherent to reality itself, so I tend to ask why they do not ask the mathematicians themselves.
For example when Albert Einstein is asked:
"How can it be that mathematics, being after all a product of the independent human thought of experience, is so admirably adapted to the objects of reality?"
This one responds (and knows what it says):
"... when the laws of mathematics refer to reality and Limit Calculator, they are not exact;" "When they are exact, they don't refer to reality." So he wanted to remind us that each model has a limited scope. Any formula, model, process, mock-up, etc. does not substitute or constitute a complete reality, it is limited to the variables most relevant to the particular point of view that is being studied. So you should not confuse or equate a model with the reality you emulate.
Conclusion demonstrated in 1931 by the American logic Kurt Gödel, according to which in any system of axioms complex enough to be useful to mathematics it is possible to find propositions whose certainty cannot be demonstrated within the system.
On the other hand, it is necessary to wonder, why in different times and cultures in principle disjointed, they obtained a coincident mathematics?
These dimensions are important as mathematics is supported on well-defined axiomatic and operational bodies, but the definition of mathematics itself seems elusive. So for my fine effects that:
"Mathematics is the science of structuring a studied reality, it is the whole of its elements, proportions, relationships and patterns of evolution in ideal conditions for a delimited scope." ... In other words, "doing math is to unravel the rhythms of the universe." .
It is inherent to that reality, regardless of the observer, or that it is interpreted as wave or as a particle, or vibratory level and number of reference dimensions.
Definiciones relevantes por matemáticos y filósofos famosos:
John D. Barrow: Mathematics is the name we give to the collection of all possible patterns and interrelationships. The essence of mathematics is in the relationship between quantities and qualities.
Philip J. Davis and Reuben Hersh: The study of mental objects with reproducible properties is called mathematics.
Murray Gell-Mann: It is the rigorous study of hypothetical worlds. It is the science of what might have been or could be, as well as of what it is.
Benjamin Peirce: Mathematics is "The science that points the necessary conclusions"
David Deutsch: Mathematics. Study of the absolutely necessary truths.
Murray Gell-Mann: Mathematics. It is the rigorous study of hypothetical worlds. It is the science of what might have been or could be, as well as of what it is.
Albert Einstein: How can it be that mathematics, being after all a product of human thought independent of experience, is so admirably adapted to the objects of reality?
Georg Wilhelm Friedrich Hegel: Object of mathematics is the abstract number and space. Being a mathematician is still a sentient being, albeit abstractly.
Davis and Hersh: The study of mental objects with reproducible properties is called mathematics.
David Hilbert: Mathematics is the system of demonstrable formulas. In a certain sense, mathematical analysis is a symphony of infinity.
Friedrich Nietzsche: Mathematics is only the instrument of the general and ultimate knowledge of the human being.
Charles S. Peirce: Mathematics is the study of the trueness of the hypothetical situations
Richard P. Feynman: Mathematics is the search for guidelines.
Philip J. Davis and Reuben Hersh: The study of mental objects with reproducible properties is called mathematics.
Murray Gell-Mann: It is the rigorous study of hypothetical worlds. It is the science of what might have been or could be, as well as of what it is.
Benjamin Peirce: Mathematics is "The science that points the necessary conclusions"
David Deutsch: Mathematics. Study of the absolutely necessary truths.
Murray Gell-Mann: Mathematics. It is the rigorous study of hypothetical worlds. It is the science of what might have been or could be, as well as of what it is.
Albert Einstein: How can it be that mathematics, being after all a product of human thought independent of experience, is so admirably adapted to the objects of reality?
Georg Wilhelm Friedrich Hegel: Object of mathematics is the abstract number and space. Being a mathematician is still a sentient being, albeit abstractly.
Davis and Hersh: The study of mental objects with reproducible properties is called mathematics.
David Hilbert: Mathematics is the system of demonstrable formulas. In a certain sense, mathematical analysis is a symphony of infinity.
Friedrich Nietzsche: Mathematics is only the instrument of the general and ultimate knowledge of the human being.
Charles S. Peirce: Mathematics is the study of the trueness of the hypothetical situations
Richard P. Feynman: Mathematics is the search for guidelines.