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Inquiring_Mike
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What is mathematics? I like to think of mathematics as the language in which nature speaks... What is mathematics to you?
Originally posted by selfAdjoint
Sasha, in grad school I discovered that different mathematicians have different talents. It appears that the algebraic talent, doing things with abstract counters in your head, is more widely distributed than the geometric one, manipulating pictures in your head.
By which I don't mean that either algebra or geometry is those simple qualities, but that those talents are what you need to succeed in algebric or geometrical fields.
Originally posted by sascha
By language I mean its very principle: being a structure of several signs, interrelated according to a basic idea (axiom, choice, desire, principle, etc.) -- as opposed to the very principle of thinking, which is to integrate and find the common basis of diversities. These two principles are not man-made; only this or that language, and this or that thought, are man-made.
Sure, a talent for this or that is not distributed evenly. But here we are seeking, if I understand this thread correctly, the systematic reason and structure of math, not some contingent aspects. Or not?
Originally posted by selfAdjoint
Mathematics is the study of patterns. This is a recursive study because the relationship of two patterns itself makes a pattern.
i looked at the definition of the word language on dictionary.com and mathematics seems to be a language.mathematics is a language -- in contrast to others a thoroughly formalized one
what this language describes is another question... sometimes people find out correlations with the external world only very much later than the formulation
what do you mean by contiuous?There I say "Geometry has been engulfed by algebraic analysis", which corresponds to what you tell me about the projective geometry you are familiar with. This is just my point: the universality of the subject matter (as possible in a purely qualitative approach, thinking in geometrical way of thinking, in continuous terms) has been lost by subjecting it to the gesture of algebraization, thinking in discontinuous terms. This is the fashion nowadays, and mathematicians have not yet grasped what they have lost.
Mathematics is the study of numbers, quantities, and shapes, and the relationships between them. It is used to describe and analyze patterns and structures in the world around us, and to solve problems and make predictions.
Mathematics is important because it is the foundation for many fields, including science, technology, engineering, and economics. It also helps us to develop critical thinking and problem-solving skills, and to make informed decisions in our daily lives.
Mathematics is relevant to everyday life in countless ways. It helps us to manage our finances, understand and interpret data, and make informed decisions in areas such as health, transportation, and consumer choices. It also plays a crucial role in many professions, from medicine to architecture.
Yes, anyone can learn mathematics. While some people may have a natural aptitude for certain aspects of math, with dedication and practice, anyone can develop their math skills and understanding. It is important to approach math with a growth mindset, believing that with effort and perseverance, you can improve.
Yes, there are many different branches of mathematics, each with its own focus and applications. Some examples include arithmetic, algebra, geometry, calculus, and statistics. There are also interdisciplinary fields such as mathematical biology and mathematical economics that combine mathematics with other subjects.