Why math

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Why math is important Why math is important in life? Why is math so hard? Recent Articles. Check out some of our top basic mathematics lessons. Riemann's generalization of Euclid's geometry, for instance, turns out to be exactly the language Einstein and others needed to explain gravitation. Mathematics is humanity's best tool for trying to describe how the world works; indeed, the unreasonable effectiveness of mathematics at explaining the world is a bit of a mystery.

This unreasonable effectiveness of mathematics is both a asset and a curse. It's clearly an asset in that it generates interest in the subject and funding for research from private companies and government agencies willing to pay to have key problems solved. On the other hand, it's a curse because it leads people to misunderstand the reason for doing mathematics in the first place; because some math turns out to be just what we need to solve certain problems, suddenly people expect all math to have obvious immediate applications.

It's sort of like a musical group that starts composing and performing music out of love for their art form, but then has a hit song which sells well -- people then get the idea that music is about making money, and if the group's next album doesn't sell as well as their first hit, suddenly they're considered laughable failures, even though to the group it was never about the money.

A record that doesn't sell well initially may become a big retro hit in later years, and records can have big success within smaller music circles without necessarily topping the mainstream charts. Similarly, mathematical concepts that are not successfully applied to real-world problems immediately after their conception are frequently found to have important applications later on as the subject matures or as new developments in the other sciences call for new mathematical approaches.

Some mathematical ideas may be useful for very specialized problems without necessarily having a broad range of applications. In any case, the study of mathematics motivated by sheer intellectual curiosity is known as 'pure mathematics,' while mathematics studied as means for solving practical problems rather than as an end in itself is known as 'applied mathematics.

This can even lead to some pure mathematicians criticizing other pure mathematicians for wasting time on ideas without applications!

The moral is that what counts as an 'application' depends entirely on what you're interested in. A topologist might study group theory as a way of developing methods for distinguishing topological spaces, while an algebraist might study group theory because she's interested in groups themselves. In particular, for most non-mathematicians, mathematics is at best a means to some practical end, whether optimizing costs, calculating the trajectory of a spacecraft, or just finishing a degree and getting a job.

Anyone interested in a technical career will need to be familiar with some level of mathematics, and the cumulative nature of mathematics makes it inevitable that students will end up studying some topics that don't directly contribute to the mathematics they'll use in their career. Nevertheless, the fact that a student can't see an immediate application for a particular topic does not imply that the student will never use that topic; in many cases, the techniques ones studies in early classes are used to construct the more advanced and powerful machinery one uses later.

For example, integration and power series techniques that students see as 'pointless' in calculus become valuable tools for solving differential equations, which are the natural language in which most of the practical problems in the real world are expressed.

This example brings up another reason why students who view mathematics as a means to the end of solving practical problems often don't see the point of many math classes, namely the simple fact that most of us vastly underestimate the complexity of the world we live in.

Most of the quantities in which we have a natural interest, such as what the temperature will be tomorrow or what the Dow will be at closing, are functions of that is, they depend on many variables, each of which is changing over time. The equations which model such complex quantities are called partial differential equations , and to solve them requires a good understanding of topics such as trigonometry, multi-variable calculus, and linear algebra, at a minimum.

Even so, it is not hard to write down partial differential equations which no one yet knows how to solve. Therefore, when we write 'word problems' in early classes such as algebra, trig, and even calculus, the problems frequently sound phony and contrived, and in large part this is because they are phony and contrived; we have to make many unrealistic simplifying assumptions in order to make the problems actually solvable with the limited mathematics available to students at these early stages.

Secondly, since mathematics provides foundational knowledge and skills for other school subjects, such as sciences, art, economy, etc. In addition to this quantitative analysis, information about the qualitative description of school mathematics in relation to other subjects also needs to be gathered. The TSG 25 organizing team cordially invites all interested researchers and teachers to submit papers related to the topic of this group, in particular to its aims and scope.

Any contribution addressing questions, problems and issues related to the topics listed above may be submitted. We welcome proposals from both researchers and practitioners, and encourage contributions from all countries with different cultural backgrounds. The role of mathematics in the overall curriculum.