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Posted Jul.9th, 2021, viewed 335 times
Why do you need math?
Some math problems have been awarded a million dollar reward. And yet they remain unresolved, no matter how the best minds fight over them. How does mathematical thought develop - isn't everything still proven? And why invest a lot of money in abstract problems? Let's take a look into the complex world of mathematics!
Math is a way of learning about our world
Mathematics studies our world in its maximum abstraction. Physicists are accustomed to working with manifestations, and mathematicians work with abstraction: they are looking for those properties of our world that are purified from manifestations, which can be studied and then applied. There is an amazing article by our great mathematician Manin, it is entitled "Mathematics - the language of describing possibilities." At the end of his article, Yuri Ivanovich cites the example of a shaman who did not decide what to do with the tribe, but gave advice to the leader of the tribe on how best to act. And Yuri Ivanovich ends with the following words: “Mathematics describes the phase space of the real world, the space of possibilities. It studies the laws that determine the possible trajectories in this phase space, as well as the conditions, the set of information that is needed to choose a specific phase trajectory. " That is, she, in principle, tells the society that you will do this - you will go like this, you will do this - you will develop like this. And this is such a supreme view of mathematics.
[Russian mathematician] Aleksey Nikolaevich Krylov compares mathematics to a workshop: mathematicians prepare all kinds of tools for different needs. And when mankind has to solve a problem, the professors of mathematics - scientists who are experts in this toolkit - give mankind the tool that is needed to solve the next problem: sometimes a rough file, sometimes a file ...
More and more new areas are constantly emerging, mathematics is expanding a little, and from new boundaries those areas that can be continued to be studied and which will then lead to benefits for all mankind become visible. A very simple example can be given here - the article "From the" crazy "geometry of Lobachevsky to GPS navigators. Lobachevsky came up with his own geometry. He died without even seeing a single working model. And of course, he could not have thought that then Riemannian geometry would be created . And later, on the basis of Riemannian geometry, Einstein will create his theories of relativity, special and general theory of relativity. And now we, every day using a GPS-navigator, use, among other things, the general and special theories of relativity. Because if we did not take into account the effects they give, the error in determining the coordinates on the ground would be huge and GPS would not be needed. The power of mathematics is that, in one way or another, these seemingly abstract studies then find their application for humanity.
Proofs as the foundation of mathematics
When trying to solve a problem, you have to go through a ton of different options. And mathematics immediately tells you that these options can not even be considered. Rigor is the power of mathematics. If you could not realize this and have difficulty solving the problem - ask someone to
write an essay on mathematics for you, so that with a specific example you realize how rigor works in mathematics
In fact, even within mathematics, the concept of proof was changing. In the days of Ancient India, it was enough to draw a picture from which the proof follows, and write: "Look" - they already considered this as proof. It is clear that now such a proof is not even considered, well, only as an illustration. One of the big, important turning points came in the time of Hilbert, who began to systematize the evidence.
In 1900, at the International Mathematical Congress, Hilbert's famous lecture was delivered, in which he posed his famous "Hilbert problems", which were very prestigious to solve. And it should be noted that more than half of the solutions were solved by the staff of our institute. And here I will refer readers to the article by Lev Dmitrievich Beklemishev, our academician, it is interestingly called: "Mathematics and Logic". Indeed, logic is sometimes called the foundation of mathematics, because proofs are the subject of the study of logic. A lot of things were born from logic, about which we, again, do not even suspect that they are based on logic. For example, databases are one of the branches of this science. Linguistics also relies heavily on logic.
ADDITIONAL RESOURCES:
https://beyondvela.com/how-to-get-your-dream-job-after-university-a-student-guide/https://programminginsider.com/how-to-save-money-for-a-student-a-list-of-benefits-and-discounts/https://chi-nese.com/practical-benefits-of-transcendental-meditation-improving-the-performance-of-the-ones-who-study/
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