Happy Birthday, Pi!
Today marks exactly 250 years since that day, as German physicist and mathematician Johann Heinrich Lambert, having distracted himself from his treatises on optics and astronomy, proved that Pi is an irrational number . This means that there are no such integers p and q for which the equality Pi = p / q would be true.
At first glance, what is so important here? Rational or irrational - what's the difference? In practical engineering use, this does not change anything, because with the construction of any cylinder or surgical needle, they still approximate Pi with the error allowed for each design. The engineers of the Roman Empire could do this almost as successfully as we, equipped with powerful computer equipment (although Pythagoras, for example, the concept of irrational numbers caused such a strong aversion that he denied their existence at all).
But still, what is the meaning of the work of Lambert? What is its benefit to society?
The Oxford mathematician Edward Titchmarsh gave the fullest and at the same time concise answer to this question: "From what we know that Pi is irrational, there is no practical use, but if we can know this, then not knowing it becomes unbearable." This is the essence of mathematics. Science exists, because there are still unresolved problems and unanswered questions.
')
In this sense, mathematicians are in the same boat with philologists, philosophers and historians who can devote their whole lives to the study of some small linguistic nuance or historical fact that has absolutely no practical use for modern society. For example, could erectus live in extremely cold temperatures? Why were there more literate women in Novgorod of the 10th century than in the 15th century Moscow? There are a lot of such questions. If there is an opportunity to find out the answer, then we cannot stop and just have to satisfy our curiosity. We enjoy the study of such problems. The same is true in mathematics, and there can be no practical meaning here.
There are problems that need to be solved, there is knowledge that needs to be improved. People in schools and universities are faced with questions a thousand years ago that no one has yet answered. And they try their hand. If in the process of this appears a by-product, useful to society, then good. For example, the creation of electric batteries was made possible by the work of James Maxwell on the study of magnetism and electricity, but the Scottish physicist was not engaged in science for the sake of batteries.
Lambert's proof gave food for the study of mathematics students and raised new questions, which, in turn, gave rise to a new wave of research. But most importantly, Lambert answered the question that no one could answer for centuries. That is the main point. This must be remembered by those who ask about the “practical benefits” of discoveries.
via Timothy Trudgian
At first glance, what is so important here? Rational or irrational - what's the difference? In practical engineering use, this does not change anything, because with the construction of any cylinder or surgical needle, they still approximate Pi with the error allowed for each design. The engineers of the Roman Empire could do this almost as successfully as we, equipped with powerful computer equipment (although Pythagoras, for example, the concept of irrational numbers caused such a strong aversion that he denied their existence at all).
But still, what is the meaning of the work of Lambert? What is its benefit to society?
The Oxford mathematician Edward Titchmarsh gave the fullest and at the same time concise answer to this question: "From what we know that Pi is irrational, there is no practical use, but if we can know this, then not knowing it becomes unbearable." This is the essence of mathematics. Science exists, because there are still unresolved problems and unanswered questions.
')
In this sense, mathematicians are in the same boat with philologists, philosophers and historians who can devote their whole lives to the study of some small linguistic nuance or historical fact that has absolutely no practical use for modern society. For example, could erectus live in extremely cold temperatures? Why were there more literate women in Novgorod of the 10th century than in the 15th century Moscow? There are a lot of such questions. If there is an opportunity to find out the answer, then we cannot stop and just have to satisfy our curiosity. We enjoy the study of such problems. The same is true in mathematics, and there can be no practical meaning here.
There are problems that need to be solved, there is knowledge that needs to be improved. People in schools and universities are faced with questions a thousand years ago that no one has yet answered. And they try their hand. If in the process of this appears a by-product, useful to society, then good. For example, the creation of electric batteries was made possible by the work of James Maxwell on the study of magnetism and electricity, but the Scottish physicist was not engaged in science for the sake of batteries.
Lambert's proof gave food for the study of mathematics students and raised new questions, which, in turn, gave rise to a new wave of research. But most importantly, Lambert answered the question that no one could answer for centuries. That is the main point. This must be remembered by those who ask about the “practical benefits” of discoveries.
via Timothy Trudgian
Source: https://habr.com/ru/post/114906/
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