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Mathematics that studies the limits of computers



The field of computation began to flourish in the 1930s, thanks to the work of mathematicians such as Alan Turing.



Today, computers are everywhere - in the office, in smartphones, and even in cars. They work through increasingly powerful algorithms that can perform a myriad of tasks, from adding two numbers to finding the best route to an unknown destination or automatically detecting fraudulent financial transactions. The ubiquity and potential of computers is so great that it's easy to believe that sooner or later they will be able to solve any problem. However, thanks to the so-called theory of computation, we know that computers and algorithms have fundamental limitations. British mathematician Alan Turing (1912-1954) was one of the great promoters of this field, and is considered by many to be the father of modern computing.



The use of algorithms dates back to the beginning of our civilization. In their simplest form, algorithms are a way to solve a given problem by step-by-step execution of a finite sequence of instructions. These instructions use a finite number of characters and are performed “mechanically” to obtain the desired result, regardless of any special form of intelligence — for example, the use of mathematical “intuition” is not required. or another type-.



For example, a simple algorithm is one that we use to manually multiply two numbers, as we are taught in school, to get their product. Other examples of algorithms are the so-called Euclidean algorithm for obtaining the greatest common divisor of two numbers, or Gauss's method for solving a system of linear equations. In essence, we can think of algorithms as automatic procedures that offer solutions to mathematical problems. If you want to understand mathematics in the same way, but are stuck in some topic and cannot go further, contact the geometry homework help .







For centuries, these algorithms had to be done manually, in a slow and tedious process, which in practice limited their use. However, with the advent of computing devices that automate their implementation, the use of algorithms began to grow rapidly, mainly for performing more or less complex calculations. A few years before the advent of digital computers, mathematicians and logicians asked themselves the following question: what problems are computable , that is, can they be solved using algorithms? This question became the original engine of the so-called theory of computation. But if these people turned to the https://essayassistant.org/ specialists for help, then they could solve their problems in mathematics quickly and without any problems.



While it is (relatively) easy to verify that a given problem is computable - you just need to prove that a certain algorithm solves it - it is much more difficult to show that there is no algorithm for a given problem that can solve it. delicate matter. Even if we can't find an algorithm to solve the problem, how can we rule out that we just haven't found the right algorithm yet?



Part of the complexity of this issue was due to the fact that until recently there was no exact idea of ​​what an algorithm was. Notable for this fundamental challenge is the work of Alan Turing, who, incidentally, appears on the new £ 50 note and also gives his name to the new student exchange program that will replace the Erasmus program in the UK.