Dear Boushra Youssif ,

I think the answer is yes.

If X is some topic in mathematics, one can prove that there exists

some mathematical model in our life that used (partially) the concepts of that topic X. You know that all branches of knowledge and sciences in general rich with technical applications as physics, computer, chemistry, biology, economics, etc., all need mathematics and their concepts.

On the other hand, have you in your mind any mathematical concept without applications in our life?

Best regards

thanks Peter Breuer

Dear Boushra Youssif , I believe one should not do mathematics only for an application in our practical life like poet writes poems not for practical application.

Dear @ Boushra Youssif

When a mathematician initiated a mathematical concept(s), he does not bear in mind real life applications but to satisfy his scientific curiosity in the first place and to develop his studies and investigations. Despite of that, many mathematical concepts, which initiated theoritically, proved to fit quite well for real life applications. They are too many to count!, but I can only mension the case of number theory concepts which were initiated purely but proved latter to be vital in the application of information theory.

Dear Boushra Youssif ,

I think the answer is yes.

If X is some topic in mathematics, one can prove that there exists

some mathematical model in our life that used (partially) the concepts of that topic X. You know that all branches of knowledge and sciences in general rich with technical applications as physics, computer, chemistry, biology, economics, etc., all need mathematics and their concepts.

On the other hand, have you in your mind any mathematical concept without applications in our life?

Best regards

Mathematics is like a beautiful nature, it is everywhere!

Thanks Nazia Asad .

Thanks Tapas Chatterjee

Thanks Ahmed Ali Khammash

Thanks Issam Kaddoura

The original question was not one of aesthetics but of practicality. The answer is, of course, no. Not all mathematical concepts bear on practical matters in everyone's lives.

With regard to education in mathematics there seem to be two concerns. First, rational thinking and the careful use of logic and, secondly, some elements of mathematics for understanding rigorous thinking and quantitative methods that arise required in later pursuits. Sometimes, attention to elements of mathematics is about securing the option to proceed further, whether exercised or not, rather than closing off options, as with self-fulfilling claims that it will never be needed.

Nowadays, having a rational foundation for fluency with computers (whether spreadsheets or programming systems) is also a consideration, and that arises everywhere. There are growing numbers of practical cases where some mathematical capability is advantageous, especially if one is attracted to STEM areas for pursuing a vocation.

thanks Dennis Hamilton

An important question and wonderful answers

The mathematical method is practical, when it does formally and abstractly reflect (reduce) phenomena of the natural world (nature) for research purposes of the scientific method (from mathematical idea to technical calculation as Gauss opined).

If I understand the question very well, I think that not all mathematical concepts have an application in our practical life because some of the concepts are just set to prove or establish other theories.

It is quite difficult to draw a line between applicable and non-applicable concepts of mathematics. This is because what is seen to be non-applicable (or pure) today can be vitally applicable tomorrow. I can mention several examples but I shall only refer to number theory which was initiated theoretically and nowadays has huge application in communication theory. You can say the same about concepts like ring , group and field which have vital applications in coding theory and cryptograph. Many mathematical concepts which have real life applications today were initiated theoretically.

Interesting!

Quoted from the original question:

" many students find it difficult in mathematics ".

So what, they should not study math and not insist on becoming scientists, that's all! They can become farmers, workers, artists, art performers, professional sports figures, whatever. There is plenty of choice.

When I went to University, 60 years ago, in Prague, that was the official doctrine of the government. You got one chance; if you failed, you were out of univerity-level science or math studies and encouraged to do something else. One of the official duties of university teachers was to ensure this policy and weed out the unfit ones during the first 2 years.

Now the premises have changed, swinging completely to the other extreme.

It is kind of amusing to observe.

" Do all concepts in mathematics have an application in our practical life? "

The answer is of course NO, at least for many results of higher mathematics. For high school or calculus level mathematics, there are lots of applications however. It's the teacher's job to slowly prepare the students for the higher level of abstraction and applications to other mathematical results (rather than "practical life" applications) during these years. That's part of acquiring "mathematical maturity"...

thanks Peter Breuer