I agree with Artur, there is no hierarchy in science. There exists the problem in classification of different field of science. What is the difference between chemical physics and physical chemistry? Some fields of mathematics are tool.  in physics and chemistry. The theoretical physics is commonly considered as physics, but some physicists consider it as a field of mathematics.

"Actually, maybe the arts stand on the top of the human existence." I completely disagree with this statement. What is the difference between the art and the science?

"And science shan't be divided in disciplines." In general, I agree. At the same time It's beyond of intellectual capacity of any scholar to be an expert in all fields of science. Therefore, the science is divided into different fields. In all these fields  "the scientific method" (https://en.wikipedia.org/wiki/Scientific_method) is used. If not, this is not the science but the psuedo-science (https://en.wikipedia.org/wiki/Pseudoscience) . 

Dear Dr. Geletii,

thank you for your interesting answer. However, I would not agree that theoretical physics could be a part of mathematics. Strictly speaking, every statement of mathematics is a tautology (in the sense of "A = A", but more complicated, and of course more meaningful). By contrast, every statement of physics is a statement about our world, which relies on observation, is not a priori true but needs to be tested by the experiment. Nevertheless, physical theories are mostly formulated in a mathematical language, and mathematical methods are very useful for practical calculations in physics.

In my humble opinion, one can also distinguish between science and art: while science is concerned with objective statements, art is concerned with subjective statements about our world. Of course, this does not mean that there cannot be an overlap between these two fields, but personally, I would not give up the whole distinction.

My answer to Artur Braun written last night,

You obviously have misunderstood the text, you change the meaning of what I wrote, citing Turner pyramid of knowledge. Turner did not speak about superiority of one science in relation to the other, he was not saying that one is better than another, or that one is more loved than others, but only that each of sciences builds on other in a natural way and that one can’t be without the other, especially without mathematics. And that is true !!

Mathematics as one of the oldest sciences, from the time of old Greece, Babylon and Arabs will exist at the same time as applied science (together with all natural, technical, biotechnical sciences, ...), but also as an independent science, independent of all other sciences. And this is exactly what make it different from other sciences.

I do not consider myself a physicist, although besides of mathematics I completed three years of serious study of physics (not like Bologna) and have a solid knowledge of physics! ! Besides I was teaching students of physics various mathematical courses, as wel linear algebra, equations of mathematical physics, theory of groups with applications in physics, theory of representations of finite groups, and wrote a book for students of physics. I want to say I know well both sciences. Concerning you I think mathematics is not your strong side  !

And at the end, I do not understand why you mentioned the social sciences and art ?? They have nothing to do with mathematics, physics and other natural sciences! This is an other story, I think interesting !

Frederick Turner was a professor of social sciences at the University of Texas, but his story did not include neither social sciences nor the arts. So, it is not necessary to protect the social sciences from him.

Dear Mirijana, I do not think that the math is the independent science. The mathematics is a common tool in natural science. The progress in natural and in social science depends on the development of tools, including math. 

There is the fundamental difference between science and art. Each piece of art is unique, not reproducible. Otherwise it's not the art. The science is all about reproducibility. If the results are not reproducible. this is not the science. 

To Giulio. "I would not agree that theoretical physics could be a part of mathematics."

I did not say this. I wrote "Some physicists consider" 

Dear Yurii, I did not assume that you said this. But as you mentioned a "problem in classification of different fields of science", I just wanted to express my opinion that I do not see such a problem in the case of theoretical physics / mathematics.

Dear Yurii,

You are not right. Those of you who are not mathematicians, when you talk about mathematics, you think about that mathematics with which you meet, that you are familiar with and that you are using . For others , such as abstract algebra, topology, mathematics fundamentals, often do not even know they exist.

The mathematics of which I speak is often so difficult to understand that we often do not understand each other, if we don’t work in the same area. I'm talking about such mathematics, mathematics as theoretical, fundamental science that is not tied neither to any concrete problem, nor the applications. Of course, this does not mean that after 20, 30 or more years it will not find some application. And when we introduce a new concept based on logic, we wonder if it has to use, and we are looking for examples. If you wonder where we are looking for examples and applications, the answer is, of course, first in physics!

I wanted to say that mathematics is not and should not only serve other sciences !

All best

Dear Colleague  Schober ·

I would agree with you, young colleague. I do not see any problem between mathematics and theoretical physics.

These are the two at the same time very similar and close sciences on the one hand and different from the other side. And that theoretical physics has no without mathematics, I think it is pointless to argue. It is very clear to every physicist.

All best

Dear Mijana, 

First, please never judge the background of other people.

Second, before whatever discussion we must define each term. Please define what is the mathematics? If this is the science, define what is  the science?

I believe that the fundamental science (based on my definition of science) can be divided into three family: natural, social, and formal science.Formal science includes logic, mathematics, statistics, theoretical computer science, information theory, game theory, systems theory, decision theory, theoretical linguistics, etc. Mathematics is not unique, it's just a part of science with its own language and methods. It overlaps with numerous fields.

"The mathematics of which I speak is often so difficult to understand that we often do not understand each other, if we don’t work in the same area. "  This is a very common phenomenon in any area of science. 

Hi both,

Here people write  often, about something they know little or almost nothing to get points. I do not intend to discuss about the fundamental sciences with those who think they know all, but they don't know almost nothing about the fundamental science.

According to people like you the social fundamental sciences such as, for example, philosophy should abolished because they are not generally expected benefit.

Mirjana

Dear Mirjana,

How very interesting. I'm thrilled to learn more from so many interesting contributes, here.

Please allow me to introduce my personal view of the problem. fFrom my perspective, I wouldn't go so far as to differentiate or "hyerarchyse" Science.

There is only Good Science, or poor quality,dishonest sciences... (Whatever the Field or subject of work, you'll find excellent performances, side by side with "poor quality" performances, that may lead you to erroneously discharge interest on some valuable fields of scientific research).

 I would neither hierarchise sciences. Surely, all modern sciences as we know them are connected by using mathematical models (NB: today this is evident. But there has been a chemistry before the law of multiple proportions and there has been a descriptive biology before biological processes were quntified etc.);in the same way chemistry is linked with (quantum) physics and biology  is linked with (bio)chemistry. Psychology might be linked over neurology to biochemistry. Linguistics might be linked to psychology and mathematics might be linked to linguistics. I could say, closing the cycle  - when I would even know it is a cycle. Maybe it's a sphere? A n-sphere? A tesseract? Anything but a pyramid in my view.

Dear Mirjana,

Who is these "both," which  don't know almost nothing about the fundamental science." 

Please, define what is the fundamental science. What you are talking about?  After reading your comments I feel myself as a full idiot. 

"According to people like you (who is this you?),the social fundamental sciences such as, for example, philosophy should abolished because they are not generally expected benefit." Again, what is the fundamental science? I would expect benefits from the applied science but not from the fundamental. 

The last point. You wrote "

I do not intend to discuss about the fundamental sciences with those who think they know all, but they don't know almost nothing about the fundamental science.

What can be said about the hierarchy in science ? - ResearchGate. Available from: https://www.researchgate.net/post/What_can_be_said_about_the_hierarchy_in_science [accessed Aug 5, 2016]."

Why do you believe that you know better than others what is the fundamental science. Please, provide references on your publications on this question in peer reviewed journals. Please, teach us what is the fundamental science. 

I did never said that I know better than others. I'm just quoting the article in which it was brought opinion with which I agree.

But really I wouldn't have argued with someone who asks what is the fundamental science -- who does not know what is the fundamental science.

That was me who asked you  what is the fundamental science. I believe I know the answer, but I would like to know your definition. Why do you believe that someone who asks what is the fundamental science does not know what is the fundamental science? 

You did not respond to my questions. You wrote, " I do not intend to discuss about the fundamental sciences with those who think they know all, but they don't know almost nothing about the fundamental science."  At the same time you write "I did never said that I know better than others." 

In mathematics, there are terms that are considered to be the primary and which are not defined.

In short, one of the divisions of sciences is at a fundamental or basic or pure from one and in applied sciences from the other side. The first one, is for itself, although abstract, important and although it does not bring immediately benefit, it as a part of other science and dislike indirectly benefit. Of course it does not mean that itself will not bring benefit when it finds some application.

Let's just say, a simple general-known example are differential and integral calculus: when they were discovered they were abstract. Today, without them you cannot imagine solving even the simplest problems in all spheres of life and work.

Honestly, I do not understand your answer. I guess that the fundamental and applied science have different goals. The fundamental science is looking for new knowledges, while applied science is looking for the solutions to solve some practical problems. Mathematics can be fundamental or applied. 

You added a new term "abstract."  This requires a separate discussion what is abstract. 

Greetings to all this honorable audience. I have read questions that are of great interest, this is one of them. And as I pondered, I asked myself a question: Who builds the hierarchy of science? Is it man or is it the same science that describes his hierarchy?

I am going to present a historical account: Saint Thomas Aquinas, seeking the answer to the questions "What is God, Who is God and How is God?", Chose the method of putting his head inside a tabernacle (thinking about the fact That God is there). After spending 2 hours in the evening, at dawn the next day he searched the volumes of his writings (Summa Theologica), placed them on empty ground in his abbey to burn them. When the Superior saw him, he urged him not to, and asked him to tell him why he wanted to burn them. Thomas replied: After putting my head in the tabernacle I have known that there are no words to answer such great questions. "

Whatever the result that any branch of the sciences finds, it indicates in which direction the truth is. Perhaps building a pyramid is a starting point and indicates a direction, this construction is a perception of the author about the structure of science (" Words are enough?"). My perception is that we are immersed in an infinite network . In the node that I have to occupy (Mathematics) come many, many edges. Any path that leads us build toward a goal: Truth

Dear Jorge Eliecer Hernandez,

Thank you very much for your nice question: "Who builds the hierarchy of science? Is it man or is it the same science that describes his hierarchy?"  that suggests the answer. I think both: the science itself, together with man, because without of a man, there would be no of science. Very nice comment with which I agree completely. 

I like Your great selected quote from Saint Thomas Aquinas, also, and wise words of this influential philosophers: "After putting my head in the tabernacle I have known that there are no words to answer such great questions."

All of your comments sounds very nice and presents you as a very wise and educated man.

Mirjana

Dear Mirjana Vucovick: Thank you. Thank you very much for your comment.

 to Yurii V Geletii

I think that you understand my response, in your own way. There are many various branches of mathematics: mathematics can be pure theoretical as well as applied (in physics, chemistry, biology,...) science. That 's  why mathematics is the base of the pyramid of sciences.

Mirjana

As I wrote in my previous post there is no hierarchy in science.

It is your opinion, but other don' t think so. I think In general you know a little about sciences: if you don't  know what is fundamental science (You've admitted that ) ! You don't need to include in discussions about what you don't know, don' t understand.  

Dear Mirjana,

By your posts, You are attempting to discredit my reputation as a scientist. 

"It is your opinion, but other don' t think so." Yes,  It's its my opinion and at least some people agree with me.

 "I think, In general you know a little about sciences."  You have all rights to think whatever about my contribution to the fundamental science. What are your criteria? Have you ever looked at my profile, my H-index, my publication list? I looked at your profile and read the questions you have posted earlier. 

"if you don't  know what is fundamental science (You've admitted that ) !" PLease, read my posts. I gave my definition of the fundamental science. If you disagree, please give your definition.

"You don't need to include in discussions about what you don't know, don' t understand." Why do you believe that you understand better then others? I express my opinion only in the areas, where I feel myself comfortable. I asked you several questions and received your answers: "you don't understand," or "I do not intend to discuss about the fundamental sciences with those who think they know all, but they don't know almost nothing about the fundamental science." These are not the answers.

This message is not  intended to insult you but to defend my own opinion. 

There is no point in having this discussion. Either the hierarchy exists or not, all the branches of mathematics and science and everything are inter dependent and one cannot exist without other. It is the harmony between different disciplines that is needed for better research and innovation. 

End of the day knowledge is what matters.

Yes it's true. But nobody talks about the fact that there is no harmony of doctrine, but we're talking about the fact that without some sciences, that we call the fundamental, would not exist others (very important) that are connected to them: say physics without mathematics and technical without mathematics and physics,...

But this can understand only very educated people, or those who use some of fundamental sciences: You obviously don't belong in these two categories.

I recommend that you read the section of the book "The God Particle" by Leon Lederman, which includes the answer to the question (What can be said about the hiearchy in science ?) of Frederick Turner, an expert in social sciences at the University of Texas.

In this book you will find also a lot of things about sciences and their development through history, which you obviously don't know.

And I'm going to finish with the comment on your end: "End of the day knowledge is what matters". I would agree with you, but there are broad and very narrow general knowledge and education today mostly present.

very closely, which is today the General is present.

Dear Mirjana,

I have to disagree. It might be that, for you, ' "The God Particle" by Leon Lederman [...] includes the answer to the question'. But I don't think that the question has one simple answer as a question from a TV quiz. There are several possible opinions, and obviously, you have your opinion, but others have other opinions, that are, in my view, more convincing. Surely, modern physics is nothing without mathematics. But also parts of modern mathematics wouldn't exist without physics. And, as I pointed out earlier, historically speaking, e.g. there was a successful chemistry which was not based on strict mathematical rules. I mostly agree with Yurii.

Dear Eric,

I didn't say that  "The God Particle" by Leon Lederman [...] includes an answer to the question ? I agree with you that the question has no one simple answer... but what tell to someone who don't know what is fundamental sciences ?? 

However, I agree with you concerning physics: "modern physics is nothing without mathematics". That is what Frederic Turner wanted to says: natural sciences and mathematics rely on each other and they can't do one without the other, but the mathematics -- pure mathematics, exist and is important even when it's quite abstract -- when it brings no benefit.  Let's say, differential account was an abstraction when it showed up for the first time, and today it can't imagine anything without this account !

"You say historically speaking, e.g. there was a successful chemistry which was not based on strict mathematical rules." Maybe once upon a time, but science progresses, it's going on. Now it's hard to believe in this: every experimental obtained result should be prove by an account in order to be valid, and vice versa, the theoretical  obtained results should be checked by an experiment, too

I'm mathematician, but I finished three years of study of physics; I was taught Algebra to students of physics,and wrote the book "Theory of group and representation with applications in physics" in which there are many nice examples for chemists, too. But, to be able to read, they need to know math !