Is math a science? What is the science of mathematics?

Yes, mathematics is a discipline that studies concepts such as quantity, structure, change, space, and information, and belongs to a formal science from a certain point of view. Mathematicians and philosophers have a range of opinions about the exact scope and definition of mathematics.

Mathematics also plays an irreplaceable role in the historical development and social life of mankind, and is also an indispensable basic tool for learning and researching modern science and technology.

The basic characteristics of mathematics are:

1. A high degree of abstraction and strict logic.

2. The extensiveness of the application and the accuracy of the description.

Mathematics is the language and tool of all sciences and technologies, and the concepts, formulas, and theories of mathematics have permeated textbooks and research literature in other disciplines.

Many mathematical methods have been written into software, some mathematical software as a commodity, and some have been made into chips and installed in hundreds of millions of computers and various advanced equipment, becoming the core of high-tech content of products.

3. The diversity of research objects and the unity of internal research.

Mathematics is an "organic" whole, which is like a vast, multi-layered, ever-growing, infinitely extending network. A higher-level network is made up of low-level networks and nodes, which are various concepts, propositions, and theorems.

The networks and nodes at all levels are connected by strict logic. This connection is a reflection of the inner logic of objective things.

Quotes on the definition of mathematics:

1. Mathematics is God's symbol for describing nature. —Hegel.

Mathematics is the highest form of all knowledge. —Plato.

2. Books on the natural world are written in the language of mathematics. - Galileo.

The essence of mathematics lies in its freedom. - Cantor.

3. The universe is big, the particles are small, the speed of rockets, the ingenuity of chemical industry, the changes of the earth, the mystery of biology, the complexity of daily use, and mathematics is everywhere. - Hua Luogeng.

4. Mathematics is the study of abstract structures. - The Bourbaki School.

5. Mathematics is a tool of knowledge and a source of other knowledge tools. —Descartes.

With one, from nothing, all things can be born. - Leibniz.

6. Mathematicians are trying to discover prime numbers on this day.

Some order of the sequence, we have reason to believe that it is a mystery that the human mind can never penetrate. - Euler.

Mathematics is the king of science. - Gauss.

7. Mathematics is symbolic logic. – Russell.

It can inspire or soothe feelings, painting can make people pleasing to the eye, poetry can move people's heartstrings, philosophy can make people gain wisdom, science can improve material life, but mathematics can give all of the above. —Klein.

8. Everything counts. - Pythagorean geometry, there is no king. —Euclid.

Mathematics is a formal science, not a natural science.

Mathematics is a general means for humans to strictly describe the abstract structure and pattern of things, and can be applied to any problem in the real world, and all mathematical objects are inherently artificially defined. Different mathematicians and philosophers have a range of opinions on the exact scope and definition of mathematics. In the historical development and social life of mankind, mathematics plays an irreplaceable role, and it is also an indispensable basic tool for learning and researching modern science and technology.

Mathematics is a measurable property of anything, i.e., a mathematical property is the most basic property of a thing. The existence of measurable attributes is independent of the parameter, but its result depends on the choice of the parameter. For example:

Time, whether measured in days, months, years, hours, minutes, and seconds, will always have measurable properties, but accuracy depends on these parameters. Mathematics is the study of concepts such as quantity, structure, change, and spatial models. Through the use of abstraction and logical reasoning, it is generated from counting, calculating, measuring, and observing the shape and motion of objects.

Mathematicians have expanded these concepts in order to formulate new conjectures and to establish rigorously deduced truths from appropriately selected axioms and definitions. Mathematics is the science that studies quantitative relationships and spatial forms in the real world. To put it simply, it is the science of numbers and shapes.

Due to the demands of life and labor, even the most primitive peoples knew simple counting, and developed from counting with fingers or objects to counting with numbers.

In the final analysis, mathematics is a tool, it is a tool to help people calculate, not science, because the definition of science is to discover the original laws of the universe, and mathematics is an artificial way of operation under an established rule, for example, people stipulate that there are positive numbers and negative numbers, but these things do not exist in nature, but people put forward to understand a certain state, for example, above 0 degrees, water will melt below 0 degrees, and water will freeze. People use this point of condensation of water as the category of zeroTherefore, there is Lin Xiang in the spirit, and even the difference between positive and negative numbers, but this is all artificially prescribed, not scientific.

Scientific research is about natural phenomena that can be observed by various means. Mathematics is the study of numbers and graphs, looking for very abstract laws. Mathematics, especially pure mathematics, is a system of its own, can have no relationship with the natural world, the most important feature of science is its research method, science proves a conclusion through empirical methods, it values evidence the most, reasoning on the basis of evidence.

Mathematical proofs are carried out entirely through logical reasoning, without looking for evidence, which can only be used to establish conjectures at best, and does not help the proof. For example, the Pythagorean theorem needs to be proved through logical reasoning. So science is empirical, evidence plus logic, while mathematics is pure logical reasoning.

Science is divided into three categories: natural sciences, social sciences, and thinking sciences. The science of mind is the science that specializes in the study of the laws and forms of thinking activities. Mathematics is a fundamental discipline that falls under the category of the science of thinking.

This is because science encompasses a very wide range of fields, including mathematics, and the fields of scientific research are very broad, including nature, society, and the mind.

Mathematics is a discipline of thinking that studies the internal relationship between abstract things, and science is the study of the objective world, the characteristics of science are verifiable and repeatable, and verification and repetition are also the process of falsification, science is always moving forward in the continuous correction of errors, and mathematics requires the completeness of the system, and there can be no internal logical errors, so mathematics does not belong to science in the strict sense, but all scientific research must rely on the foundation.

Many mathematical objects such as numbers, functions, geometry, etc., reflect the internal structure of the successive operations or relations in which they are defined. Mathematics is the study of the properties of these structures, for example, number theory is the study of how integers are represented in arithmetic operations.

In addition, it is not uncommon for different structures to have similar properties, which makes it possible to describe their state by further abstraction and then by axioms on a class of structures, and it is necessary to find the structures that satisfy these axioms among all the structures.

Thus, we can learn about groups, rings, domains, and other abstract systems. Taking these studies (through structures defined by algebraic operations) can form the field of abstract algebra. Due to its great versatility, abstract algebra can often be applied to seemingly unrelated problems, such as the ancient problem of ruler diagramming, which is finally solved using Galois theory, which involves domain theory and group theory.

Another example of algebraic theory is linear algebra, which makes a general study of the vector space in which its elements are quantitative and directional. These phenomena show that geometry and algebra, which were previously thought to be unrelated, actually have a strong correlation. Combinatorics is the study of methods for enumerating number objects that satisfy a given structure.