2. The research methods of geography and mathematics are different.

3. The conclusions of geography and mathematics have different application orientations.

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1: Geography is the study of regional differences. It organizes the complex earth surface world into regions with different attributes or scales by the method of "zoning", and then describes and explains each "mosaic" separately, aiming at clarifying the infinite diversity of the complex surface and revealing the geographical and spatial order behind it. For example, due to the geographical complexity, China is placed in East Asia on the continental scale, and then divided into Northeast China, North China, Northwest China, South China and Qinghai-Tibet region. For another example, the "semi-roof" (non-axisymmetric) in northwest China is different from the "herringbone" (axisymmetric) side structure in north China. In a word, geography learning provides us with a spatial-regional perspective and way of thinking to understand the complex world.

Compared with other basic sciences, the most important personalized feature of mathematics is the abstraction of its research object, which also determines other characteristics of mathematics and distinguishes it from natural sciences. The essence of mathematics can be summarized as abstraction, reasoning and model. People with good mathematical literacy look at the world, and everything has a very important feature that it is highly abstract. For example, although the flags on both sides of Tiananmen Gate fly in the same direction, the abstract outline of Tiananmen Gate is still axisymmetric geometry; Although the rural or urban environment we live in is complex and diverse, it is essentially a three-dimensional geometric space. Generally speaking, learning mathematics helps to understand the real world in an abstract way.

2. Geography is famous for its comprehensiveness, and one of the core qualities of geography is comprehensive thinking. In the eyes of geographers, it is necessary to observe, analyze and solve practical geographical problems from a comprehensive perspective. Therefore, the research methods of geography include the experimental methods of controlling variables commonly used in general physics and chemistry, the analysis methods of historical documents, the construction methods of econometric models in economics, the social investigation methods commonly used in sociology, and the rational thinking methods commonly used in philosophy and other disciplines. According to different problems, different regions and different time periods, geographers will fully mobilize the existing material basis and cognitive experience, collect relevant materials and data in many ways, and adopt appropriate methods to solve specific geographical problems.

Compared with geography, the research method of mathematics is relatively simple. Mathematics studies the stipulation of things, not the stipulation of things. Many people have laughed and said, "When geographers travel across mountains and rivers, mathematicians can draw an important scientific conclusion with a pen and a piece of paper." . Although this statement is somewhat exaggerated, it can reflect the differences in research methods between the two disciplines to some extent. At present, the interdisciplinary is deepening, but the traditional practices and classical research paradigms of the two disciplines will not converge, because this is the premise of disciplinary differentiation and independence.

3. Mathematical conclusion is the result of logical deduction, or inductive logic or deductive logic. Usually, as long as the mathematical concept is accurate, the logic is reasonable and the conditions are suitable, mathematical conclusions are generally widely used. For example, the model of "unit price × quantity = total price" and the formula of 99 multiplication are very universal and generally do not need to be adjusted according to time and place.

Geography is different. "There are few universally applicable laws in geography. The regionality of geography determines that its scientific conclusions "originate from the region" and "fall in the region". The book Rediscovering Geography points out that geographers are often curious about "why a phenomenon only occurs in one place and not in other places". It is the unique phenomenon in this area that causes geographers to think, and finally completes the geographical description and explanation of a specific area. For example, geographers have rich experience in regional development, town design, resource development and pollution control. However, they never apply A's development model or planning scheme to B intact. If it can be widely used, it will still be debugged according to the specific regional conditions before use.

Therefore, in the face of the specific problem-solving process, the application of mathematical conclusions can follow the "loyalty orientation" relatively, while the application of geographical conclusions adheres more to the "debugging orientation" of the region. This is a logical standard and a basic principle and methodology.