1. The frontier of biological future is mathematics, and the frontier of mathematical future is biology.
Mathematical model can quantitatively describe the movement process of biological substances, and a complex biological problem can be transformed into a mathematical problem with the help of mathematical model. Through the logical reasoning, solution and operation of mathematical model, the relevant conclusions of objective things can be drawn, so as to achieve the purpose of studying life phenomena. For example, Verhulst-Pearl equation describing the growth law of biological population, Lotka-volterra equation describing the reciprocal relationship between predator and prey, and so on. The mathematical model of reaction-diffusion equation is widely used in biology, which is closely related to physiology, ecology, population genetics, epidemiology and pharmacology in medicine.
The deep interaction between mathematics and biology will change the biological science. The involvement of mathematics has improved the research of biology from qualitative and descriptive level to quantitative, accurate and regular level. The progress in many biological fields, such as computational neuroscience, population dynamics, ecology, disease transmission and phylogeny, is driven by mathematics. The application of mathematics in biology has also promoted the development of mathematics. The emergence of system theory, cybernetics, model mathematics and the rise of multivariate statistics in statistical mathematics are all related to the application of biology. Many mathematical problems raised by mathematical biology and many growing points of mathematical development are attracting many mathematicians to engage in research. A series of mathematical studies, such as reaction-diffusion equation, pattern recognition, stochastic differential equation, numerical method of partial differential equation, and mixed method of connecting discrete and continuous models, have been developed under the impetus of biological application. Since the autumn of 2008, two seminars held in the American Institute of Mathematical Biology have provided many research results of interdisciplinary research between mathematics and biology, such as multi-scale problems in thrombosis, biochemical reaction network, blood flow calculation and modeling, topology and imaging of medical data, lung response to infection, reaction-diffusion-hyperbola equation in nerve filament transportation in axons, tissue transplantation and so on. This shows that the application of mathematics from non-life to life is a profound change, and under the impetus of life science, mathematics will achieve great development.
2. Mathematics and Economics
Although there is no Nobel Prize in Mathematics for various reasons, economists closely related to mathematics have frequently won prizes for their achievements in mathematics in recent years, and the further development of mathematics can more and more influence the development trend of economics.
At the beginning of the 20th century, some people said, "Mathematics and social science will be the controlling factor of future civilization" (W·F· White). Now more and more branches of social science use mathematics, the most prominent example is economics. Since the 1940s, the mathematicization of economic research has led to the birth of an interdisciplinary subject-mathematical economics. Famous mathematicians such as von Neumann participated in the establishment and development of this discipline. The Game Theory and Economic Behavior written by von Neumann and Morgenstein in 1944 put forward a mathematical model of competition and applied it to economic problems, which became the beginning of modern mathematical economics. Since 1950s, mathematical methods have occupied a major position in western economics, which can be clearly reflected from the proportion of mathematical economics in Nobel Prize-winning works. ?
According to statistics, from 1699 to 200 1 year, there were 49 winners in the 33rd * * *. Some scholars divide the applied mathematics depth of award-winning works into four grades according to the standard: super-strong, strong, average and weak. The results show that 27 of the 49 winners can be rated as "super", accounting for more than half of all winners; The number of people who can be rated as "strong" is 14, which means that there are 4 1 person, accounting for more than 80% of the total number, and won the award of "strong" in applied mathematics. This shows the mathematical content of these economic theories. No wonder some people say that the Nobel Prize in Economics is mainly awarded to "mathematicians among economists".
There are many other aspects ~
(Content transferred from Mathematical Jingwei)