[cloud co creation] what is the role of AI in mathematics? What will be the disruptive impact on the mathematical world in the future?

AI What role does it play in Mathematics ？ What will be the disruptive impact on the mathematical world in the future ？

as everyone knows , Mathematics plays a vital role in science . Einstein once said ,“ Pure mathematics enables us to discover concepts and the laws that connect them , It gives us the key to understand natural phenomena . Mathematics is more respected than all other sciences , One reason is that its proposition is absolutely reliable , Indisputable , Other sciences are often in danger of being overturned by newly discovered facts .” From this we can see that , Mathematics can formalize the core content of a subject , And we can also use mathematical tools to infer many undiscovered laws . that ,AI What role does it play in Mathematics ？AI What will be the disruptive impact on the mathematical world in the future ？ Or in AI Whether mathematics is still so important in research ？ Which mathematics is related to AI Are more closely related ？ Now let's discuss and discuss .

One 、 Mathematics and artificial intelligence

Artificial intelligence is an interdisciplinary , The application field is also very broad . Different application fields require different mathematical background knowledge . But linear algebra 、 probability theory 、 Calculus and statistics are expressions of artificial intelligence “ Language ”. Learning mathematical knowledge will help to deeply understand the underlying algorithm mechanism , Easy to develop new algorithms .

Linear algebra is the basis and core of describing deep learning algorithm . It realizes the deep learning method through matrix representation , Transform the unstructured data to be processed into discrete matrix or vector form . For example, an image can be represented as an array of pixels arranged in order , Sound data can be expressed in vector form , Neural network is the combination of countless matrix operations and nonlinear transformations . Everybody knows , Probability theory and statistics can be used to study data distribution and how to deal with data . The vast majority of what deep learning algorithms do is predict , Prediction comes from uncertainty , Probability theory and statistics are the subjects that discuss uncertainty . in addition , Calculus is the basis of mathematical analysis .

Two 、AI The role in Mathematics

The biggest advantage of AI , It can help people find out the connection that human thinking is not easy to find , That is to help human beings find “ intuition ”. current AI, It can already pass a certain algorithm , Analyze the relationship and laws between a large number of data , So as to help find some new conjectures . Once in a AI Find new conjectures with the help of , Next, mathematicians will make these new conjectures , Carry out in-depth deduction and proof . Those proved to be “ really ” guess , Finally, it will be directly applied to human beings as a theorem . at present ,AI It can already provide a powerful framework , In the field of mathematics where there are a lot of data or it is difficult to use classical methods , Found many interesting and arguable conjectures .

Mathematics plays an important role in the field of artificial intelligence . For example, all parameters in the neural network are stored in the matrix ; Linear algebra makes matrix operations faster and simpler , Especially in GPU On the training model , because GPU You can operate with vectors and matrices in parallel . The image is represented in the calculation as an array of pixels arranged in order . Video games use a huge matrix to create a dazzling gaming experience . In machine translation , How to detect the type of language you input will use the relevant knowledge of probability theory . A simple way is to break down the words or sentences you enter , Calculate the probability of each language model , Then the language model with the highest probability is finally determined . in addition , Image classification using neural network , The output of the network is the probability value that measures the credibility of the classification results , That is, the confidence of classification , We choose the one with the highest confidence as the result of image classification . And Gaussian mixture model 、 Hidden Markov model and other traditional speech processing models are based on probability theory .

3、 ... and 、AI The disruptive impact of the future on Mathematics

Just like computers have caused a series of effects on the development of Mathematics , Varying degrees of “ Artificial intelligence ” At present, it has blended with Mathematics , It may also play a disruptive role in various ways in the future . Such as being able to hand over the simple and repeated calculation work to the computer , bring “ Numerical solution ” Become “ Analytic solution ” A major supplement to , It also makes part of the analytic expression （ For example, series ） There are more applications besides theoretical analysis .

Due to the intervention of powerful computing power , To iterate 、 Algorithms based on large-scale computing and so on no longer exist only in theory , It's optimizing 、 Solution and other aspects have greater practical value . This has changed the research of mathematics from the way of thinking , It not only provides more tools to solve problems , It also enriches the research content of Computational Mathematics and other fields .

The intervention of artificial intelligence makes “ Leave the simple and repeated reasoning and verification work to the computer ” Make it possible . Even in these very weak sense “ Artificial intelligence ” It can also further change the way of mathematical research . For example, limit the number of situations discussed by manual derivation , Then the machine will verify one by one to complete the proof .

One side , Artificial intelligence provides us with convenience . On the other hand , Artificial intelligence can also learn and understand human beings through data . The wave of AI has spawned a number of Internet companies driven by AI algorithms . We are in a time of great change , Beyond all doubt , Artificial intelligence has become one of the frontiers of science and Technology , It will have a disruptive impact on many industries . Artificial intelligence based on data and mathematical method based on model , The combination of the two , It can promote the progress of artificial intelligence , It also promotes the innovation of mathematical research . With “ Artificial intelligence ” Ability improvement and application promotion , Mathematical research in other fields will also get some help , Even with the help of new tools, unprecedented results have been achieved . For example, some conjectures that limit the number of discussions to a small range or that the accumulated results are rich enough , It can be proved that the last step can be achieved by machine .

in summary ,AI It plays a decisive role in the field of Mathematics , Many AI applications need mathematical knowledge to support . meanwhile ,AI It will also have a far-reaching and disruptive impact on the mathematical community in the future .

This article participates in Huawei cloud community 【 Content co creation 】 Activity number 18 period .
https://bbs.huaweicloud.com/blogs/364560

Mission 32：AI What role does it play in Mathematics ？ What will be the disruptive impact on the mathematical world in the future ？