相关论文: WZ Theory, Chapter II
The future of mathematics is described, by using the WZ algorithmic proof theory as a parable.
Since its existence, the computer tool has often supported mathematicians, whether it is to implement an approximation method (numerical calculation of a root, of an integral, ...) or to simulate a phenomenon (geometric in nature,…
The article gives a survey of mathematical proofs that rely on computer calculations and formal proofs.
This essay considers ways that recent uses of computers in mathematics challenge contemporary views on the nature of mathematical understanding. It also puts these challenges in a historical perspective and offers speculation as to a…
We discuss the idea that computers might soon help mathematicians to prove theorems in areas where they have not previously been useful. Furthermore we argue that these same computer tools will also help us in the communication and teaching…
In this talk I would like to illustrate with examples taken from Quantum Field Theory and Biophysics how an intelligent exploitation of the unprecedented power of today's computers could led not only to the solution of pivotal problems in…
The essay consists of three parts. In the first part, it is explained how theory of algorithms and computations evaluates the contemporary situation with computers and global networks. In the second part, it is demonstrated what new…
We describe the Turing Machine, list some of its many influences on the theory of computation and complexity of computations, and illustrate its importance.
The advent of electronic computers has revolutionised the application of statistical mechanics to the liquid state. Computers have permitted, for example, the calculation of the phase diagram of water and ice and the folding of proteins.…
In this short essay, we show how computer experiments, and especially visualization, allowed for the investigation and discovery of phenomena which would have passed unnoticed. We shall also highlight the importance of interactivity between…
Recent theoretical results confirm that quantum theory provides the possibility of new ways of performing efficient calculations. The most striking example is the factoring problem. It has recently been shown that computers that exploit…
Quantum computing technologies have become a hot topic in academia and industry receiving much attention and financial support from all sides. Building a quantum computer that can be used practically is in itself an outstanding challenge…
Quantum computing is a rapidly developing field in the second wave of quantum development, with the potential to revolutionize a wide range of industries and fields of study. As the capabilities of quantum computers continue to advance,…
Wireless technology can provide many benefits to computing including faster response to queries, reduced time spent on paperwork, increased online time for users, just-in-time and real time control, tighter communications between clients…
In this Book we argue that the fruitful interaction of computer vision and belief calculus is capable of stimulating significant advances in both fields. From a methodological point of view, novel theoretical results concerning the…
The article retraces major events and milestones in the mutual influences between mathematical logic and computer science since the 1950s.
This paper reviews connections between physics and computation, and explores their implications. The main topics are computational "hardness" of physical systems, computational status of fundamental theories, quantum computation, and the…
``The purpose of life is to obtain knowledge, use it to live with as much satisfaction as possible, and pass it on with improvements and modifications to the next generation.'' This may sound philosophical, and the interpretation of words…
Computers have a direct impact on our lives nowadays. Human's interaction with the computer has modified with the passage of time as improvement in technology occurred the better the human computer interaction became. Today we are…
The problem of advancing coordinatization of mathematics is considered. The need to develop a theory for measuring value and complexity of mathematical implications and proofs is discussed including motivations, benefits and implementation…