自上古以来，数学一直存在，并且已经吸引并激发了数千年的创造性思维和逻辑思维。它在自然和科学中无处不在，并且在现实世界中具有丰富的应用。许多数学家都将数学之美描述为描述宇宙的语言。但是，数学不仅是一门科学，而且是一门艺术。尽管数学家被认为是直率的，但当我们从数学的基本性质，全知，艺术和科学的角度来思考数学时，我们都会感到激动。做纯粹的数学（没有在任何其他领域提出建议的数学应用）是真正的事情。数学研究是对新的数学思想，定义和定理的发现。布尔代数（George Boole，1854年）在被发现时被认为没有任何价
Mathematics has been around since antiquity and has fascinated and stimulated creative and logical thought for millennia. It is ubiquitous in nature and science and is rich in applications to the real world. Many mathematicians speak of the beauty of mathematics as a language for describing the universe. However, mathematics is not only a science; it is also an art. Although mathematicians are perceived as straight-laced, we all feel emotion when we think of math in terms of its fundamental nature, its omniscience, its art, and its science. To do pure math – math with no proposed application to any other field – is to get to the very heart of things. Math research is the discovery of new mathematical ideas, definitions, and theorems. Boolean algebra (George Boole, 1854) was thought to be of no value at the time of its discovery. It was rediscovered a hundred years later and now serves as the basis of modern computation and digital logic. Calculus, now a common mathematical system, did not exist four hundred years ago. And although it was discovered four centuries earlier, we still find new uses for it today<br>Calculus relied on the intuition of an infinitesimal. However, it was still almost three hundred years later that Abraham Robinson showed how the existence of an infinitesimal could be formalized using the Compactness Theorem of First Order Logic. Mathematics is a formal language for human intuitions, and it still remains an open question whether all our intuitions can be ultimately formalized.