Gauss' quadratic reciprocity theorem and mathematical fruitfulness

Audrey Yap

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Gauss' quadratic reciprocity theorem and mathematical fruitfulness

机译：高斯二次互易定理和数学成果

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This paper presents an account of the fruitfulness of new mathematical calculi in terms of their relationship to existing mathematical methods which is suggested by Carl Friedrich Gauss. This is done by considering some remarks that Gauss made explaining the fruitfulness of new calculi. These can be clarified in the context of his own (very fruitful) theory of congruences, which is considered as a case study for this alternative account. Such an account has the benefit of not being dependent on a particular metaphysical view in the philosophy of mathematics.

机译：本文就卡尔·弗里德里希·高斯（Carl Friedrich Gauss）提出的新数学计算与现有数学方法之间的关系进行了介绍。这是通过考虑高斯解释新结石的成果的一些评论来完成的。这些可以在他自己的（非常有成果的）全等理论的背景下加以阐明，这被认为是该替代性案例的案例研究。这样的解释的好处是不依赖于数学哲学中的特定形而上学观点。

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《Studies in history and philosophy of science》 |2011年第3期|p.410-415|共6页
作者
Audrey Yap;
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作者单位

Department of Philosophy, University of Victoria, P.O. Box 3045, Victoria, Canada BC V8W 3P4;

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正文语种 eng
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number theory; philosophy of mathematics; carl friedrich gauss; mathematical fruitfulness; congruence notation;

机译：数论数学哲学;卡尔·弗里德里希·高斯数学成果同余记法;

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1. Quadratic Reciprocity and the Sign of the Gauss Sum via the Finite Weil Representation [J] . Roger Howe Int Math Res Notices . 2010,第19期

机译：二次互易和有限威尔表示的高斯和的符号
2. A quadratic reciprocity theorem for arithmetical logic [J] . Yvon Gauthier International journal of algebra . 2019,第5a8期

机译：算术逻辑的二次互易定理
3. A block symmetric Gauss-Seidel decomposition theorem for convex composite quadratic programming and its applications [J] . Li Xudong, Sun Defeng, Toh Kim-Chuan Mathematical Programming . 2019,第1a2期

机译：凸复合二次编程及其应用的块对称高斯-Seidel分解定理
4. On a reciprocity theorem of Gauss [C] . Lynne H. Walling International Conference on the Algebraic and Arithmetic Theory of Quadratic Forms . 2009

机译：关于高斯的互惠定理
5. Bifurcation in complex quadratic polynomial and some fold theorems involving the geometry of bulbs of the Mandelbrot set. [D] . Begum, Monzu Ara. 2001

机译：复杂二次多项式的分支和涉及Mandelbrot集球的几何形状的一些折叠定理。
6. Theorems on Quadratic Partitions [O] . Albert Leon Whiteman 1950

机译：二次分区定理
7. A note on Gauss’ first proof of the quadratic reciprocity theorem [O] . L. Carlitz 1960

机译：关于高斯首次证明二次互惠定理的说明
8. Electromagnetic Scattering by Inhomogeneous Objects. Solution Methods Based upon Reciprocity Theorems of Time-Convolution and Time-Correlation Type [R] . Remis, R. 1993

机译：非均匀物体的电磁散射。基于时间卷积和时间相关类型的互易定理的求解方法

Gauss' quadratic reciprocity theorem and mathematical fruitfulness

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