About
About this site
I am a graduate student in mathematics, and this blog is a site where I organize what I have studied. As of writing this post, I am not yet a senior scholar, the content is mostly written by adapting well-known references in each field, with some modifications.
This blog’s title comes from something one of my seniors once told me. Roughly, it was about not trying to study everything when doing research, but to deciding what to accept as facts and putting the proofs into my own black box. This is entirely the right direction for research, I think anyone in mathematics also has the desire to have a solid, logically complete background. This blog is a sort of hobby to satisfy that desire, which means that the posts will be updated very seldomly.
Operating an English Site
When I started this blog, AI didn’t appear and I had to choose whether to write posts in Korean or English. In Korea, we often use English textbooks to study mathematics, and I chose to write posts in Korean so that it can be a process of understanding in my own word rather than copying.
As of 2026, the development of AI has progressed rapidly, and translating existing Korean posts into English — even in the field of mathematics — is no longer a difficult task. Therefore, within the limits of my AI’s rate limit – I think it’s gonna be one or two a week – I started translating existing Korean documents back into English. Of course, I also review the translated results, but the task is not a priority for me so there might be misleading translations. Please let me know if you find one.
References
As mentioned at the beginning, the posts in these categories all heavily based on existing references, which I’ve also listed at the end of each post. Here are some of major references.
Linear Algebra
[Goc] M.S. Gockenbach, Finite-dimensional linear algebra, Discrete Mathematics and its applications, Taylor&Francis, 2011.
[Lee1] 이인석, 선형대수와 군, 서울대학교 출판문화원, 2005.
Set Theory
[Bou1] N. Bourbaki. Elements of the History of Mathematics. Springer, 2013
[HJJ] K. Hrbacek, T.J. Jeck, and T. Jech. Introduction to Set Theory. Lecture Notes in Pure and Applied Mathematics. M. Dekker, 1978.
Category Theory
[Rie] Emily Riehl. Category Theory in Context. Dover Publications, 2016.
Algebraic Structures
[Bou2] Bourbaki, N. Algebra I. Elements of Mathematics. Springer. 1998.
Multilinear Algebra
[Bou2] Bourbaki, N. Algebra I. Elements of Mathematics. Springer. 1998.
Homological Algebra
[Hu] S.T. Hu, Introduction to homological algebra. University Microfilms, 1979.
[Wei] C.A. Weibel. An Introduction to Homological Algebra. Cambridge Studies in Advanced Mathematics. Cambridge University Press, 1995.
Commutative Algebra
[AM] M.F. Atiyah and I.G. Macdonald, Introduction to commutative algebra, Basic Books, 1969.
[Eis] David Eisenbud. Commutative Algebra: with a view toward algebraic geometry. Springer, 1995.
Topology
[Bou3] N. Bourbaki, General Topology. Elements of mathematics. Springer, 1995.
[Mun] J.R. Munkres, Topology. Featured Titles for Topology. Prentice Hall, Incorporated, 2000.
Manifolds
[Lee2] John M. Lee. Introduction to Smooth Manifolds, Graduate texts in mathematics, Springer, 2012
[War] Frank W. Warner. Foundations of Differentiable Manifolds and Lie Groups, Graduate texts in mathematics, Springer, 2013
Differential Geometry
[Lee3] John M. Lee. Introduction to Riemannian Manifolds, Graduate texts in mathematics, Springer, 2019
Algebraic Geometry
[Har] R. Hartshorne, Algebraic geometry. Graduate texts in mathematics. Springer, 1977.
[Vak] R. Vakil, The Rising Sea: Foundation of algebraic geometry. Available online.