NP-Incompleteness
Customization Point Objects in C++
10 Sep 2025
In this post I’d like to share my notes on customization point objects (or CPOs) in C++. This is a mechanism that allows users of libraries to provide overloads for their custom types.
Hadamard Factorization Theorem
30 Aug 2025
Jacques Salomon Hadamard was a French mathematician. Among his contributions, Hadamard proved the prime number theorem and has his name on the Hadamard product (element-wise product of matrices) and the Hadamard matrices. Even though he didn’t work in quantum mechanics, Hadamard gates are also named after him because its matricial representation is a Hadamard matrix.
Being of Jewish descent, in 1941 Hadamard left France for the United States during the antisemitic Vichy government. He returned in 1945 after the end of World War II.
In this post I’d like to explore the Hadamard Factorization Theorem.
Horseshoe Theory
24 Aug 2025
According to Wikipedia [1], the horseshoe theory asserts that:
“The extreme left and the extreme right, rather than being at opposite and opposing ends of a linear political continuum, closely resemble each other, analogous to the way that the opposite ends of a horseshoe are close together.”
In this post I’d like to share some anectodes and thoughts on it.
C++ Concepts
17 Aug 2025
In this post I’d like to share my notes of concepts in C++. This feature was added to the standard in C++ 20 and is related to the metaprogramming (templates) system.
The content is mostly my notes on the tech talk by Nicolai Josuttis at CppCon 2024. I used simpler examples and a different structure for the subtopics.
Harmonic Functions
01 Aug 2025
The concept of harmony in mathematics has been used since 6th century BC. Pythagoras is credited with this early association [6]:
“Pythagorean philosophers advanced the unshakable belief that the essence of all things are numbers and that the universe was sustained by harmony.”
He also associated harmony with music. Centuries passed and further associations between music and trigonometric functions (sine waves) occured, leading to terminology such as harmonic series, harmonic analysis and harmonic functions. In this post we’ll study harmonic functions.
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