This is a list of Vietnamese inventions and discoveries which includes technological, cultural and historical inventions. This list is incomplete.
Academia Brieskorn–Phạm manifold: a term for a mathematical object defined as the intersection of a small sphere around the origin with a complex hypersurface with singularities, essentially creating a "knot-like" structure in higher dimensions. Brieskorn-Phạm manifolds are important in the study of topology, particularly in the field of exotic spheres, as they can provide examples of smooth manifolds that are topologically equivalent to a standard sphere but have different differential structures. The term was first introduced in 1966 and was further studied and perfected by Vietnamese mathematician Frédéric Phạm. Circular law conjecture in random matrix theory: a conjecture, established by Terence Tao and Vietnamese mathematician Vũ Hà Văn, asserts that for large random matrices with i.i.d. entries of zero mean and unit variance, the scaled eigenvalues asymptotically follow a uniform distribution over the unit disk in the complex plane, regardless of the specific distribution of the matrix entries. Inverse Littlewood-Offord theorem: a result in additive combinatorics that addresses the structure of sets that exhibit concentration of linear combinations of elements. It builds on the classical Littlewood-Offord theorem, which estimates the probability that a random sum of weighted vectors lands in a small region. The theory was developed by Vietnamese mathematician Vũ Hà Văn and Terence Tao. Phong reflection model: an empirical model of the local illumination of points on a surface designed by the computer graphics researcher Bui Tuong Phong, who published it in his 1975 Ph.D. dissertation. It was published in conjunction with a method for interpolating the calculation for each individual pixel that is rasterized from a polygonal surface model; the interpolation technique is known as Phong shading, even when it is used with a reflection model other than Phong's. Phong's methods have proven popular due to their generally efficient use of computation time per rendered pixel. Phong shading algorithm: an interpolation technique for surface shading invented by computer graphics pioneer Bui Tuong Phong. Phong shading interpolates surface normals across rasterized polygons and computes pixel colors based on the interpolated normals and a reflection model. Proof of Brauer's height zero conjecture: a conjecture in modular representation theory of finite groups relating the degrees of the complex irreducible characters in a Brauer block and the structure of its defect groups. This notorious old problem, which has perplexed mathematicians for decades, was finally solved by Vietnamese mathematician Phạm Hữu Tiệp in a September 2024 paper. Proof of Fundamental lemma for automorphic forms: in the mathematical theory of automorphic forms, the fundamental lemma relates orbital integrals on a reductive group over a local field to stable orbital integrals on its endoscopic groups. The fundamental lemma, a problem that had been open for decades, was solved by Vietnamese mathematician Ngô Bảo Châu. His work earned him the Fields Medal in 2010, the most prestigious award in mathematics. Proof of Ore's conjecture: As the commutator subgroup is generated by commutators, a perfect group may contain elements that are products of commutators but not themselves commutators. Øystein Ore proved in 1951 that the alternating groups on five or more elements contained only commutators, and conjectured that this was so for all the finite non-abelian simple groups. Ore's conjecture was finally proven in 2008 by Vietnamese mathematician Phạm Hữu Tiệp and colleagues. Shamir conjecture in random graph theory: Vietnamese mathematician Vũ Hà Văn along with Johansson and Kahn solved the Shamir conjecture in random graph theory. Among others, they established the sharp threshold for the existence of a perfect matching in a random hypergraph. Solution to the Deligne-Lusztig Theory: a way of constructing linear representations of finite groups of Lie type using ℓ-adic cohomology with compact support, part of the foundational machinery of representation theory. Vietnamese mathematician Phạm Hữu Tiệp solved the problem in 2024. The breakthrough touches on traces, an important feature of a rectangular array known as a matrix. The trace of a matrix is the sum of its diagonal elements. The work is detailed in two papers. One was published in Inventiones mathematicae, the second in Annals of Mathematics. The Erdos-Folkman problem: Vietnamese mathematician Vũ Hà Văn solved the Erdos-Folkman problem in 2003, answering the following question in number theory: How dense should a set of positive integers be so that every sufficiently large integer can be represented as a subsum?
Arts Tò He: a traditional toy for children made from glutinous rice powder in form of edible figurine such as animals, flowers or characters in folk stories. Vietnamese calligraphy: includes calligraphic works using a variety of scripts, including historical chữ Hán (Chinese characters), chữ Nôm (Vietnamese-derived characters), and the Latin-based Vietnamese alphabet. Historically, calligraphers used the former two scripts. However, due to the adoption of the Latin-based chữ Vietnamese alphabet, modern Vietnamese calligraphy also uses Latin script alongside chữ Hán Nôm.
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