Due to World War II the publication of the journal stopped in 1943 with volume 49. Publication was resumed in 1949 with the volume numbering starting again at 1. In order to distinguish between the identical numbered volumes, volumes in the first publishing period are referred to as the *first series* whereas the later volumes are called *second series*.

Before volume 51 of the second series the journal was called *Tôhoku Mathematical Journal*, with a circumflex over the second letter of *Tohoku*.

- Sprague, R. P. (1936), "Über mathematische Kampfspiele",
*The Tohoku Mathematical Journal*(in German),**41**: 438–444, JFM 62.1070.03, Zbl 0013.29004 . The first publication of the Sprague–Grundy theorem, the basis for much of combinatorial game theory, later independently rediscovered by P. M. Grundy. - Weiszfeld, E. (1937), "Sur le point pour lequel la somme des distances de n points donnes est minimum",
*The Tohoku Mathematical Journal*(in French),**43**: 355–386. This paper describes Weiszfeld's algorithm for finding the geometric median. - Grothendieck, Alexander (1957), "Sur quelques points d'algèbre homologique",
*The Tohoku Mathematical Journal*, Second Series (in French),**9**: 119–221, MR 0102537 . This paper, often referred to as "The Tohoku paper" or simply "Tohoku",^{ [1] }introduced the axioms of abelian categories. - Sasaki, Shigeo (1960), "On differentiable manifolds with certain structures which are closely related to almost contact structure. I",
*The Tohoku Mathematical Journal*, Second Series,**12**(3): 459–476, doi: 10.2748/tmj/1178244407 , MR 0123263 . Part II,**13**: 281–294, 1961, doi : 10.2748/tmj/1178244304, MR 0138065. The introduction of Sasakian manifolds.

In mathematics, **injective sheaves** of abelian groups are used to construct the resolutions needed to define sheaf cohomology.

**Tsuruichi Hayashi** was a Japanese mathematician and historian of Japanese mathematics. He was born in Tokushima, Japan.

In differential geometry, a **hypercomplex manifold** is a manifold with the tangent bundle equipped with an action by the algebra of quaternions in such a way that the quaternions define integrable almost complex structures.

**Vikraman Balaji** is an Indian mathematician and is currently a professor at Chennai Mathematical Institute. He completed his doctorate in Mathematics under the supervision of C. S. Seshadri. His primary area of research is in algebraic geometry, representation theory and differential geometry. Balaji was awarded the 2006 Shanti Swarup Bhatnagar Award in Mathematical Sciences along with Indranil Biswas "for his outstanding contributions to moduli problems of principal bundles over algebraic varieties, in particular on the Uhlenbeck-Yau compactification of the Moduli Spaces of µ-semistable bundles." He was elected Fellow of the Indian Academy of Sciences in 2007, Fellow of the Indian National Science Academy in 2015 and was awarded the J.C. Bose National Fellowship in 2009.

In mathematics, the **Bogomolov–Miyaoka–Yau inequality** is the inequality

In mathematics, a **fake projective plane** is one of the 50 complex algebraic surfaces that have the same Betti numbers as the projective plane, but are not isomorphic to it. Such objects are always algebraic surfaces of general type.

In mathematics, **surfaces of class VII** are non-algebraic complex surfaces studied by (Kodaira 1964, 1968) that have Kodaira dimension −∞ and first Betti number 1. Minimal surfaces of class VII (those with no rational curves with self-intersection −1) are called **surfaces of class VII _{0}**. Every class VII surface is birational to a unique minimal class VII surface, and can be obtained from this minimal surface by blowing up points a finite number of times.

In mathematics, a **Kato surface** is a compact complex surface with positive first Betti number that has a global spherical shell. Kato (1978) showed that Kato surfaces have small analytic deformations that are the blowups of primary Hopf surfaces at a finite number of points. In particular they have an infinite cyclic fundamental group, and are never Kähler manifolds. Examples of Kato surfaces include Inoue-Hirzebruch surfaces and Enoki surfaces. The global spherical shell conjecture claims that all class VII surfaces with positive second Betti number are Kato surfaces.

In the mathematical field of functional analysis, a **nuclear C*-algebra** is a C*-algebra A such that for every C*-algebra B the injective and projective C*-cross norms coincides on the algebraic tensor product *A*⊗*B* and the completion of *A*⊗*B* with respect to this norm is a C*-algebra. This property was first studied by Takesaki (1964) under the name "Property T", which is not related to Kazhdan's property T.

In mathematics, Alexander Grothendieck (1957) in his "Tôhoku paper" introduced a sequence of axioms of various kinds of categories enriched over the symmetric monoidal category of abelian groups. Abelian categories are sometimes called **AB2 categories**, according to the axiom (AB2). **AB3 categories** are abelian categories possessing arbitrary coproducts. **AB5 categories** are the AB3 categories in which filtered colimits of exact sequences are exact. Grothendieck categories are the AB5 categories with a generator.

**Shigeo Sasaki** (佐々木 重夫) was a Japanese mathematician working on differential geometry who introduced Sasaki manifolds. He retired from Tohoku University's Mathematical Institute in April 1976.

**Indranil Biswas** is an Indian mathematician. He is professor of mathematics at the Tata Institute of Fundamental Research, Mumbai. He is known for his work in the areas of algebraic geometry, differential geometry, and deformation quantization.

The article "**Sur quelques points d'algèbre homologique**" by Alexander Grothendieck, now often referred to as the ** Tôhoku paper**, was published in 1957 in the

**Patrick Michael Grundy** was an English mathematician and statistician. He was one of the eponymous co-discoverers of the Sprague–Grundy function and its application to the analysis of a wide class of combinatorial games.

**Matsusaburo Fujiwara** was a Japanese mathematician and historian of mathematics.

**Kaoru Ono** is a Japanese mathematician, specializing in symplectic geometry. He is a professor at the Research Institute for Mathematical Sciences (RIMS) at Kyoto University.

**Toshiki Mabuchi** is a Japanese mathematician, specializing in complex differential geometry and algebraic geometry. In 2006 in Madrid he was an invited speaker at the International Congress of Mathematicians. Mabuchi is known for introducing the Mabuchi functional.

In the mathematical field of differential geometry, a **Kenmotsu manifold** is an almost-contact manifold endowed with a certain kind of Riemannian metric. They are named after the Japanese mathematician Katsuei Kenmotsu.

In the mathematical field of differential geometry, an **almost-contact structure** is a certain kind of geometric structure on a smooth manifold. Such structures were introduced by Shigeo Sasaki in 1960.

**Morihiko Saitō** is a Japanese mathematician, specializing in algebraic analysis and algebraic geometry.

- ↑ Schlager, Neil; Lauer, Josh (2000),
*Science and Its Times: 1950-present. Volume 7 of Science and Its Times: Understanding the Social Significance of Scientific Discovery*, Gale Group, p. 251, ISBN 9780787639396 .

- Kümmerle, Harald (2018), "Hayashi Tsuruichi and the success of the Tôhoku Mathematical Journal as a publication", in Ogawa, T.; Morimoto, M. (eds.),
*Mathematics of Takebe Katahiro and History of Mathematics in East Asia*, Advanced Studies in Pure Mathematics, vol. 79, Tokyo: Mathematical Society of Japan, pp. 347–358 - Oda, Tadao (2011), "The first hundred years of the Tohoku mathematical journal",
*Tohoku Mathematical Journal*, Second Series,**63**(4): 461–470, doi: 10.2748/tmj/1325886276 , MR 2872951

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