We are deeply saddened to share with the community the news of the passing of Mitsuyasu Hashimoto on December 29, 2025, at the age of 63.
Below is a message we received from Kazuhiro Kurano:
Hashimoto had long pursued research in the boundary between commutative algebra and invariant theory/representation theory. He did his mathematics with extreme care and, in that sense, he also had an uncompromising side. At the same time, he was very kind to those around him.
Hashimoto and I entered Kyoto University in 1981. As I recall, we first became acquainted in our third year. In our fourth year, we were both assigned to the laboratory of Professor Masayoshi Nagata, where we began studying commutative algebra. At that time, the members of Nagata’s group included Assistant Professor Jun-ichi Nishimura and a senior student, Mitsuhiro Miyazaki, who was two years ahead of us. Hashimoto and I worked on the problem of whether the minimal free resolution of determinantal ideals can be realized over the integers — in other words, whether the Betti numbers depend on the characteristic of the base field. Hashimoto resolved this problem by showing that, in the case of the ideal generated by the 2×2 minors of a generic 5×5 matrix, the second Betti number does depend on the characteristic of the field. I greatly admired his quick thinking and sheer intellectual power. Hashimoto and I were the last students to receive a doctoral degree under Nagata.
After that, Hashimoto took a position at Nagoya University. We were able to meet several times a year at symposia. Later, Hashimoto moved to Okayama University, and then to Osaka Metropolitan University. He wrote a Springer Lecture Notes on twisted inverse functors with group actions. In our second joint paper, we determined the canonical module of the Cox ring, and in the proof we made use of this twisted inverse functor with group actions. He also conducted research on a positive-characteristic version of Boutot’s theorem. In recognition of these achievements, he was awarded the Algebra Prize of the Mathematical Society of Japan in 2017.
Hashimoto devoted a great deal of energy towards settling the Jacobian conjecture; he even took a vow to abstain from alcohol until the day that he was successful.
About forty days before his passing, Hashimoto, Nishimura and I had dinner together and enjoyed fugu cuisine. Hashimoto had a good appetite, and spoke very positively about the future. However, I was told that his condition suddenly worsened in mid-December 2025. We had talked about continuing to enjoy mathematics together, without rushing, taking things slowly; it is deeply regrettable that this will no longer be possible.
We will remember Mitsuyasu Hashimoto and his work forever.