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Heisuke Hironaka, Groundbreaking Mathematician, Is Dead at 94
A recipient of his profession's prestigious Fields Medal, he devised an algorithm that helps solve mathematical "singularities." It now permeates the field.
Heisuke Hironaka, an influential mathematician who received one of his profession's highest honors for devising an algorithm to handle the sharp edges and pointy peaks of geometry, died on March 18 at his home in Tokyo. He was 94.
His death was confirmed by his daughter Eriko Hironaka, who is also a mathematician.
For smooth surfaces, the mathematical machinery of calculus, invented by Isaac Newton and Gottfried Wilhelm Leibniz in the late 17th century, works well to solve problems like calculating the motions of planets. Finding solutions is much more difficult when an equation jumps sharply or makes an instantaneous turn to another direction at a certain value or blows up to infinity — what mathematicians call singularities.
In the 1960s, Dr. Hironaka figured out how to perform "resolutions of singularities," turning something sharp or undefined into something smooth, which can then be tackled by the tools of calculus. His technique, which generalized earlier work to dimensions higher than the three-dimensional universe we live in, now permeates many fields of mathematics.
"A singularity might be a crossing or something suddenly changing direction," Dr. Hironaka said in an interview published in 2005 in The Notices of the American Mathematical Society. Without singularities, he added, the world "would be completely flat. If everything were smooth, then there would be no novels or movies. The world is interesting because of the singularities."
Dr. Hironaka explained the general idea of his work through an example of a roller coaster. "A roller coaster does not have singularities — if it did, you would have a problem!" he noted in the 2005 interview. "But if you look at the shadow that the roller coaster makes on the ground, you might see cusps and crossings."
The cusps and crossings represent singularities, but they would be understood as projections of a smooth, higher-dimensional object — the roller coaster. "You can pull back to the smooth thing, and there the calculation is much easier," Dr. Hironaka added.
By Kenneth Chang
March 25, 2026
A recipient of his profession's prestigious Fields Medal, he devised an algorithm that helps solve mathematical "singularities." It now permeates the field.
Heisuke Hironaka, an influential mathematician who received one of his profession's highest honors for devising an algorithm to handle the sharp edges and pointy peaks of geometry, died on March 18 at his home in Tokyo. He was 94.
His death was confirmed by his daughter Eriko Hironaka, who is also a mathematician.
For smooth surfaces, the mathematical machinery of calculus, invented by Isaac Newton and Gottfried Wilhelm Leibniz in the late 17th century, works well to solve problems like calculating the motions of planets. Finding solutions is much more difficult when an equation jumps sharply or makes an instantaneous turn to another direction at a certain value or blows up to infinity — what mathematicians call singularities.
In the 1960s, Dr. Hironaka figured out how to perform "resolutions of singularities," turning something sharp or undefined into something smooth, which can then be tackled by the tools of calculus. His technique, which generalized earlier work to dimensions higher than the three-dimensional universe we live in, now permeates many fields of mathematics.
"A singularity might be a crossing or something suddenly changing direction," Dr. Hironaka said in an interview published in 2005 in The Notices of the American Mathematical Society. Without singularities, he added, the world "would be completely flat. If everything were smooth, then there would be no novels or movies. The world is interesting because of the singularities."
Dr. Hironaka explained the general idea of his work through an example of a roller coaster. "A roller coaster does not have singularities — if it did, you would have a problem!" he noted in the 2005 interview. "But if you look at the shadow that the roller coaster makes on the ground, you might see cusps and crossings."
The cusps and crossings represent singularities, but they would be understood as projections of a smooth, higher-dimensional object — the roller coaster. "You can pull back to the smooth thing, and there the calculation is much easier," Dr. Hironaka added.
By Kenneth Chang
March 25, 2026