Masaki Kashiwara, a Japanese mathematician, received this year’s Abel Prize, which aspires to be the equivalent of the Nobel Prize in math. Dr. Kashiwara’s highly abstract work combined algebra, geometry and differential equations in surprising ways.

       The Norwegian Academy of Science and Letters, which manages the Abel Prize, announced the honor on Wednesday morning.

       “First of all, he has solved some open conjectures — hard problems that have been around,” said Helge Holden, chairman of the prize committee. “And second, he has opened new avenues, connecting areas that were not known to be connected before. This is something that always surprises mathematicians.”

       Mathematicians use connections between different areas of math to tackle recalcitrant problems, allowing them to recast those problems into concepts they better understand.

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       That has made Dr. Kashiwara, 78, of Kyoto University, “very important in many different areas of mathematics,” Dr. Holden said.

       But have uses been found for Dr. Kashiwara’s work in solving concrete, real-world problems?

       “No, nothing,” Dr. Kashiwara said in an interview.

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