Isadore Singer, who combined vast fields of mathematics and physics to become one of the most important mathematicians of his day, died Thursday at his Boxborough, Massachusetts home. He was 96 years old.

His death was confirmed by his daughter Natasha Singer.

Dr. Singer created a bridge between two apparently unrelated areas of mathematics and thus built another bridge into theoretical physics. The achievement laid the foundation for a bloom in mathematical physics that has not been seen since Isaac Newton and Gottfried Wilhelm Leibniz, when analysis first provided tools to understand how objects moved and changed.

Dr. Singer’s work with British mathematician Michael Atiyah enabled the development of critical areas of physics such as oak theory and string theory that can revolutionize our understanding of the most fundamental structure of the universe.

He “changed the way people view math by showing that what appeared to be different areas have deep connections,” said Jeff Cheeger, a mathematician at New York University.

“It opened up a whole new world that is expanding and expanding,” he said.

Dr. Singer was an influential voice in scientific matters outside of the theoretical realm as well. From 1975 to 1980 he chaired the Science and Public Order Committee of the National Academy of Sciences, the main scientific advisory board to the President and other government officials.

In this post he organized a report on the disposal of nuclear waste, defended President Ronald Reagan’s “Star Wars” missile defense initiative, despite his political opposition to many Reagan measures, and warned for decades about the pressing public problem of the loss of privacy the growth of the internet.

Under Reagan, he was a member of the White House Science Council from 1982 to 1988 and a member of the Board of Directors of the National Research Council from 1995 to 1999.

Dr. Singer was awarded the National Medal of Science in 1983 and the Abel Prize in 2004, which is often considered the Nobel Prize in Mathematics.

Isadore Manuel Singer – known to his friends as Is – was born in Detroit on May 3, 1924, to Simon and Freda Singer, immigrants from Poland. His father, who only spoke Yiddish, was a printer; his mother was a seamstress. Isadore quickly learned English and taught the language to his family. His brother Sidney became a particle physicist at Los Alamos National Laboratory in New Mexico. (He died in 2016.)

Isadore studied physics at the University of Michigan and graduated in two and a half years to join the Army as a radar officer during World War II. He was stationed in the Philippines and ran a communication school for the Philippine Army during the day. At night he filled the gaps in his short training and studied mathematics in correspondence courses in order to learn the requirements for relativity theory and quantum mechanics.

After retiring from the army, he studied mathematics for a year at the University of Chicago. Although he had planned to return to physics, he fell in love with mathematics and stayed to do his PhD. He completed a postdoctoral fellowship at the Massachusetts Institute of Technology, where he taught for most of his career.

During an interlude at the University of California at Berkeley, he helped found the Mathematical Sciences Research Institute. He also began to prove a number of important theorems, keeping the mathematical literature peppered with his name: the Kadison-Singer conjecture (formulated in 1959 and only proven in 2013), the Ambrose-Singer theorem, the McKean-Singer formula, and the Ray-Singer torsion.

But all of these were dwarfed by its unique contribution, the Atiyah Singer Index theorem. Together with Dr. Atiyah, he created an unexpected connection between the mathematical subfields of analysis and topology – and then linked these fields with theoretical physics.

Dr. Singer was the expert in analysis, that is, the study of differential equations used to describe physical phenomena in the language of analysis. Such equations are extremely useful for describing real-world situations, but they have one problem: nobody knows how to solve them exactly. Scientists are getting closer.

Dr. Atiyah has now specialized in topology, which studies the shapes of abstract mathematical objects, often in many more dimensions than our usual three. Topology considers shapes to be elastic, so objects can be pulled or squeezed without changing their basic nature.

The two fields appeared to be split almost irretrievably, as the topology twists objects and the analysis requires them to be rigid. Still, Dr. Singer and Dr. Atiyah in the early 1960s figuring out whether Dr. Atiyah were able to find solutions to analytical problems that Dr. Singer had with differential equations.

Finding the exact solutions was too difficult. But they found a way to find out the number of solutions to the equations, even without their exact values. This was the set of the Atiyah Singer Index.

The result formed a bridge between topology and analysis, which Dr. Atiyah, Dr. Singer and others expanded and expanded over the next decade, creating a new field called index theory.

That was just the beginning. In 1975, James H. Simons, a mathematician and close associate of Dr. Singer (and later a noted hedge fund manager and philanthropist), and Chen Ning Yang, a Nobel Prize-winning physicist, about their work. They realized that in their own scientific languages ​​they were each talking about a common underlying structure. What the physicists called an “oak theory”, the mathematicians called a “bundle of fibers”.

Due to this connection, the theorem of the Atiyah-Singer index was valid for physics as well as for mathematics. The revolution that had brought them to mathematics was now also being carried over to physics.

“This was the big bang of the union of mathematics and physics in the late 20th century,” said mathematician and economist Eric Weinstein. “It was Is Singer who lit the spark that started the fire.”

Dr. Singer’s first marriage to Sheila Ruff, a play therapist for children with disabilities, ended in divorce. Alongside his daughter Natasha, a technology reporter for the New York Times, his wife Rosemarie Singer survived. three other children, Eliot, Emily, and Annabelle; two stepchildren, Giles and Melissa; and four grandchildren.

Dr. Singer was at the intellectual center of developments in mathematical physics. A weekly seminar he held for decades became a breeding ground for new ideas, perhaps fitting a man who broke new ground in his chosen field and refused to conform to the dry image of a scholar and academic.

“He drove a sports car when everyone else drove a Volvo,” said Dr. Tartar. “He showed up with a tie when nobody was wearing neckwear.”

He added, “He had a very romantic vision of living life through math to the fullest, with style and vigor, and he used his taste and style as a tool in math like no other.”