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Mary L. Bonauto was on a recent getaway to Little Cranberry Island, a lovely spot off the coast of Maine where cellphone service can be spotty. So it took a while before she saw that someone had tried to reach her about a half-dozen times.

“They kept calling,” the civil rights lawyer recalled Wednesday. “I thought it was an emergency.”

As it turns out, it was the MacArthur Foundation trying to track her down, and with big news. Bonauto, a leading force in the legal fight for same-sex marriage in Massachusetts and across the country, had received a MacArthur Fellowship, a prize familiarly known as a “genius grant.”

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Bonauto, 53, was among 21 fellows announced Wednesday by the John D. & Catherine T. MacArthur Foundation, including four from New England. Along with Bonauto, the foundation selected Harvard mathematician Jacob Lurie; Yitang Zhang, a mathematician at the University of New Hampshire; and cartoonist Alison Bechdel of Bolton, Vt.

Fellows receive a $625,000 stipend, which is paid out in quarterly installments during five years and comes with no strings attached.

“The fellowship is not a reward for past accomplishment, but rather an investment in a person’s originality, insight, and potential,” the foundation said.

Bonauto said it took her several moments to realize that she had won the award, and she was taken aback by the news. “At first I just didn’t understand,” she said. “This wasn’t even on my radar.”

Bonauto, who directs the Civil Rights Project at Gay and Lesbian Advocates and Defenders in Boston, was lead counsel in the landmark Massachusetts case that legalized marriage for same-sex couples and led challenges to the federal Defense of Marriage Act, which was eventually struck down by the Supreme Court in 2013.

She played a pivotal role in Baker v. Vermont, a 1999 case that ruled that same-sex couples must be provided the same protections as married couples.

Bonauto said she had not considered what she might do with the stipend, but said she would not be quitting her “day job.” Despite enormous gains, much work remains in the fight for lesbian, gay, bisexual, and transgender equality, she said.

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“I don’t think we’re there yet as a nation,” she said.

Job discrimination remains pervasive, and violence against gays and lesbians remains a fear, she said. Too many children are kicked out of their homes because of their sexual orientation, she added, and many elderly people have no family to help them as they age.

“There are any number of issues,” facing the LGBT community, she said.

At the same time, the award made her think of the progress made since she joined GLAD nearly 25 years ago.

“It’s been a sea change,” she said.

At the University of New Hampshire, Yitang Zhang learned he had won the award a couple of weeks ago, but was asked to keep the news quiet.

Zhang, 59, leapt into prominence with a breakthrough in one of the oldest and most intractable problems in mathematics: the twin prime conjecture, which states that there are an infinite number of prime numbers that differ by two.

Mathematicians had not been able to rule out the possibility that gaps between primes widened, but Zhang determined the gaps are bounded.

“He moved the goal post infinitely far, bringing something that had not been proved into the realm of fact,” said Edward Hinson, chairman of the department of mathematics and statistics at the University of New Hampshire.

Zhang said he worked on solving the problem for several years and was at times frustrated by his setbacks. But in July 2012, he had a sudden realization that made him think, “This can be done.” The following year, his “bounded gap” proof was hailed as a landmark achievement in analytic number theory.

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Zhang said he was very surprised by the award and the size of the stipend. “I didn’t consider it a possibility,” he said.

The MacArthur Fellowships are awarded to scholars, artists, and other professionals who have shown “extraordinary originality and dedication in their creative pursuits and a marked capacity for self-direction,” according to the foundation.

The program does not accept applications or unsolicited nominations.

Harvard mathematician Jacob Lurie, 36, was honored for his transformative work in derived algebraic geometry. His ideas and methods are altering a range of fields and “rewriting large swathes of mathematics from a new point of view,” the foundation said.

Lurie graduated from Harvard College in 2000 and received his doctorate in mathematics from MIT in 2004. He was named a full professor at Harvard in 2008, at age 31.

Bechdel, 54, had a comic strip that ran from 1983 to 2008 that depicted the lives of women in the lesbian community and how they are influenced by cultural and political events of the day.

She has also published two memoirs, “Fun Home: A Family Tragicomic” and “Are You My Mother? A Comic Drama.”