Dr. Sudheer gained some attention for developing a landslide-detection program that impressed R. Chidambaram, the principal scientific adviser to the Indian government. One of Mr. Chidambaram’s goals is to create a system to predict Himalayan landslides, which cause hundreds of deaths and costly damages each year. The technology seemed so promising that Mr. Chidambaram made a trip to visit Amma at the ashram. He told me that Amma, who has only a fourth-grade education, was “far more successful” than the Indian government in attracting top-caliber scientific minds.

Dr. Sudheer invited me to her lab at the university, reached by a short walk from the temple. She showed me a gigantic landslide simulator that she had helped design to test her wireless landslide sensors. Many of the labs looked like ones you might see at M.I.T., save for the fact that Amma’s picture was displayed more or less everywhere.

Amrita University has 17,000 students, who pay tuition that is much higher than that of state-run schools. Critics complain that the university caters mainly to the wealthy, and to a great extent it does, but it’s hard to argue with the school’s success. Its medical school is generally well regarded, and Amrita also offers a dual-degree program in business with the State University of New York at Buffalo.

“We call Amma the best headhunter there is,” said Bipin Nair, who is a dean of Amrita’s school of biotechnology and is leading an effort to create an affordable insulin pump for diabetics. “Every year, when she comes back from a trip to North America or Europe, she has a list of people who have expressed their desire to be a part of the ashram.”

Born and schooled in India, Mr. Nair did postdoctoral work at the University of Tennessee at Memphis. He landed a job at a biotech company in Seattle and bought a six-bedroom house, and yet he felt dissatisfied. He and his wife, Dr. Geetha Kumar, met Amma during one of her American tours and decided to move to the ashram in 2004.

Mr. Nair does not take a salary, working only for room and board. “What we live in now is probably smaller than most bathrooms in the U.S.,” he told me, but added: “I don’t have to do anything. I am not paying a mortgage. I am not cooking, cleaning or shopping — everything is taken care of — all I need to do here is focus on my work.”

People who work without pay keep costs down at the ashram, a selling point that entices donors. “When someone gives one dollar to Amma,” one ashram spokesman told me, “it is really worth 100 times more than that, because if you give that same money to another institution, they have to pay the administrative costs.” Benefactors have included people like Jeff Robinov, the president of the Warner Bros. Pictures Group.