That Sweet Little Old Lady (Brain Twister) is a science fiction novel by Randal Garrett and Laurence M. Janifer under the pen-name of 'Mark Phillips', first published in 1959. It was nominated for the Hugo Award in 1960 under the name Brain Twister.
In the not too distant future, Ken Malone, young but promising FBI agent, is given the most important and difficult assignment of his career: find a spy who is stealing information from the Ultra Top Absolute Secret project to develop a non-rocket space ship at Yucca Flats Labs in Nevada.
But this is not a normal spy, this spy laughs at the FBI and all attempts to find him or her because they use an unknown new method to steal the information directly from the minds of the scientists.
And then of course, there is the Sweet Little Old Lady who is immortal and the stunning nurse and the Las Vegas gangsters and... well, you had better listen to the story to find out the details.
His first problem: how do you find a telepath to catch the first telepath?