Francoise Gilot, at breakfast on Capitol Hill, let the tasteless question hover over her table until it had become as cold and stale as her toast.

How, in her opinion, did two great men from opposite ends of our century -- Pablo Picasso and Jonas Salk -- come to be attracted to the same woman?

Then, with a smile and a flash of her green eyes, she answered it: "Because men like that are surrounded by hangers-on," she said. "Some women, you know, are too eager, and that does not attract. If you think about it much, you can't succeed. But I am very self-centered and independent and I never thought about it. I knew, you see, that it is the man who makes the choice anyhow."

Gilot was the mistress of Picasso for nine years, during which she produced two children, and after which she produced her memoirs, which he attempted to suppress. She is now Mrs. Jonas Salk of La Jolla, Calif., wife of the developer of the first polio vaccine.

The men's careers are notably different -- the one a bare-chested artist, the other a famous research scientist -- but in each case the woman was the same: an articulate beauty, knowlegeable and self-assured; a tough competitor trained in childhood never to doubt herself. She is also a painter with more than 50 solo shows to her credit since 1951, a writer who has written five books and illustrated four others.

She also knew Henri Matisse, about whose life and work she lectured last night to a full Baird Auditorium. She thinks that an academic analysis of an artist's technique is useful as long as vocabularly does not attempt to replace mystery.

"As an artist, I perceive consciously how paintings are made. But somebody else can be equally moved by the harmony in a picture without understanding why. I've noticed that those who know art and those who don't often like the same things about a picture."

But Gilot knows more of art than what's inside the frame. Now, after a 12-hour day in her California studio, she finds herself dining with Nobel prize-winners, and sees achievement in art and science as stitched with a common thread: the thread of ego. Sometimes it is in control, and sometimes not.

"I first met Matisse in 1946, in the south of France. He as quite ill, and had been operated on for cancer of the intestine in 1945. At that time he lived in the Hotel Reginald, in a series of rooms, and made paper cut-outs which his secretary would arrange on the walls at his direction."

Henri Matisse was 85 then, a kindly old man whose famous painting "The Joy of Life," had 40 years before established him in the public eye as prime exponent of his own title.

"In the first place, he was not that kind," Gilot said. "He had serenity, yes, and great self-assurance. But he was, in fact, extremely domineering. He was a patriach, a benevolent despot, to those around him. He was very direct.

"I remember that he was doing some drawings of his grandson, who was extremely handsome. But the boy was involved in a terrible cycling accident, which somewhat disfigured him for a while. Matisse made no expression of sympathy. What he said was, 'Your face is no longer symmetrical, therefore I can no longer draw it.'

"The artist always sacrifices his life to his art, of course. I once asked Matisse about a famous painting of his, 'Oranges' of 1914, which also shows great joy of life. And he told me that when he was painting it, he was hungry and poor in North Africa, and ready to commit suicide."

By 1944, Gilot had joined Pablo Picasso, and the two had begun their years together. But Matisse and Picasso had known each other since 1905, when they had met at Gertrude Stein's apartment in Paris. By the 1940s, they were both giants in the art world who always described each other as friends.

"But in fact, their temperaments were opposed, and in the beginning they didn't especially like each other," Gilot said. "I learned this from each, in separate conversations. For one thing, Matisse was more renowed at first. Also, he was taller. Picasso was shorter than I am -- but he had a large head, which made him look big in photographs.

"Picasso loved winning, and power. That was really all he understood. It disgusted me, that love of power he had. You couldn't be kind to him, he wouldn't understand it.

"He would associate with only the very best people in every field. The best doctors, lawyers, artists. He used to say it would take him less time to learn what they knew if they were really the best. When he met me, I was 21 years old, and considered the best painter of my generation, so I was fine.

"Every artist is an egocentrist, of course. They have to be. I am like that myself. But there has to be a limit, I tell you. It isn't right when you become actively disagreeable to those around you, and nasty, and cause hardships intentionally.

"Picasso had a habit of setting traps all the time, to see if you would fall into them. It was a nasty habit. I would tell him frankly, 'You don't need these tricks, these props and devices, to prove your worth.' I told him that he must doubt himself."

Such exchanges, in which the prideful, 65-year-old master is told of his shortcomings by his lovely, raven-haired mistress, must have caused plaster to fall from ceilings hither and yon. Gilot grants him the quality of the child, and the wonderment of the artist, but her memory also charges him with grave shortcomings as companion and man. Some of the charges -- including her claim that he used his influence to damage her career after their parting -- appeared as revelations in "Life With Picasso," which came out in 1964 and became a best seller.

"There were three lawsuits in which he tried to stop the book," she said. "In the first lawsuit, he said that the book was not true. But, of course, eveything in it was true -- I was very careful about that. Then in the second lawsuit, he claimed that if it was true, it was at least indiscreet. Then the third time, he told the court that whether or not it was true, and whether or not it was indiscreet, it was his life and he was entitled to it. But the judge ruled that it wasn't his life. It was our life.

"When it was over, and I had won, we never saw each other again. But he did call me up to congratulate me, and was very freiendly. You see, when I became the winner, he came back to my side."

Gilot sipped her coffee, completely at ease, one purple suede cowboy boot balanced exquisitely before her and the cold morning sun illuminating her blue-on-magneta outfit like a modern canvas on a gallery wall. She seems to hold little fear of judgement, or of being judged.

"The difference between the two of them was that in Matisse, the man was as great as his art. I'm afraid that that was not the case with Picasso. wIf you had to be around him much, you suffered."

Gilot's life has changed much in 30 years, of course.

She and Dr. Salk were married in a civil ceremony in a suburb of Paris in June of 1970. Their home in La Jolla overlooks the Pacific, and each morning when they are there, they arise early and go their separate ways -- her husband to his labs and offices at the Salk Institute, where he is at work on a cure for multiple sclerosis; and she to her studio, five miles away.

"We are very good together, because the two of us are the same -- we work like horses every day, 9 to 9 at least. I have built my own studio to my own specifications, with 30-foot ceilings and a northern exposure, and some writing rooms attached to it. I like to work long hours and see nobody. There is an answering service which takes my calls.

"Then at night, Jonas will call. 'Are you finished yet?' 'Yes, how about you?' We are two people who understand the need to work, but sometimes we laugh to think we each have a partner of that type."

Gilot has met many scientists, she says, and finds their work of great interest. She's especially fascinated with research about how the brain works.

"You know, they have placed electrodes on a person's head, and shown that different cells in the brain react to different colors, and shapes. And what a painter is trying to reach is those same parts of the brain. So perhaps we're facing a new renaissance."

In fact, Dr. and Mrs. Salk are not in California much of the time, and so she maintains a studio in Paris as well, and spends as much as four months a year there. This gives her the opportunity to visit Claude and Paloma, her children by Picasso; and Aurelia, whose father, the french painter Luc Simon, she married and divorced after leaving Picasso.

"Maybe I am better prepared than others to understand some things," she said yesterday, perhaps speaking of egos and artists and the requirements of accomplishment. "But the source of self-assurance is always within yourself.

"When I was a girl, I remember getting the top grade in one of my classes.

But when the report card came home, the teacher had written 'Francoise can do better work.' I was outraged. From that point on, I set my own goals, and judged myself."