She believed that the radium element, and all elements discovered in the future, belonged to the whole world and all mankind. Applying for a personal patent is a selfish act. She hopes not to apply for a patent to make better use of this element.
In order to benefit mankind, she did not apply, and she also hoped that she would not apply for elements discovered in the future.
Because she believes that this is her duty as a scientist, and this is where her greatness lies.