Mr. Carson, whose mother at times received food stamps to provide for her family, grew up surrounded by some of the housing assistance programs he will now oversee. Yet, rather than embrace the programs that once sustained his family and the families around him, he has adopted standard Republican beliefs that too much government help — both in desegregating neighborhoods and in lifting people from poverty — can discourage people from working hard.

Mr. Carson was awarded a scholarship to Yale University, and at 33, he was named director of pediatric neurosurgery at Johns Hopkins Children’s Center. He later became an author and a philanthropist supporting scholarships for young, often impoverished students.

After his medical career, Mr. Carson turned to politics and competed with Mr. Trump for the Republican presidential nomination.

Mr. Carson’s views worry many of his critics, who believe the federal government should be doing more, not less, for the nation’s cities, where glittering downtowns and increasingly gentrified neighborhoods are often surrounded by areas of poverty and violence, with predominantly minorities.

It is unclear how much Mr. Carson will seek to change housing policy. During his confirmation hearing, he would not commit definitively to avoid directing tax dollars to Trump businesses.