“The really striking thing about Musk is the disjuncture between his outsized public persona, and his very, very minimal philanthropic presence,” said Benjamin Soskis, who studies philanthropy at the Urban Institute. Where other billionaires have aimed for a broad impact on society, Mr. Soskis said Mr. Musk’s foundation lacks “any direction or any real focus, outside his business ventures.”

Mr. Musk did not respond to requests for comment.

A school for his children

Mr. Musk and his younger brother, Kimbal, started the Musk Foundation in 2001, a year before the sale of PayPal, the online payments company he co-founded, to eBay for $1.5 billion. He made more than $175 million in the sale, and would seed his namesake foundation with about $2 million worth of eBay shares.

The Musk Foundation’s website initially included slick animations, featuring pictures of satellite dishes and children in classrooms, while encouraging people to apply for grants. By 2005, however, it was wiped clean, replaced by plain black text stating that the foundation was interested in “science education, pediatric health and clean energy.”

It listed no contact information. It still does not.

By September 2014, Forbes estimated that Mr. Musk’s net worth was more than $10 billion, driven up by the value of his holdings of Tesla stock. But he gave little to his own charity. That year, tax filings show, his foundation had $40,121 in the bank.

That fit with Mr. Musk’s public stance on philanthropy. His for-profit companies, he said, were his way of changing the world.