Three hundred professors at Stanford, including Nobel laureates and this year’s Fields medal winner, are calling on the university to rid itself of all fossil fuel investments, in a sign that the campus divestment movement is gathering force.

In a letter to Stanford’s president, John Hennessy, and the board of trustees, made available exclusively to the Guardian, the faculty members call on the university to recognise the urgency of climate change and divest from all oil, coal and gas companies.

Stanford, which controls a $21.4bn (£14.2bn) endowment, eliminated direct investments in coalmining companies last May, making it the most prominent university to cut its ties to the industries that cause climate change. Months later, however, the university invested in three oil and gas companies.

Campus divestment campaigns have spread to about 300 universities and colleges over the last few years, but are largely dominated by students. The Stanford letter was initiated by faculty, and signed by the first female winner of the prestigious Fields prize in mathematics, Maryam Mizarkhani, as well as the Nobel laureates Douglas Osheroff and Roger Kornberg, Paul Ehrlich, a population analyst, Terry Root, a biologist and UN climate report author, and others – 300 faculty members in total.

The letter calls on Stanford to pull out of all fossil fuel investments, not just coal. “The urgency and magnitude of climate change call not for partial solutions, however admirable; they demand the more profound and thorough commitment embodied in divestment from all fossil-fuel companies,” the letter says.

“The alternative – for Stanford to remain invested in oil and gas companies – presents us with a paradox: if a university seeks to educate extraordinary youth so they may achieve the brightest possible future, what does it mean for that university simultaneously to invest in the destruction of that future? Given that the university has signalled its awareness of the dangers posed by fossil fuels, what are the implications of Stanford’s making only a partial confrontation with this danger?”

Elizabeth Tallent, an English professor and one of the organisers of the letter, said she saw the campaign as a natural extension of her work as a professor. “I think if you want what you do to matter, and not only for a moment in the classroom, you think: how can students make use of this in 10 years or 20 years? If you are imagining the future of youth in 20 years, then you run into the problem of what the world will look like.”

Ehrlich, known for his warnings about overpopulation, said Stanford had an obligation to protect its endowment. “It’s crystal-clear that fossil fuels, most of them, are going to have to remain in the ground if we are going to avoid a real catastrophe and of course the value of stock is tied to that,” he said. “If we are not going to be able to use those fossil fuels, the stock is going to tank and places like Stanford have a fiscal responsibility to maintain the endowment. Having an investment in fossil fuels is a very bad investment.”

Stanford would not comment directly on the petition. But a spokeswoman, Lisa Lapin, said in an email that Stanford had completely withdrawn its investments from coalmining companies.

She said an advisory panel was studying the feasibility of further fossil fuel divestment. “Stanford takes all concerns raised with the university about the nature and impact of its investments very seriously,” Lapin said.

The fossil-fuel divestment campaign has grown rapidly over the past few years, driven by the deepening awareness that most of the world’s coal, oil and gas reserves must stay in the ground to avoid catastrophic climate change. According to the world’s leading climate scientists, those safety limits could be breached within 30 years if the world goes on burning fossil fuels at the current rate,

Last September, the heirs to the Rockefeller oil fortune withdrew their $860m philanthrophic fund from investments in tar sands, coal, and oil. Campaigners claimed at the time to have persuaded 800 investors – foundations such as the Rockefeller brothers, religious groups, healthcare organisations, cities and universities – to withdraw a total of $50bn from fossil fuel investments over the next five years.

But Harvard rejected a campaign by students and 100 faculty to remove fossil fuel holdings from its $32bn endowment, claiming such a move would have only a negligible financial impact.

George Shultz, secretary of state under Ronald Reagan and a fellow at Stanford’s Hoover Institution who has tried to push fellow Republicans to act on climate, said the university should think instead about imposing a revenue-neutral carbon tax.

“I am very much on the side of worrying about climate issues,” he said. But he did not support the divestment campaign, adding: “It’s mainly to make people here feel good.”

Ehrlich said it was important for leading universities such as Stanford to take a stand. “It is very important that educational institutions in particular and organisations that think of themselves as part of civil society make this important step,” he said. “It is symbolic. It is not going to instantly change the amount of greenhouse gas emissions, but it is damn important.”