The crucial turning points of the climate era can be found in a series of sentences, some of them pretty opaque, but all of them critical. The latest came on Tuesday morning in a report from the International Energy Agency, in Paris, and it could very well signal the start of the end of the fossil-fuel era. So it’s important to first set it in the context of a few other such statements.

In 1995, the Intergovernmental Panel on Climate Change said, “The balance of evidence suggests a discernible human influence on global climate.” Ever since NASA’s Jim Hansen told Congress, in 1988, that climate change was under way, the world’s scientists and governments had been scrambling to reach workable conclusions on which to base policy. This sentence was the key line of the I.P.C.C.’s Second Assessment Report: close observers understood that, over the objections of countries such as Saudi Arabia, the world’s scientific community was announcing, irrevocably, that global warming was very real.

In 2015, in Article 2 of the Paris climate accord, the world’s governments committed to “holding the increase in the global average temperature to well below 2°C above pre-industrial levels and pursuing efforts to limit the temperature increase to 1.5°C above pre-industrial levels, recognizing that this would significantly reduce the risks and impacts of climate change.” This was the first time that the world had set a solid target, and that target was a hard one: holding the rise in warming as close as possible to 1.5 degrees Celsius, a goal urged by climate activists and the most vulnerable nations.

In 2018, the I.P.C.C. reported on what it would take to meet that Paris goal, saying, “In model pathways with no or limited overshoot of 1.5°C, global net anthropogenic CO₂ emissions decline by about 45% from 2010 levels by 2030 (40–60% interquartile range), reaching net zero around 2050 (2045–2055 interquartile range).” Translation: if you want to have any chance of limiting warming to 1.5 degrees, you have to cut emissions in half by 2030, and to net zero by 2050.

The statement on Tuesday from the I.E.A. is a recommendation. It reads, “There is no need for investment in new fossil fuel supply in our net zero pathway. Beyond projects already committed as of 2021, there are no new oil and gas fields approved for development in our pathway, and no new coal mines or mine extensions are required.” That emphasis is in the original—in fact, in the new report that sentence is in headline-size type, as well it should be. It says that, after two hundred and fifty years, in the view of the I.E.A., the time has come to stop exploring for oil, gas, and coal. No rational plan for getting to 1.5 degrees (or anywhere near it) can deal with any new supply. Instead, the “the focus for oil and gas producers switches entirely to output—and emissions reductions—from the operation of existing assets.” That is, we obviously can’t stop burning fossil fuel tomorrow, but we have to be headed decisively in that direction—which means stopping the development of new fields and draining what we must from existing fields to hold us over until we’ve built enough solar panels and wind turbines.

This message comes from a credible source—indeed, the I.E.A. has always been captive to the fossil-fuel industry, or at least to the countries, such as the United States, where that industry has held sway. For years, its forecasts of how fast renewable energy would spread were understatements; it was an engine of the status quo.

But now governments and corporations, pushed by civil society—and, perhaps, by a recognition of our climate plight—are suddenly committing to net-zero targets. Virtually all the big banks, for instance, have made this pledge. And now the I.E.A. has told them what it means. If they’re serious about it, they don’t just have to lend money to people who want to set up solar panels. (Clearly, they have to do that. “Policies need to be designed,” the report says, “to send market signals that unlock new business models and mobilise private spending, especially in emerging economies.”) Just as important, they must now stop doing what they’ve long been doing, which is pumping trillions of dollars into fossil fuels. No new pipelines. No new liquefied-natural-gas projects on the Gulf Coast. No “gas led recovery” in Australia. No TMX pipeline from Canada’s tar sands. None of it.

As Elizabeth Bast, the executive director of Oil Change International, a nonprofit that has worked for a fossil-fuel nonproliferation treaty, told me, “The I.E.A. is finally recognizing the lock-in risk of new fossil-fuel extraction. It’s clear that what’s already developed is enough to meet demand in a world aligning with 1.5 Celsius. And, at some point, the numbers just don’t add up. Further fossil-fuel expansion just isn’t compatible” with a working planet.

The fact that the I.E.A. is now saying this so loudly and clearly will be an immeasurable boost to campaigners around the world who have been working to block the fossil-fuel industry and its backers among the banks, insurance companies, and asset managers. It’s also a reflection of how much the world is changing. Part of that is due to the election of Joe Biden, of course, but the sheer logic of the scientific argument can eventually cut through even vested interest. It’s been an agonizing three-plus decades since Hansen’s warning, and that vested interest may have delayed action too long; waiting until the icecaps were actually melting was an incredible mistake.

But the strength of these four sentences is what our hope for a livable world rests on, the intellectual scaffolding erected by science and reason—and the passion of hardworking activists—on which to base our future. We will all find out if they’re strong enough for that daunting task.