Does the human lifespan have a limit?

Michael Eisenstein in Nature:

In the late eighteenth century, while in hiding from his fellow French revolutionaries, the philosopher and mathematician Nicolas de Condorcet posed a question that continues to occupy scientists to this day. “No doubt man will not become immortal,” he wrote in Sketch for a Historical Picture of the Progress of the Human Mind, “but cannot the span constantly increase between the moment he begins to live and the time when naturally, without illness or accident, he finds life a burden?”

The answer to that question remains the subject of debate. Some researchers posit that modern human lifespans are nearing a natural ceiling, whereas others see no evidence for such a limit. Arguments have often become heated, with research articles occasionally prompting angry letters to journal editors and even allegations of fraud.

More here.