Mathematicians have called into question the old adage that a monkey typing randomly at a keyboard for long enough would eventually produce the complete works of Shakespeare.

Two Australian mathematicians have deemed it misleading, working out that even if all the chimpanzees in the world were given the entire lifespan of the universe, they would “almost certainly” never pen the works of the bard.

The paper tested the “infinite monkey theorem”, a thought experiment demonstrating that an infinite amount of time can make something that is incredibly unlikely become probable, by asking what would happen if generous yet finite limits were placed on the monkey typists.

Their calculations were based on a monkey spending about 30 years typing one key a second at a keyboard with 30 keys – the letters of the English language plus some common punctuation. It found that the time it would take for a typing monkey to replicate Shakespeare’s works would be longer than the lifespan of our universe.

The “heat death” of the universe was assumed to take place in around a googol of years – that is a one followed by 100 zeroes. Other more practical considerations – such as what the monkeys would eat, or how they would survive the Sun engulfing Earth in a few billion years – were set aside.

There was only around a 5% chance that a single monkey would randomly write the word “bananas” in their lifetime, according to the study in the journal Franklin Open.

Shakespeare’s canon includes 884,647 words – none of them banana.

To broaden out the experiment, the Australian mathematicians turned to chimpanzees, the closest relative of humans. There are currently about 200,000 chimps on Earth, and the study presumed this population would remain stable until the end of time.

Even this massive monkey workforce fell very, very short.

“It’s not even like one in a million,” study co-author Stephen Woodcock of the University of Technology Sydney told New Scientist. “If every atom in the universe was a universe in itself, it still wouldn’t happen.”

And even if many more chimps who typed much quicker were added to the equation, it was still not plausible “that monkey labour will ever be a viable tool for developing written works of anything beyond the trivial”, the authors wrote in the study.

A previous trial into the thought experiment, which gave six Sulawesi crested macaque monkeys four weeks with a computer, produced just five pages of text, primarily filled with the letter S.