Just in case you were banking on science coming up with a way to let you hold onto your youthful looks forever, we have some disappointing news. It's just not going to happen.

Mathematically speaking, multicellular organisms like us will always have to deal with a cellular competition where only one side will win. And ultimately, that means our vitality will always come out as the loser.

We have a pair of researchers from the University of Arizona to blame for this depressing conclusion, who crunched the numbers on a hypothesis involving the weeding out of unfit cells and found it amounted to a catch-22 situation.

"Ageing is mathematically inevitable – like, seriously inevitable," says evolutionary biologist Joanna Masel.

"There's logically, theoretically, mathematically no way out."

Ageing – and all of the biological changes that come with it – is more or less the result of cells slowing down and losing their functions.

For example, the steady greying of hair as we age is the result of pigment-producing melanocytes failing to replenish with the slow loss of their tissue's stem cells.

And wrinkles are a sign that cells called fibroblasts aren't as good at producing the protein collagen as they once were.

But what if there was a way to encourage the more active cells to stick around at the expense of their sluggish siblings? Surely if we knocked off those old cells we could keep making pigments and collagen a little longer.

Researchers have pinned hopes on reversing the inevitable decay of biochemistry by repairing DNA or extending the shrinking bits of chromosome called telomeres, for example.

While it's good in theory, there is a catch.

Another feature of ageing is a number of cells start to populate like there's no tomorrow, reproducing in uncontrolled ways that look too close to cancer for comfort.

According to the researchers, this means we're damned either way.

"If you get rid of those poorly functioning, sluggish cells, then that allows cancer cells to proliferate," says lead researcher Paul Nelson.

"And if you get rid of, or slow down, those cancer cells, then that allows sluggish cells to accumulate."

The way we grow old poses something of a mystery. If replicating biology is good enough to continue for generations, why do our own cells wind down after just a few decades?

A simple answer is evolution isn't strong enough to weed out genes that only cause us grief after we've popped out a few offspring.

But this model of ageing adds a new element to the existing hypothesis – even if evolution did select for eternal youth, competition inside our own bodies would see us to an inevitable grave.

In other words, since multicellular organisms are the cumulative effect of bunches of cooperating cells, we logically can't have it both ways – if you clear the way for 'younger' cells to keep your skin baby-smooth, you're just asking for the big C.

"So you're stuck between allowing these sluggish cells to accumulate or allowing cancer cells to proliferate, and if you do one you can't do the other," says Nelson.

None of this means there is zero headway that can be made in retaining some youthful characteristics longer, or staving off cancer for a few more years.

It just means fixing one problem makes the other one more of a challenge, so eventually one of those issues – cancer or senescence – is going to catch up.

"We have a mathematical demonstration of why it's impossible to fix both problems," says Masel.

Given that kind of choice, maybe a few more wrinkles and failing eyesight isn't sounding all that bad.

This research was published in PNAS.