In 1940, when in his 60s, British mathematician GH Hardy wrote a famous defence of his discipline, and a word of caution for those choosing to follow in his footsteps. Never forget, he said, that mathematics is a "young man’s game".
The idea that truly groundbreaking ideas come only to the young has long since spread to the business world: companies innovate when they are fresh and hungry, but are doomed eventually to become victims of their own success. Scale and the efficient pursuit of regular dividends leave them fatally brittle in the face of the next disruptive start-up.
Like most such received wisdom, it is at best a half truth. Just as great thinkers can have a late or second wind (Darwin was 50 when On the Origin of Species was published, Newton laid out the foundations of classical mechanics at 47, and don’t get me started on Aristotle), so can companies remain innovative long after their founders have passed on - it's just rather rare.
One prominent example is WL Gore & Associates, an American business that has for 60 years devised, manufactured and licensed novel products derived from fluoropolymers. The most famous among these is the waterproofing material Gore-Tex, though Gore also produces materials used in state-of-the-art filtration systems, medical devices, electronics and cables for spacecraft.
What’s remarkable is that despite its relatively limited innovation brief - one would have imagined, a generation ago, that there couldn’t be that many more product lines left in fluoropolymers - the company has kept innovating, driven by a company culture and flat management structure which have frequently been the object of business school research, and which led the company onto numerous best-places-to-work lists.
"Our hypothesis is that by creating an inclusive environment, where all 10,000 of our associates are oriented to the same mission - which is products that make an impact on society - we create an environment of personal commitment and responsibility, which allows associates to bring their best ideas and do their best work," explains CEO Jason Field.
That may sound like any other chief executive talking up the virtues of their business, real or imagined, but Gore’s results speak for themselves. Its latest revenues were $3.5bn, an entirely organic increase of 260 per cent since the turn of the millennium.
The culture of innovation underpinning this long-term growth derives from several fairly straightforward sources, says Field, who took the top job a year ago after joining Gore in 2005.
The central concept is ownership, which can be taken both literally (all associates, as Gore’s staff are known, own stock in the family firm) and figuratively (in a flat structure, passing the buck is tricky - associates are held accountable for their projects, although they are involved in realistic goal-setting).
Innovation-killing bureaucracy, meanwhile, is prevented by capping the size of business units broadly in line with Dunbar’s Number - the supposed upper limit to cohesive communities proposed by anthropologist Robin Dunbar, which is anywhere between 100 and 230.
"By having small units, associates develop relationships, understand where knowledge resides in the organisation and can tap into the capabilities they need to make quality decisions for our enterprise," says Field.
For this structure - called the ‘lattice organisation’ by co-founder Bill Gore - to work, people need to understand the limits of their own knowledge and understanding, so as to be willing to ask for help when it’s needed.
Here’s how the innovation process works. An employee has an idea for an entirely new product line, which is perhaps tangential to their day job, or even unrelated, as often happens at Gore.
The business makes time and limited resources available to staff to explore the idea, while it’s in its infancy. But there comes a time when the business has to choose which ideas to progress to the next stage.
"You might be surprised to learn that we do actually have a fair bit of structure here. There is a process where ideas are submitted and reviewed centrally, because the evidence shows that existing businesses tend to suppress those ideas that take them away from their core," explains Field.
Once an idea is selected, it enters a more formal stage-gate innovation system, with expertise drawn in from around the business. The associate behind the idea is encouraged to stick with their new project, even if it involves months seconded from the day job.
People with the right expertise will be drawn from across the business, and indeed from outside, with new recruits selected as much for their values - humility, competitiveness and an appetite for risk first and foremost - as their skills.
"We provide a lot of freedoms, but in order to capitalise on that freedom, you have to be a self starter, you have to be willing to step out of your comfort zone," says Field.
Mimicking this approach to innovation may be easier imagined than done, especially outside of the framework of a growing family business - few ownership models would afford the same willingness to experiment, both with product ideas and with organisational structure.
But the key principle behind Gore’s success - that the quality of your innovation depends on unleashing the potential of your people, and not on the chief executive’s genius or force of will - is one that any business would do well to emulate.