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The Gap Between Truth And Proof

The 1930 Königsberg conference hosted two of the greatest minds in mathematics engaged in a profound struggle. The conference saw David Hilbert, largely regarded as the father of 20th-century mathematics, admonish the crowd that all problems in mathematics are solvable, declaring, “We must know. We will know.”

At the same conference, Kurt Gödel sat at a humble roundtable sharing the beginnings of the Incompleteness Theorems, two mathematical theorems that would soon upend the assumptions of the scientific world.

The war of “provability” represented by Hilbert and Gödel still rages on in marketing. Modern marketing has experienced a fundamental shift from an emphasis on creativity and insight to an obsession with efficiency and marketing attribution.

When digital marketing promised to close the gap between effort and ROI at the turn of the century, one could virtually hear the primal roar of business executives everywhere. Almost in unison, the C-suite thundered, “We must know. We will know!”

But a curious thing happened. As I wrote about previously, digital marketing hasn’t led to a nirvana in which effort and ROI can be perfectly linked. While we can now measure marketing more precisely than ever, consumer behavior is only getting more uncertain.

This paradox leads to a fundamental question: Is marketing attribution a bust, or could modern business practices be built on a 100-year-old lie? The answer may be a matter of faith.


The Latin maxim “Ignoramus et ignorabimus” means “We do not know and will not know.” It represented a popular assertion in the 19th century about the limits of scientific knowledge and was heretical to mathematician David Hilbert.

In response to the assertion, Hilbert declared at the Königsberg conference that, “For us there is no ignorabimus, and in my opinion even none whatever in natural science. In place of the foolish ignorabimus let stand our slogan: We must know. We will know.”

Hilbert’s motto is eerily similar to a demand marketing experts receive from business leaders every day: “How do we know this will work?”

“How do we know this will work?” is a dangerous question. It is both the first and worst question, like asking for guarantees from a financial advisor. Things that we know will work are, by definition, consistent, repeatable, mundane, systematic and efficient. As a business leader, you should already be doing the things that you know will work. But for the tough problems, the unusual circumstances, the challenges for which insight and creativity must come together to pioneer a new solution, you cannot know if it will work.

In other words, “We do not know and will not know” if a new creative idea will work until the marketplace tells us. Moving forward, despite the inability to answer the question “How do we know this will work?” requires business leaders to demonstrate something that is uncommon and uncomfortable in business culture: faith.

The Gap

Just as David Hilbert stood at a podium at the Königsberg conference and proudly declared that all problems in mathematics can be proven, Kurt Gödel sat at a round table and shook the foundations of mathematics and philosophy by revealing his Incompleteness Theorems.

Marcus du Sautoy, Professor of Mathematics at the University of Oxford, explained the profound meaning of Gödel’s theorems in an interview, saying they “[place] this extraordinary limitation on what we might be able to know in mathematics. In fact, it’s quite an unnerving theorem … Gödel shows that actually there is a gap between truth and proof.”

Ironically, Gödel proved there will always be truth that we cannot prove. This gap between truth and proof represents the most important zone of decision making for exceptional business leaders. It requires faith in the face of fear. And it has arisen repeatedly in my firm’s research.

My firm has conducted three national studies and published multiple books exploring the factors that affect growth in business. Again and again, the loss of nerve is a reoccurring factor that precedes growth problems. The loss of nerve most often arises when facing a decision in this gap between truth and proof. And it results in specific and predictable bad decisions by management teams, including resisting narrowly defining target audiences and not investing in employee training, marketing and R&D.

The gap between truth and proof was navigated when executives at Avis considered pointing out its own weaknesses in the classic “We Try Harder” campaign.

The gap was navigated when Geico executives considered using humor in the insurance industry, a previously unthinkable strategy. Their choice would lead to the Gecko and Cavemen campaigns and the Geico we know today.

The gap was navigated by a boardroom of executives at Dos Equis when considering The Most Interesting Man in the World, a creative message that both put down beer consumption and downplayed its own product.

And it was navigated when T-Mobile contemplated highlighting the anti-consumer tendencies of its own industry, just before its “Un-Carrier” campaign upended the industry and led to years of gains.

Proof is for the repeatable, systematic and mundane. If you want special, insightful and creative, you are seeking truth that cannot be proven yet. You are seeking the very thing our business culture doesn’t believe exists — truth beyond proof.

When David Hilbert declared that “In mathematics there is no ignorabimus,” he was wrong. Gödel proved there is truth you cannot prove.

If your business needs to break out of the mundane, you don’t “need to know if this will work.” You need faith.

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Written by

Jonathan David Lewis

Vice President, Strategy Director and MW+C Partner. They’re very serious titles. And Jonathan takes his work very seriously.

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