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Carl Jacobi was a German-born mathematics whiz kid.

Among the accomplishments in his short life - he died at 46 - were significant contributions to elliptic functions, dynamics, differential equations, determinants, and number theory.

One of the techniques he used to achieve all of these breakthroughs was “inversion.”

In problem-solving, inversion is the practice of taking the opposite perspective of a desired outcome to unlock new ideas, approaches, and solutions.

Jacobi coined the phrase “man muss immer umkehren."

Here’s a practical example of how it works.

Let’s say you have a goal to improve your eating habits and take in fewer than 2000 calories per day.

(As my trainer says, “Abs are made in the kitchen, not the gym.”)

To invert this goal, you’d ask the opposite question: “What would cause me to eat poorly?”

I can easily identify how to do that...

Keep plenty of empty carbs on hand, including a bowl of candy on the kitchen counter for grazing.

Eat out for most meals, fast food whenever possible.

Stay up late every night watching TV (staying up late correlates with increased daily caloric intake).

Avoid water at all costs and drink plenty of alcohol and soft drinks when thirsty.

Pretty easy!

Now all I have to do is take steps to avoid these pitfalls.

Clear out the pantry and fill it up with healthy, nutrient-rich foods.

Get rid of the candy bowl on the kitchen counter.

Go to bed by 10:30pm, or better yet, make it 9.

Drink two liters of water every day.

At first glance, it feels counterintuitive to dwell on all the ways to fail at meeting a goal, but it’s also enlightening. Inversion uncovers flawed thinking and the unobvious aspects of solving a problem.

Consider guidance from the book “Extraordinary Tennis Ordinary Players.”

The same concept applies in golf.

Tiger Woods is one the best pro golfers in history.

Not only could he hit all of the required shots, but he consistently made great decisions. He didn’t beat himself by making the same mistakes as every other player.

Charlie Munger, billionaire investor and businessman, quips, "All I want to know is where I’m going to die so I’ll never go there."

Munger also applied inversion to business:

But how does the concept of inversion apply to SaaS?

Let’s take a look.

Most marketing teams aim to create awareness and differentiate their brand to target buyers. Applying inversion, you could ask, “What if we wanted to blend in and appear the same as everyone else in our category?”

Well, you’d probably want to copy your competitors’ messaging and use the same channels and marketing tactics to reach your target customers.

To avoid blending in, marketers might target a niche or lean into an under-appreciated channel.

Sales's goal is to convert demand into paying customers. But what if the opposite was true? How could you minimize the conversion of inbound demand into ARR?

Pretty simple. You'd skip customer discovery questions and jump right into a feature demo on the first call. You’d also leave all follow-up to the prospect and not worry about mapping out the steps required to close a deal.

To avoid this, sales leaders are likely to make investments into training, certifying, measuring, and coaching their sales reps on fundamentals.

The goal of customer success is to ensure that existing customers maximize value, usage, and buy more.

By inverting, you may ask, “How could we ensure that our customers don’t renew at their next opportunity?”

Easy. You’d bypass onboarding, keep them in the dark about new product releases, and make it difficult to get help when they need it. You’d only contact them when it’s time to renew (and increase prices).

That would do the trick.

Even a basic onboarding program and a set of success-focused interactions throughout the course of the year, would be a major improvement.

Most product development teams desire to build simple products that generate healthy Gross Margins. But as products mature they become bloated, more difficult to use, and more costly to deliver.

A good inversion question for product might be, “What wold make our product more complex for existing customers?”

This might lead you to consider an addition by subtraction strategy.

Paul Graham, founder of Y Combinator, explains how he assesses a startup’s viability in the essay, Default Alive or Default Dead:

Assuming the goal is “default alive,” you can invert by asking the opposite: “What would make our company 'default dead?'”

Simple. Hire a a bunch of marketers and salespeople before you prove a repeatable, non-founder-led selling motion.

To avoid this mistake, you’d define metrics and stage gates that signal product-market fit. Furthermore, you'd prove repeatable demand creation and conversion tactics with a handful of marketing and sales ninjas before attempting to scale up.

I admit, some of this sounds silly.

But what becomes obvious as you practice inversion is that consistency is the currency of good execution, and fundamentals are often more important than strokes of brilliance.

Use whichever sports analogy you like:

Blocking and tackling.

Dribbling and passing.

Base hits versus home runs.

Success is about avoiding self-defeat.

What’s the big outcome you’re chasing this year? And what inversion questions could you ask to find new pathways to success?

🤘