The Power of Constraints: From Fermat's Last Theorem to Market Wedges


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Aug 05, 2023

3 min read


The Power of Constraints: From Fermat's Last Theorem to Market Wedges


Throughout history, we have seen the power of constraints in various fields. From mathematics to business strategies, constraints have played a significant role in shaping outcomes. In this article, we will explore two seemingly unrelated topics - Fermat's Last Theorem and the concept of market wedges - and discover the common thread that connects them.

Fermat's Last Theorem:

In the 17th century, the French mathematician Pierre de Fermat made a claim in the margin of a book that the equation an + bn = cn had no solutions in positive integers if n is an integer greater than 2. This claim, known as Fermat's Last Theorem, remained unsolved for over three centuries. It captured the attention of mathematicians worldwide, sparking countless attempts to prove or disprove it.

The theorem's significance lies not only in its complexity but also in the constraints it imposes. Fermat's Last Theorem limited the possibilities for solutions, focusing on a specific range of integers and excluding others. This constraint fueled the curiosity of mathematicians, who tirelessly sought a proof that would satisfy Fermat's claim. It was not until 1994 that the British mathematician Andrew Wiles finally provided a proof, using advanced mathematical concepts that were previously unavailable.

Market Wedges:

In the realm of business strategies, market wedges offer a similar approach based on constraints. The concept of a market wedge, popularized by Chris Dixon, involves focusing on serving the needs of a specific niche before expanding to broader markets. By deliberately narrowing their target audience, startups can allocate their limited resources strategically and gain a foothold in a competitive landscape.

A market wedge strategy entails sacrificing immediate growth for long-term power. Instead of pursuing mass adoption, companies concentrate on a smaller segment within their target market. This approach allows them to refine their product or service, build strong customer relationships, and establish a solid reputation before scaling up.

The Connection:

At first glance, Fermat's Last Theorem and market wedges may seem unrelated. However, a closer examination reveals the underlying connection - the power of constraints. Both concepts rely on setting boundaries and working within them to achieve remarkable results.

In the case of Fermat's Last Theorem, the constraint was the limitation on the values of variables in the equation. Mathematicians embraced this constraint and channeled their efforts towards finding a solution within those boundaries.

Likewise, market wedges capitalize on constraints by intentionally narrowing their focus. By concentrating on a small niche, companies can better understand their target audience, deliver tailored solutions, and establish a strong foundation for growth.

Actionable Advice:

  • 1. Embrace Constraints: Whether you're a mathematician or an entrepreneur, embrace constraints as opportunities for innovation. Constraints force us to think creatively and find unique solutions within limited parameters.
  • 2. Prioritize Focus: When developing a business strategy, prioritize focus over immediate growth. By targeting a specific niche, you can refine your offerings, build a loyal customer base, and position yourself for long-term success.
  • 3. Sacrifice for Long-Term Gain: Don't be afraid to sacrifice short-term gains for long-term power. By sacrificing growth in the early stages, you can establish a solid foundation, develop a strong value proposition, and ultimately achieve sustainable growth.


Fermat's Last Theorem and market wedges demonstrate the power of constraints in driving remarkable outcomes. Whether in the realm of mathematics or business, embracing constraints can lead to innovative solutions and long-term success. By setting boundaries and focusing on specific niches, we can leverage constraints to our advantage and achieve extraordinary results. So, the next time you face a constraint, remember that within those limitations lies the potential for greatness.

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