Carl Friedrich Gauss

"A mathematical guide to thinking with the end in mind"

By Hamzah Javaid

December 21, 2022

Gaussian Thinking.

Gaussian Thinking.

Carl Friedrich Gauss, a towering figure in the realm of mathematics, achieved great feats from a young age. As the anecdotes recount, Gauss’s teacher tasked the class with adding all numbers from 1 to 100. Gauss, displaying his mathematical brilliance, discerned that adding the first and last numbers, 1 and 100, yielded 101. The same result was true from combining 2 and 99, 3 and 98, and so forth. Gauss’s insight revealed that there were precisely 50 pairs totalling 101 within the range of 0 to 100. The answer to the question therefore was simply 5050, short and simple.

Mathematical Thinking - the art of the shortcut

As human beings, we have an innate affinity for order, often adhering to the adage “first things first.” However, Gauss demonstrated the advantages of conceiving the end before beginning. In mathematics, this approach is akin to a shortcut—an art form where the destination is envisioned even before the journey begins. Gauss’s method mirrors Amazon’s philosophy of “working backwards” from a problem, a testament to thinking outside the box.

In our professional endeavors, whether at work or within projects, we frequently plunge headlong into tasks without a clear vision of the final outcome. There exists a pervasive belief that innovation necessitates reinventing the wheel, starting from scratch, adhering doggedly to “first things first.” Rarely do we conduct comprehensive literature reviews, browsing resources on the internet or literature, to discern existing solutions. Emulating Gauss’s approach, why not explore diverse avenues of thought and shortcuts, rather than adhering to a linear, brute-force methodology?

Consider a data science project:

  • Beginning

Initiate by surveying the landscape—comprehend the available data, its sources, and identify initial obstacles. This initial phase often aligns with what’s referred to as “Sprint Zero.”

  • End

Contemplate the eventual deployment and service of the model—cloud-based, through an API (such as FastAPI), or for batch inference and streaming. Delve into the intricacies of productionisation and monitoring.

The beginning and the end - both are equally important!

The beginning and the end - both are equally important!

Two approaches

    1. Working Backwards

According the “Working Backwards” authors Colin Bryar and Bill Carr, “in a working-backwards world, starting with the customer and working backwards is the only way to build products and services that customers actually want.” The approach is centered around the customer’s needs and incorporates sentiments of testing and validation during the development process. As Bryar and Carr explain, “The sooner you can validate an assumption, the sooner you can move on to the next assumption or pivot your approach.”

This is also emphasised by Peter Drucker in his writing:

“The purpose of a business is to create a customer. The test of the organisation is its capacity to create customers.”

    1. “Build It And They Will Come”

“Build It And They Will Come” is an approach where the team develops the solution with the assumption that there is a demand for it. This approach is useful when there is a high level of certainty that the solution will be useful to customers, and there is no need for further validation. The “Build It And They Will Come” approach assumes that there is a demand for the product or service, but this is not always the case

Laying the track, digging the tunnel

Consider both the beginning and end in mind when formulating the problem

“7 Habits of Successful People, Habit 2: Begin with the end in mind”

Lay the groundwork first.

Lay the groundwork first.

Closing Thoughts Inspired by Aristotle

Aristotle distinguished between two distinct types of work:

  • Praxis: Work undertaken for its inherent value.
  • Poesis: Work directed toward a specific goal or objective.

We can harness Carl Friedrich Gauss’s philosophy of starting with the end in mind, embracing shortcuts, to achieve success in Poesis while retaining the freedom to engage in activities akin to Praxis—activities that bring us closer to the essence of human freedom.

Posted on:
December 21, 2022
3 minute read, 636 words
Thinking model Reflections
See Also:
Charlie Munger - LatticeWork
Active Listening
Charlie Munger - 12 key learnings