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Introduction

Mathematics is often thought of as a world of pure logic, where discoveries are made in solitude and shared for the common good. However, history tells a different story.

Behind many of the mathematical breakthroughs we take for granted today lie fierce rivalries, accusations of plagiarism, and battles for credit.

In this article, we explore some of the most contentious disputes among mathematicians, where the line between independent discovery and intellectual theft became blurred.

Fast forward to today, and we’re seeing a similar kind of battle—but now it’s unfolding in the world of AI.

What can these past conflicts teach us about the challenges we're facing with AI right now? Let’s dig in and find out.

1. L’Hôpital and Bernoulli: The Case of the Secret Deal

Anyone who has studied calculus has encountered L’Hôpital’s Rule, a method for evaluating limits. But what if I told you the rule was not actually discovered by Guillaume de L’Hôpital?

In the late 1600s, L’Hôpital, a French nobleman and mathematics enthusiast, struck a deal with the Swiss mathematician Johann Bernoulli. The agreement was simple: Bernoulli would send L’Hôpital his mathematical discoveries in exchange for financial support. Essentially, Bernoulli acted as his personal mathematics tutor, regularly sending him new results.

One of these results was the famous rule for solving certain limits (now called L'Hôpital’s Rule). L'Hôpital later published a textbook in 1696, presenting this rule without clearly mentioning Bernoulli’s contributions.

Years later, Bernoulli publicly accused L’Hôpital of taking credit for his work. While there was no outright plagiarism (Bernoulli had willingly shared his ideas), historians have since confirmed that the rule should rightfully bear Bernoulli’s name. Nevertheless, L’Hôpital’s name remains attached to the rule in textbooks worldwide.

2. Newton vs. Leibniz: The Calculus Controversy

Few disputes in the history of mathematics are as infamous as the battle between Isaac Newton and Gottfried Wilhelm Leibniz over the invention of calculus. Both men independently developed the fundamental ideas of calculus, but who was first?

Newton had worked on calculus as early as the 1660s but did not publish his findings immediately. Leibniz, working independently, developed his version in the 1670s and published his results in 1684. When Newton saw Leibniz’s work, he and his supporters accused Leibniz of plagiarism, claiming he had seen Newton’s unpublished notes.

The dispute escalated into a bitter international controversy. In England, Newton’s followers ensured that Leibniz was portrayed as a fraud. Meanwhile, in Europe, Leibniz’s notation and approach gained widespread acceptance.

Today, historians generally agree that both men independently discovered calculus. It's a perfect example of how two great minds can reach similar discoveries independently, but disputes can still arise.

3. Cardano and Tartaglia: A Broken Promise

In the 16th century, mathematicians struggled to solve cubic equations. Niccolò Tartaglia, an Italian mathematician, discovered a general solution but kept it secret, fearing others would steal his work.

Enter Girolamo Cardano, a prominent mathematician and physician, who convinced Tartaglia to reveal the solution under oath that he would never publish it. However, Cardano discovered later that another mathematician, Scipione del Ferro, had actually discovered the same solution before Tartaglia. Cardano saw this as permission to break his promise. He published the cubic solution in his famous book Ars Magna in 1545, crediting both del Ferro and Tartaglia.

Tartaglia felt deeply betrayed, accusing Cardano of dishonesty. This situation turned into a bitter public dispute, tarnishing their reputations and leading to heated exchanges of letters.

4. Taylor and Maclaurin: A Case of Overshadowing

Brook Taylor and Colin Maclaurin both worked on function expansions, but their contributions are remembered very differently.

Taylor introduced what we now call the Taylor Series in 1715. His work was groundbreaking but somewhat difficult to use in practice. Decades later, Maclaurin, a Scottish mathematician, published a special case of the Taylor Series in 1742, expanding functions specifically around zero. This became known as the Maclaurin Series, which was much easier to apply in many problems.

Although Maclaurin openly acknowledged Taylor’s prior work, his name became more closely associated with the series due to its practical applications. Today, students often learn Maclaurin Series before encountering the more general Taylor Series, demonstrating that sometimes being firs doesn’t always mean being best remembered.

Conclusion: The Human Side of Mathematics and AI

These stories remind us of that mathematics, like any field of human endeavour, is not free from disputes, ambition, and sometimes deception. Whether through secret agreements, broken promises, or bitter rivalries, mathematicians have fought for recognition throughout history.

But isn’t the same happening now—with AI?

The AI revolution is being shaped by the same forces that have driven mathematical discovery for centuries. Behind every breakthrough, every model, every paper—there are people and companies. Companies competing for market share and recognition, building on past knowledge while pushing boundaries forward.

Who will be remembered? The true pioneers? Or the ones who claim the spotlight?

Understanding these human stories makes both math and AI more fascinating—and reminds us that behind every theorem, proof, or algorithm is a person—or, more often, a team—with all the complexities that brings.

Hope you enjoyed exploring these stories together!