Mistakes in Mathematics: When the Greatest Blunders Took the Longest to Correct

Mathematics, lauded for its precision and correctness, is not immune to human errors. Just like any other field, mathematics has experienced significant blunders that took years, sometimes even decades, to correct. In this article, we explore three of the most notable blunders in the history of mathematics, each taking a long time to be resolved.

1. The Proof of Fermat's Last Theorem by Wiles and Taylor (1995-2018)

One of the most discussed mathematical errors is the proof of Fermat's Last Theorem (FLT). In 1995, Andrew Wiles and Richard Taylor submitted their proof of the theorem that had eluded mathematicians for over 350 years. However, the paper took an additional 23 years to be fully corrected and verified. In 2018, the definitive edition was published, drawing a line under this long-standing controversy.

2. Hilbert's Sixth Problem and the Dulac Lemma (1900-1987)

David Hilbert's famous list of 23 problems in 1900 included the sixth problem, which focused on the axiomatization of probability theory. In the 1950s, two Russian mathematicians claimed to have solved this problem based on a lemma by Dulac in 1920. This lemma later turned out to be false. The entire situation was resolved only in 1987 when it was discovered that the proof relied on an incorrect lemma.

3. William Shanks' Calculation of Pi (1873-1944)

Avoiding the conceptual difficulties, one of the most prominent mistakes in mathematics occurred in 1873. William Shanks performed an extensive calculation of π, reaching just over 700 decimal places. However, only 527 decimal places were correct. The remaining 173 digits were incorrect, a mistake that went unnoticed until 1944 when the English mathematician D.F. Ferguson verified Shanks' work.

The Struggle with Infinity

Including conceptual difficulties, the concept of infinity has posed significant challenges to mathematicians. Dealing with infinite sets, limits, and infinitesimal quantities requires a precise understanding of the underlying concepts. The struggle with infinity is closely tied to the development of calculus and set theory, areas where even the greatest minds have faced conceptual hurdles.

Conclusion

Blunders in mathematics, such as the proof of Fermat's Last Theorem, the mistaken proof of Hilbert's sixth problem, and the incorrect calculations of π, highlight the human element in the pursuit of mathematical perfection. These mistakes, while troubling, serve as reminders of the continuous advancement and correction of mathematical knowledge. The journey to understanding infinity remains an ongoing process, continually pushing the boundaries of human understanding.

Key Takeaways

Wiles and Taylor's proof of Fermat's Last Theorem took 23 years to be fully corrected. A proof of Hilbert's sixth problem based on a mistaken lemma was corrected only in 1987. William Shanks' calculation of π contained incorrect digits, which were only caught in 1944. Conceptual difficulties with infinity persist in the field of mathematics.

Understanding these historical blunders provides valuable insights into the nature of mathematical research and the importance of rigorous verification in the process of making and correcting mistakes.