What Is the Oldest Unsolved Problem in Math?

TL;DR

The oldest unsolved problem in mathematics is whether any odd perfect numbers exist. Despite extensive research spanning over 2000 years, no examples have been found, and modern heuristic arguments suggest they are unlikely to exist. However, proving their existence or non-existence remains a significant mathematical challenge.

Transcript

• This is a video about the oldest unsolved problem in math that dates back 2000 years. Some of the brightest mathematicians of all time have tried to crack it, but all of them failed. In the year 2000 the Italian mathematician, Piergiorgio Odifreddi, listed it among four of the most pressing open problems at the time. Solving this problem could be... Read More

Key Insights

• #️⃣ Perfect numbers are numbers whose proper divisors add up to the number itself.
• 💯 Only 51 perfect numbers are known, and all of them are even.
• 💯 The problem of odd perfect numbers has been studied for over 2000 years without a solution.
• #️⃣ Modern techniques, such as computer algorithms and the study of spoof numbers, have been used in the search for odd perfect numbers.
• 💯 Heuristic arguments suggest that odd perfect numbers are unlikely to exist, but a proof has not been found yet.
• 💯 The problem of odd perfect numbers continues to inspire mathematicians and offers an opportunity for individual exploration and discovery.
• 🙈 Mathematical research, even on seemingly abstract problems, can have surprising real-world applications, as seen with cryptography.

Summary & Key Takeaways

• The problem of odd perfect numbers dates back 2000 years and has stumped mathematicians throughout history.

• Perfect numbers are numbers whose proper divisors add up to the number itself.

• The search for odd perfect numbers has been conducted using computers and algorithms, but no solution has been found so far.