The Oldest Unsolved Problem in Math

The oldest unsolved problem in mathematics is often considered to be the **"Twin Prime Conjecture"**, which dates back over two millennia. It concerns the distribution of prime numbers and has intrigued mathematicians since antiquity. Here's an overview of this problem and some other contenders for the title:

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### **The Twin Prime Conjecture**
- **Statement:** There are infinitely many twin primes, where twin primes are pairs of primes that differ by 2 (e.g., \(3\) and \(5\), \(11\) and \(13\), \(17\) and \(19\), etc.).
- **Origins:** The conjecture is often attributed to ancient Greek mathematicians, such as Euclid (around 300 BCE). While Euclid proved the infinitude of primes, the specific question about twin primes remains unresolved.
- **Current Status:** Despite significant progress, including Yitang Zhang's breakthrough in 2013 on bounded gaps between primes, the problem remains unsolved.

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### **Alternative Contenders**
While the Twin Prime Conjecture is widely recognized as one of the oldest unsolved problems, other ancient mathematical questions also persist:
1. **Perfect Numbers and Mersenne Primes**
- The search for whether there are infinitely many perfect numbers (numbers equal to the sum of their proper divisors) and their connection to Mersenne primes (\(2^p - 1\), where \(p\) is prime) has roots in ancient Greek mathematics.

2. **Odd Perfect Numbers**
- No odd perfect number has ever been found, and it remains unknown whether they exist.

3. **Goldbach's Conjecture**
- Proposed in 1742, this states that every even integer greater than 2 is the sum of two primes. Though much younger than the Twin Prime Conjecture, it remains unsolved.

4. **Squaring the Circle, Doubling the Cube, and Trisecting the Angle**
- These problems from classical Greek geometry were proven impossible in the 19th century using algebra and analysis. However, they were "open" for centuries and reflect humanity's early engagement with mathematical puzzles.

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### Why It Matters
The Twin Prime Conjecture and similar ancient problems highlight the deep and enduring nature of mathematical inquiry. They connect modern mathematics with its historical roots and demonstrate the timeless challenge of understanding numbers and their properties.