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The Riemann Hypothesis is one of the most famous unsolved problems in mathematics. It is named after Bernhard Riemann, who first proposed it in 1859. The hypothesis relates to the distribution of prime numbers and states that all non-trivial zeros of the Riemann zeta function have a real part equal to 1/2.

The Riemann zeta function, denoted by ζ(s), is a mathematical function that is defined for complex numbers s with a real part greater than 1. It can be extended to the entire complex plane, except for the point s=1, where it has a simple pole. The non-trivial zeros of the zeta function are the complex numbers s for which ζ(s)=0 and have a real part strictly between 0 and 1.

The Riemann Hypothesis is significant because it has far-reaching consequences in number theory. It provides insights into the distribution of prime numbers and helps to explain various patterns and properties of primes. Many other conjectures and theorems in number theory have been proven or disproven assuming the truth of the Riemann Hypothesis.

Despite extensive efforts by mathematicians over the years, the Riemann Hypothesis remains unsolved. It is considered to be one of the seven "Millennium Prize Problems" which were identified by the Clay Mathematics Institute in 2000. A correct solution to the Riemann Hypothesis would not only advance our understanding of prime numbers but also have implications for various other areas of mathematics and science.

Numerous approaches and techniques have been explored in attempts to prove or disprove the Riemann Hypothesis, but none have been successful so far. The hypothesis has stood the test of time and remains a fascinating and challenging problem in mathematics.

The term "Pastry War" refers to a conflict that took place between France and Mexico between 1838 and 1839. It was named the Pastry War because it began after a French pastry cook's shop in Mexico City was damaged during riots.

The underlying cause of the war was a dispute over unpaid debts. Mexico had accumulated significant debts to various foreign powers, including France. When Mexico failed to repay the debts, France sent a fleet to Veracruz to demand payment.

However, the conflict escalated beyond the issue of debt repayment. The French navy bombarded the city of Veracruz and captured it, but Mexican resistance continued. The war lasted for several months, with both sides engaging in battles and skirmishes.

Peace was eventually negotiated between France and Mexico in 1839. Mexico agreed to pay off the outstanding debts and provide compensation to French citizens affected by the war. Additionally, Mexico ceded several territories to France, including the state of Tabasco.

Overall, while the initial cause of the conflict was a dispute over debts, the Pastry War became a broader military confrontation between France and Mexico. Its impact on Mexican history and foreign relations continues to be studied and discussed.