# Best answer to – what is the longest standing math problem?

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The longest standing math problem is the problem of Fermat’s Last Theorem, which remained unsolved for over 350 years until Andrew Wiles proved it in 1994.

The longest standing math problem is the famous Fermat’s Last Theorem, which remained unsolved for over 350 years until Andrew Wiles finally proved it in 1994. This problem, proposed by Pierre de Fermat in the mid-17th century, states that there are no three positive integers a, b, and c that satisfy the equation a^n + b^n = c^n for any integer value of n greater than 2. Fermat claimed to have a proof for this theorem, but famously wrote in the margin of a book that the margin was too small to contain it.

The theorem captured the imagination of mathematicians for centuries, but it wasn’t until the 20th century that advances in mathematics made it possible to prove such a complex problem. Andrew Wiles, a British mathematician, spent seven years working in secret on a proof, which finally culminated in 1994. When Wiles announced his achievement, it was described by the New York Times as “one of the most important mathematical proofs of the century.”

Here are some interesting facts about Fermat’s Last Theorem:

• Pierre de Fermat was a famous mathematician and lawyer, known for his many contributions to number theory. His work on this theorem was noted and studied by many famous mathematicians in the centuries that followed, including Leonhard Euler and Sophie Germain.
• For years, the theorem remained one of the most famous unsolved problems in mathematics. In the 19th century, it was even featured on a list of unsolved problems published by the Paris Academy of Sciences.
• Andrew Wiles’ proof involved combining ideas from many different branches of mathematics, including number theory, algebraic geometry, and analysis.
• The proof was not without controversy, as Wiles had initially made a mistake in his calculations that was discovered by another mathematician. Wiles was able to correct the error and complete the proof, but it was a reminder of the difficulty and complexity of working on such a problem.
• Today, Fermat’s Last Theorem is regarded as one of the most famous and important problems in the history of mathematics. As historian Amir Alexander writes, “Fermat’s Last Theorem serves as a kind of emblem of mathematical creativity and ingenuity, as well as a reminder of its limits.”
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Table:

Fermat’s Last Theorem
Problem statement
Proposed by
Year proposed
Years unsolved
Solved by
Year solved
Fields involved

As mathematician and writer Marcus du Sautoy writes, “there is something timeless and enduring about Fermat’s Last Theorem.” Its long history, complex nature, and eventual solution have made it an enduring symbol of mathematical inquiry and discovery.

## Response to your question in video format

YouTuber Michelle Khare attempts to solve the world’s longest math problem consisting of 10,000 digits on a scissor lift within six hours. She successfully solves a 10-digit problem, then a 100-digit problem while struggling with the last few lines, followed by a thousand-digit problem that she completes. Despite being pelted with water balloons for every wrong answer, Michelle uses a Chinese abacus and finishes the entire problem in 5 hours and 42 minutes, with the help of her team who check her work. The YouTuber expresses their support for those struggling with math and their pride in Michelle’s completion of the problem, and the video concludes with Michelle shedding tears of joy.

## I discovered more data

Mathematicians worldwide hold the Riemann Hypothesis of 1859 (posed by German mathematician Bernhard Riemann (1826-1866)) as the most important outstanding maths problem. The hypothesis states that all nontrivial roots of the Zeta function are of the form (1/2 + b I).

Fermat’s Last Theorem

Since the 1995 proof of Fermat’s Last Theorem, a problem which stood for 365 years, the current longest-standing maths problem is the conjecture posed by Christian Goldbach (1690-1764), a Russian mathematician, in 1742.

Some old chestnuts from additive number theory:

Collatz conjecture [ http://en.wikipedia.org/wiki/Collatz_conjecture ] (3n + 1 conjecture) – since 1937

Goldbach’s (strong) conjecture [ http://en.wikipedia.org/wiki/Goldbach’s_conjecture ] – open since 1742

Goldbach’s weak conjecture [ http://en.wikipedia.org/wiki/Goldbach%27s_weak_conjecture ] (solved 2013): Every odd number greater than 5 can be expressed as the sum of three primes, repetition allowed.

and also: What are good hitherto-unknown prime-generating formulae?
(they can’t be polynomial, they must involve e.g. exponentiation, transcendentals, rounding)

and a full list, categorized by branch, at:
List of unsolved problems in mathematics [ http://en.wikipedia.org/wiki/Unsolved_problems_in_mathematics ]

Then, What does x3 y3 z3 k equal? In mathematics, entirely by coincidence, there exists a polynomial equation for which the answer, 42, had similarly eluded mathematicians for decades. The equation x3+y3+z3=k is known as the sum of cubes problem.

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Hereof, Has 3X 1 been solved? In 1995, Franco and Pom-erance proved that the Crandall conjecture about the aX + 1 problem is correct for almost all positive odd numbers a > 3, under the definition of asymptotic density. However, both of the 3X + 1 problem and Crandall conjecture have not been solved yet.

Accordingly, What is the oldest unanswered math problem? In reply to that: Ondrej Vlcek on LinkedIn: Goldbach’s conjecture is one of the oldest unsolved problems in math.

What is the hardest math problem possible?
x3+y3+z3=k, with k being all the numbers from one to 100, is a Diophantine equation that’s sometimes known as "summing of three cubes."

Subsequently, What is the longest-standing math problem? The reply will be: Since the 1995 proof of Fermat’s Last Theorem, a problem which stood for 365 years, the current longest-standing maths problem is the conjecture posed by Christian Goldbach (1690-1764), a Russian mathematician, in 1742. Goldbach’s Conjecture states that every even positive integer greater than 3 is the sum of two (not necessarily distinct) primes.

How difficult is Fermat’s Last Theorem? As an answer to this: The proof for this simple conjecture was not solved for over 350 years and through the centuries became one of math’s greatest puzzles. Fermat’s Last Theorem has entranced so many mathematicians due to its duality between simplicity and difficulty. It is easy to understand yet almost impossible to prove or disprove.

Is the Riemann hypothesis valid in 257 years?
No one has succeeded in proving or disproving the validity of this conjecture in 257 years. Mathematicians worldwide hold the Riemann Hypothesis of 1859 (posed by German mathematician Bernhard Riemann (1826-1866)) as the most important outstanding maths problem.

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Moreover, What is a good book about unsolved problems in geometry?
Croft, Hallard T.; Falconer, Kenneth J.; Guy, Richard K. (1994). Unsolved Problems in Geometry. Springer. ISBN 978-0-387-97506-1. Guy, Richard K. (2004). Unsolved Problems in Number Theory. Springer. ISBN 978-0-387-20860-2. Klee, Victor; Wagon, Stan (1996). Old and New Unsolved Problems in Plane Geometry and Number Theory.

Keeping this in view, What is the longest-standing math problem? Answer will be: Since the 1995 proof of Fermat’s Last Theorem, a problem which stood for 365 years, the current longest-standing maths problem is the conjecture posed by Christian Goldbach (1690-1764), a Russian mathematician, in 1742. Goldbach’s Conjecture states that every even positive integer greater than 3 is the sum of two (not necessarily distinct) primes.

Correspondingly, How difficult is Fermat’s Last Theorem?
The proof for this simple conjecture was not solved for over 350 years and through the centuries became one of math’s greatest puzzles. Fermat’s Last Theorem has entranced so many mathematicians due to its duality between simplicity and difficulty. It is easy to understand yet almost impossible to prove or disprove.

Moreover, Is the Riemann hypothesis valid in 257 years?
No one has succeeded in proving or disproving the validity of this conjecture in 257 years. Mathematicians worldwide hold the Riemann Hypothesis of 1859 (posed by German mathematician Bernhard Riemann (1826-1866)) as the most important outstanding maths problem.

What is a good book about unsolved problems in geometry? Croft, Hallard T.; Falconer, Kenneth J.; Guy, Richard K. (1994). Unsolved Problems in Geometry. Springer. ISBN 978-0-387-97506-1. Guy, Richard K. (2004). Unsolved Problems in Number Theory. Springer. ISBN 978-0-387-20860-2. Klee, Victor; Wagon, Stan (1996). Old and New Unsolved Problems in Plane Geometry and Number Theory.

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