The Most Puzzling Problems in Mathematics
(with books to study each problem in depth π)
A Thread π
(with books to study each problem in depth π)
A Thread π
1/ Today, we'll explore some of the most famous unsolved problems in mathematics, discuss their significance, and look at the progress being made towards finding solutions. Let's dive in!
2/ The Riemann Hypothesis:
This conjecture, proposed by Bernhard Riemann in 1859, relates to the distribution of prime numbers. If proven true, it could have significant implications for number theory and cryptography. Despite many attempts, a proof remains elusive.
This conjecture, proposed by Bernhard Riemann in 1859, relates to the distribution of prime numbers. If proven true, it could have significant implications for number theory and cryptography. Despite many attempts, a proof remains elusive.
3/ The Collatz Conjecture:
This simple yet deceptive problem asks whether iterating a specific function on any positive integer will eventually reach the number 1. Despite its simplicity, the conjecture has resisted proof for over 80 years.
This simple yet deceptive problem asks whether iterating a specific function on any positive integer will eventually reach the number 1. Despite its simplicity, the conjecture has resisted proof for over 80 years.
4/ The Twin Prime Conjecture:
Twin primes are pairs of prime numbers with a difference of 2 (e.g., 3 and 5, 11 and 13). The conjecture posits that there are infinitely many twin primes, but a proof remains to be found.
Twin primes are pairs of prime numbers with a difference of 2 (e.g., 3 and 5, 11 and 13). The conjecture posits that there are infinitely many twin primes, but a proof remains to be found.
πBook:
"SIMILARITIES BETWEEN LANDAU'S PROBLEMS: GOLDBACH'S CONJECTURE AND OTHER CONJECTURES IN NUMBER THEORY "
by Sr Javier Santos
amzn.to
"SIMILARITIES BETWEEN LANDAU'S PROBLEMS: GOLDBACH'S CONJECTURE AND OTHER CONJECTURES IN NUMBER THEORY "
by Sr Javier Santos
amzn.to
5/ The Goldbach Conjecture:
Proposed in 1742, this conjecture states that every even integer greater than 2 can be expressed as the sum of two prime numbers. Although extensively tested and widely believed to be true, no formal proof exists yet.
Proposed in 1742, this conjecture states that every even integer greater than 2 can be expressed as the sum of two prime numbers. Although extensively tested and widely believed to be true, no formal proof exists yet.
6/ The Birch and Swinnerton-Dyer Conjecture:
This conjecture relates to elliptic curves and their rational solutions. It is one of the seven Clay Mathematics Institute's Millennium Prize Problems, with a $1 million reward for a correct solution.
This conjecture relates to elliptic curves and their rational solutions. It is one of the seven Clay Mathematics Institute's Millennium Prize Problems, with a $1 million reward for a correct solution.
π Book:
"Unsolved Problems in Number Theory" (Problem Books in Mathematics, 3rd Edition) by Richard Guy
amzn.to
"Unsolved Problems in Number Theory" (Problem Books in Mathematics, 3rd Edition) by Richard Guy
amzn.to
7/ The P vs NP Problem:
This problem asks whether every problem whose solution can be verified quickly (in polynomial time) can also be solved quickly. A proof would have profound implications for computer science, optimization, and cryptography.
This problem asks whether every problem whose solution can be verified quickly (in polynomial time) can also be solved quickly. A proof would have profound implications for computer science, optimization, and cryptography.
π Book:
"What is the P vs NP problem?: A complete explanation of the biggest unsolved problem in Computer Science"
by Ramaswami Mohandoss
amzn.to
"What is the P vs NP problem?: A complete explanation of the biggest unsolved problem in Computer Science"
by Ramaswami Mohandoss
amzn.to
8/ The Navier-Stokes Existence and Smoothness Problem: This problem concerns the equations governing fluid dynamics. Solving it would provide a better understanding of fluid behavior, with applications in weather prediction, oceanography, and engineering.
π Book:
"A Student's Guide to the NavierβStokes Equations" Student Edition
by Justin W. Garvin
amzn.to
"A Student's Guide to the NavierβStokes Equations" Student Edition
by Justin W. Garvin
amzn.to
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We hope you enjoyed this journey through the problems of mathematics! Be sure to check out these amazing books to explore each unsolved problem in more depth.
You can check out our other threads on Physics!
You can check out our other threads on Physics!
*Correction:
n/2 if n is even
3n+1 if n is odd
n/2 if n is even
3n+1 if n is odd
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