Yes, there are many math equations that haven’t been solved yet, including the Riemann hypothesis and the Birch and Swinnerton-Dyer conjecture.
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There are many unsolved math equations that still puzzle mathematicians around the world. One of the most famous of these is the Riemann Hypothesis, named after German mathematician Bernhard Riemann who proposed it in 1859. The hypothesis states that all non-trivial zeros of the Riemann zeta function are located on the critical line of 1/2. While there have been many attempts to solve this equation, it remains unsolved to this day.
Another unsolved math equation is the Birch and Swinnerton-Dyer conjecture, which deals with elliptic curves in number theory. It is believed that there is a connection between the number of points on an elliptic curve and an associated L-function. However, proving this connection has eluded mathematicians for decades.
There are many other unsolved math equations including the Poincaré conjecture, the Hodge conjecture, and the Navier-Stokes equations. Some mathematicians believe that these equations may never be solved, while others remain optimistic about future breakthroughs.
As French mathematician Pierre-Simon Laplace once said, “The calculus of probabilities, when confined within just limits and applied to the most complicated phenomena, often appears to be the last effort of human intelligence.” While there are still many math equations waiting to be solved, the pursuit of these solutions continues to be a driving force in the world of mathematics.
Interesting facts about unsolved math equations:
- The Riemann Hypothesis is one of seven Millennium Prize Problems established by the Clay Mathematics Institute, with a $1 million reward for solving each problem.
- The Navier-Stokes equations describe the motion of fluids, but because they involve millions of variables and complex interactions, no closed-form solution exists.
- In 2018, mathematician Shinichi Mochizuki claimed to have solved the abc conjecture, another long-standing math problem. However, his proof has yet to be accepted by the wider math community.
- According to mathematician Terry Tao, “sometimes incomplete proofs can be even more valuable than complete ones, because they can inspire further ideas and research.” Even if a math equation remains unsolved, it can still lead to important discoveries and advancements in the field.
|Riemann Hypothesis||All non-trivial zeros of the Riemann zeta function are located on the critical line of 1/2||Unsolved|
|Birch and Swinnerton-Dyer conjecture||Connection between elliptic curves and associated L-functions||Unsolved|
|Poincaré Conjecture||Characterizes the possible shapes of three-dimensional spaces||Solved in 2002|
|Hodge Conjecture||Every algebraic cycle on a complex algebraic variety can be realized by a sum of algebraic cycles of appropriate dimension||Solved for some special cases|
|Navier-Stokes equations||Describe the motion of fluids||Unsolved|
Answer in the video
The Collatz Conjecture is a problem in mathematics that is said to be incredibly difficult to solve. The problem involves determining whether or not a set of positive integers will eventually end up in a loop created by applying two rules. Professional mathematicians have been unable to solve the problem, but Jeffrey Lagarias is the world authority on the conjecture.
There are additional viewpoints
As you can see in the equations above, there are several seemingly simple mathematical equations and theories that have never been put to rest. Decades are passing while these problems remain unsolved. If you’re looking for a brain teaser, finding the solutions to these problems will give you a run for your money.
So far, so simple, and it looks like something you would have solved in high school algebra. But here’s the problem. Mathematicians haven’t ever been able to solve the Beale conjecture, with x, y, and z all being greater than 2.
In 1981, Richard K. Guy wrote Unsolved Problems in Number Theory . It is over 140 pages long, contains literally hundreds of different problems in number theory, most of which are still open to this day.
In 1990, Jan van Mill wrote Open Problems in Topology . It is over 600 pages long, contains 1,100 open problems about topology, most of which are still open to this day.
In 1991, Hallard T. Croft, Kenneth J. Falconer, and Richard K. Guy wrote Unsolved Problems in Geometry . It is over 180 pages long, contains hundreds of different problems in geometry, most of which are still open to this day.
None of this is a complete list. None of this is even close to a complete list.
It is, therefore, not an exaggeration to claim that there are enough such problems to fill books and books and books.
1. Unsolved Problems in Number Theory | Richard Guy | Springer [ https://www.springer.com/gp/book/9780387208602 ]