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Just one of the seven Millennium Prize Problems named 21 years ago has been solved

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- Why 2 Is the Best Number and Other Secrets from a MacArthur-Winning Mathematician
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## 10 Math Equations That Have Never Been Solved

By Kathleen Cantor, 10 Sep 2020

## 1. The Riemann Hypothesis

Equation: σ (n) ≤ Hn +ln (Hn)eHn

- Where n is a positive integer
- Hn is the n-th harmonic number
- σ(n) is the sum of the positive integers divisible by n

## 2. The Collatz Conjecture

## 3. The Erdős-Strauss Conjecture

## 4. Equation Four

Equation: Use 2(2∧127)-1 – 1 to prove or disprove if it’s a prime number or not?

Looks pretty straight forward, does it? Here is a little context on the problem.

## 5. Goldbach's Conjecture

Equation: Prove that x + y = n

## 6. Equation Six

Equation: Prove that (K)n = JK1N(q)JO1N(q)

- Where O = unknot (we are dealing with knot theory )
- (K)n = Kashaev's invariant of K for any K or knot
- JK1N(q) of K is equal to N- colored Jones polynomial
- We also have the volume of conjecture as (EQ3)
- Here vol(K) = hyperbolic volume

## 7. The Whitehead Conjecture

## 8. Equation Eight

## 9. The Euler-Mascheroni Constant

Equation: y=limn→∞(∑m=1n1m−log(n))

## 10. Equation Ten

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Posted in Mathematics category - 10 Sep 2020 [ Permalink ]

## 11 Comments on “10 Math Equations That Have Never Been Solved”

Maybe only, if you know meaning of this three symbols up writen and connected together.

8.539728478 is the answer to number 10

8.539728478 is the answer to number 10 or 8.539734221

The sum of π and e is equal to π + e = 3.14159 + 2.71828 = 5.85987.

In conclusion, the sum of π and e is equal to 5.85987, which is an algebraic number.

n = 5 3n + 1 = 3(5) + 1 = 16 n = 16/2 = 8 n = 8/2 = 4 n = 4/2 = 2 n = 2/2 = 1 n = 1/2 = 0.5

If n is equal to 4, the sequence of values will be: n = 4 3n + 1 = 3(4) + 1 = 13 n = 13/2 = 6.5

n = 6 3n + 1 = 3(6) + 1 = 19 n = 19/2 = 9.5

If n is equal to 4, the sequence of values will be:

n = 4 3n + 1 = 3(4) + 1 = 13 n = 13/2 = 6.5

n = 9 3n + 1 = 3(9) + 1 = 28 n = 28/2 = 14 n = 14/2 = 7 n = 7/2 = 3.5

n = 3 3n + 1 = 3(3) + 1 = 10 n = 10/2 = 5 n = 5/2 = 2.5

n = 2 3n + 1 = 3(2) + 1 = 7 n = 7/2 = 3.5

As we can see, the sequence of values becomes repetitive

σ(5) ≤ H5 + ln(H5)eH5 15 ≤ 2.28 + 0.83 * 2.28^2.28 15 ≤ 4.39

Since 15 is less than or equal to 4.39, the equation holds true for this specific value of n.

Now we can use the fact that n, a, b, and c are positive integers to make some observations:

4abc = 4 * 1 * 1 * 2 * 3 * 5 = 120

Some possible factorizations are:

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## 5 Simple Math Problems No One Can Solve

Easy to understand, supremely difficult to prove.

## Collatz Conjecture

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## The Simple Math Problem We Still Can’t Solve

## Introduction

This column comes with a warning: Do not try to solve this math problem.

To understand the Collatz conjecture, we’ll start with the following function:

f (10) = 10/2 = 5 f (5) = 3 × 5 + 1 = 16 f (16) = 16/2 = 8 f (8) = 8/2 = 4

10 → 5 → 16 → 8 → 4 → 2 → 1 → 4 → 2 → 1 → …

At the end we see we are stuck in the loop 1 → 4 → 2 → 1 → ….

Similarly, the orbit for 11 under f can be represented as

11 → 34 → 17 → 52 → 26 → 13 → 40 → 20 → 10 → 5 → 16 → 8 → 4 → 2 → 1 → 4 → ….

10 → 5 → 6 → 3 → 4 → 2 → 1 → 2 → 1 → 2 → … 11 → 12 → 6 → 3 → 4 → 2 → 1 → 2 → 1→ 2 → …

27 → 28 → 14 → 7 → 8 → 4 → 2 → 1 → 2 → …

… → n → n + 1 → $latex \frac{n+1}{2}$ → …

Can a similar argument work for the Collatz conjecture? Let’s go back to the original function.

… → n → 3 n + 1 → $latex \frac{3n+1}{2}$ → …

1. Show that there are infinitely many numbers whose Collatz orbits pass through 1.

Notice that every power of 2 has a simple orbit path to 1. For example,

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## 5 of the world’s toughest unsolved maths problems

## 1. Separatrix Separation

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## Solved Problems

3. The Bieberbach conjecture (L. de Branges 1985).

5. Fermat's last theorem (Wiles 1995, Taylor and Wiles 1995).

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## Famous Unsolved Math Problems as Homework

By Benjamin Braun, Editor-in-Chief , University of Kentucky

- Students are forced to depart from the “answer-getting” mentality of mathematics. In my experience, (most) students in K-12 and postsecondary mathematics courses believe that all math problems have known answers, and that teachers can find the answer to every problem. As long as students believe this story, it is hard to motivate them to develop quality mathematical practices, as opposed to doing the minimum necessary to get the “right answer” sufficiently often. However, if they are asked to work on an unsolved problem, knowing that it is unsolved, then students are forced to find other ways to define success in their mathematical work. While getting buy-in on this idea is occasionally an issue, most of the time the students are immediately interested in the idea of an unsolved problem, especially a simply-stated one. The discussion of how to define success in mathematical investigation usually prompts quality discussions in class about the authentic nature of mathematical work; students often haven’t reflected on the fact that professional mathematicians and scientists spend most of their time thinking about how to solve problems that no one knows how to solve.
- Students are forced to redefine success in learning as making sense and increasing depth of understanding . The first of the mathematical practice standards in the Common Core , which have been discussed in previous blog posts by the author and by Elise Lockwood and Eric Weber , is that students should make sense of problems and persevere in solving them. When faced with an unsolved problem, sense-making and perseverance must take center stage. In courses heavily populated by preservice teachers, I’ve used open problems as in-class group work in which students work on a problem and monitor which of the practice standards they are using. Since neither the students nor I expect that they will solve the problem at hand, they are able to really relax and focus on the process of mathematical investigation, without feeling pressure to complete the problem. One could even go so far as to evaluate student work on unsolved problems using the common core practice standards, though typically I evaluate such work based on maturity of investigation and clarity of exposition.
- Students are able to work in a context in which failure is completely normal. In my experience, undergraduates majoring in the mathematical sciences typically carry a large amount of guilt and self-doubt regarding their perceived mathematical failures, whether or not it is justified. From data collected by the recent MAA Calculus Study , it appears that this is particularly harmful for women studying mathematics . Because working on unsolved problems forces success to be redefined, it also provides an opportunity to discuss the definition of failure, and the pervasive normality of small mistakes in the day-to-day lives of mathematicians and scientists. I usually combine work on unsolved problems with reading assignments and classroom discussions regarding developments in educational and social psychology, such as Carol Dweck’s work on mindset , to help students develop a more reasonable set of expectations for their mathematical process.

## 14 Responses to Famous Unsolved Math Problems as Homework

Thanks for the great ideas Ben!

I’d love to hear more ideas of what is done in other classes.

I hadn’t heard of that problem before, it sounds like an awesome project!

Came here from https://news.ycombinator.com/item?id=9537802.

[attempted to render that in mathml:] xn=∑i=2i=x-11ai

Has a form of this been solved generally for other x values ( > 3) and 4/n is an outlier??

This is fantastic and inspiring! Thank you.

Wonderful… you are someone who should keep teaching forever. Please keep doing what you’re doing.

If I didn’t live so far from Kentucky I would be begging to audit one of your classes.

Thank you so much for such interesting post.

I think, every unsolved math problems can be solved. Thanks.

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Toggle Lists of unsolved problems in mathematics subsection 1.1Millennium Prize Problems 2Unsolved problems Toggle Unsolved problems subsection 2.1Algebra 2.1.1Representation theory 2.1.2Notebook problems 2.2Analysis 2.3Combinatorics 2.4Dynamical systems 2.5Games and puzzles 2.5.1Combinatorial games 2.5.2Games with imperfect information

These Are the 10 Toughest Math Problems Ever Solved 1 The Collatz Conjecture In September 2019, news broke regarding progress on this 82-year-old question, thanks to prolific mathematician...

There are many unsolved problems in mathematics. Some prominent outstanding unsolved problems (as well as some which are not necessarily so well known) include 1. The Goldbach conjecture. 2. The Riemann hypothesis. 3. The conjecture that there exists a Hadamard matrix for every positive multiple of 4. 4.

The Top Unsolved Questions in Mathematics Remain Mostly Mysterious Just one of the seven Millennium Prize Problems named 21 years ago has been solved By Rachel Crowell on May 28, 2021 Credit:...

The Collatz conjecture is one of the most famous unsolved mathematical problems, because it's so simple, you can explain it to a primary-school-aged kid, and they'll probably be intrigued enough to try and find the answer for themselves. So here's how it goes: pick a number, any number. If it's even, divide it by 2.

This problem, as relatively simple as it sounds has never been solved. Solving this problem will earn you a free million dollars. This equation was first proposed by Goldbach hence the name Goldbach's Conjecture. If you are still unsure then pick any even number like 6, it can also be expressed as 1 + 5, which is two primes.

Here are five current problems in the field of mathematics that anyone can understand, but nobody has been able to solve. Collatz Conjecture Jon McLoone Pick any number. If that number is...

The Simple Math Problem We Still Can't Solve Despite recent progress on the notorious Collatz conjecture, we still don't know whether a number can escape its infinite loop. BIG MOUTH for Quanta Magazine This column comes with a warning: Do not try to solve this math problem. You will be tempted.

The Unsolved Math Problems Worth $1 Million Each 6 Min Read "Mathematics is not a careful march down a well-cleared highway, but a journey into a strange wilderness, where the explorers often get lost." — W.S. Anglin, Mathematics and History In A Nutshell

math skills with some problems that go beyond the usual curriculum. These notes can be used as complimentary to an advanced calculus or algebra course, as training for math competitions or simply as a collection of challenging math problems. Many of these are my own creation, some from when I was a student and some from more recent times.

Mathematicians have discovered a problem they cannot solve. It's not that they're not smart enough; there simply is no answer. The problem has to do with machine learning — the type of ...

Get step-by-step solutions to your math problems Try Math Solver Type a math problem Solve Quadratic equation x2 − 4x − 5 = 0 Trigonometry 4sinθ cosθ = 2sinθ Linear equation y = 3x + 4 Arithmetic 699 ∗533 Matrix [ 2 5 3 4][ 2 −1 0 1 3 5] Simultaneous equation { 8x + 2y = 46 7x + 3y = 47 Differentiation dxd (x −5)(3x2 −2) Integration ∫ 01 xe−x2dx

Here are five of the top problems that remain unsolved. 1. Separatrix Separation. A pendulum in motion can either swing from side to side or turn in a continuous circle. The point at which it goes ...

The team shows AI advancing a proof for Kazhdan-Lusztig polynomials, a math problem involving the symmetry of higher-dimensional algebra that has remained unsolved for 40 years.. The research also demonstrated how a machine learning technique called a supervised learning model was able to spot a previously undiscovered relationship between two different types of mathematical knots, leading to ...

There are many unsolved problems in mathematics. Several famous problems which have recently been solved include: 1. The Pólya conjecture (disproven by Haselgrove 1958, smallest counterexample found by Tanaka 1980). 2. The four-color theorem (Appel and Haken 1977ab and Appel et al. 1977 using a computer-assisted proof). 3. The Bieberbach conjecture (L. de Branges 1985). 4. Tait's flyping ...

An unsolved math problem, also known to mathematicians as an "open" problem, is a problem that no one on earth knows how to solve. My favorite unsolved problems for students are simply stated ones that can be easily understood. In this post, I'll share three such problems that I have used in my classes and discuss their impact on my students.

Problem solving has a special importance in the study of mathematics. A primary goal of mathematics teaching and learning is to develop the ability to solve a wide variety of complex mathematics problems. Stanic and Kilpatrick (43) traced the role of problem solving in school mathematics and illustrated a rich history of the topic. To many

The Collatz Conjecture is the simplest math problem no one can solve — it is easy enough for almost anyone to understand but notoriously difficult to solve. ...

The Collatz Conjecture is the simplest math problem no one can solve — it is easy enough for almost anyone to understand but notoriously difficult to solve. So what is the Collatz Conjecture and what makes it so difficult? Veritasium investigates. Watch; Think Open review body. 5 Multiple Choice & 5 Open Answer Questions. Dig Deeper ...

Put all your earlier work aside, get a fresh sheet of paper, and try to start from scratch. Your other work will still be there if you want to draw from it later, and it may have prepared you to take advantage of insights you make in your second go-round. Give up. You won't solve them all.

These Are the 7 Hardest Math Problems Ever Solved — Good Luck in Advance. In 2019, mathematicians finally solved a math puzzle that had stumped them for decades. It's called a Diophantine Equation, and it's sometimes known as the "summing of three cubes": Find x, y, and z such that x³+y³+z³=k, for each k from one to 100.

Problems for 5th Grade. Multi-digit multiplication. Dividing completely. Writing expressions. Rounding whole numbers. Inequalities on a number line. Linear equation and inequality word problems. Linear equation word problems. Linear equation word problems.

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