Mathematics has played a major role in so many life-altering inventions and theories. But there are still some math equations that have managed to elude even the greatest minds, like Einstein and Hawkins. Other equations, however, are simply too large to compute. So for whatever reason, these puzzling problems have never been solved. But what are they?<\/p>\n
Like the rest of us, you're probably expecting some next-level difficulty in these mathematical problems. Surprisingly, that is not the case. Some of these equations are even based on elementary school concepts and are easily understandable - just unsolvable.<\/p>\n
Equation: \u03c3 (n) \u2264 Hn +ln (Hn)eHn<\/p>\n
For an instance, if n = 4 then \u03c3(4)=1+2+4=7 and H4 = 1+1\/2+1\/3+1\/4. Solve this equation to either prove or disprove the following inequality n\u22651? Does it hold for all n\u22651?<\/p>\n
This problem is referred to as Lagarias\u2019s Elementary Version of the Riemann Hypothesis and has a price of a million dollars offered by the\u00a0Clay Mathematics Foundation<\/a>\u00a0for its solution.<\/p>\n Equation: 3n+1<\/p>\n Prove the answer end by cycling through 1,4,2,1,4,2,1,\u2026 if n is a positive integer. This is a repetitive process and you will repeat it with the new value of n you get. If your first n = 1 then your subsequent answers will be 1, 4, 2, 1, 4, 2, 1, 4\u2026 infinitely. And if n = 5 the answers will be 5,16,8,4,2,1 the rest will be another loop of the values 1, 4, and 2.<\/p>\n This equation was formed in 1937 by a man named Lothar Collatz which is why it is referred to as the Collatz Conjecture.<\/p>\n Equation: 4\/n=1\/a+1\/b+1\/c<\/p>\n This equation aims to see if we can prove that for if n is greater than or equal to 2, then one can write 4*n as a sum of three positive unit fractions.<\/p>\n This equation was formed in 1948 by two men named Paul Erd\u0151s and Ernst Strauss which is why it is referred to as the Erd\u0151s-Strauss Conjecture.<\/p>\n Equation: Use 2(2\u2227127)-1 \u2013 1 to prove or disprove if it\u2019s a prime number or not?<\/p>\n Looks pretty straight forward, does it? Here is a little context on the problem.<\/p>\n Let\u2019s take a prime number 2. Now, 22 \u2013 1 = 3 which is also a prime number. 25 \u2013 1 = 31 which is also a prime number and so is 27\u22121=127. 2127 \u22121=170141183460469231731687303715884105727 is also prime.<\/p>\n Equation: Prove that x + y = n<\/p>\n 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.<\/p>\n If you are still unsure then pick any even number like 6, it can also be expressed as 1 + 5, which is two primes. The same goes for 10 and 26.<\/p>\n Equation: Prove that (K)n = JK1N(q)JO1N(q)<\/p>\n This equation tries to portray the relationship between\u00a0quantum invariants<\/a>\u00a0of knots and\u00a0the hyperbolic geometry<\/a>\u00a0of\u00a0knot complements<\/a>. Although this equation is in mathematics, you have to be a physics familiar to grasp the concept.<\/p>\n Equation: G = (S | R)<\/p>\n What you are doing in this equation is prove the claim made by Mr.\u00a0Whitehead<\/a>\u00a0in 1941 in\u00a0an algebraic topology<\/a>\u00a0that every subcomplex of an\u00a0aspherical<\/a>\u00a0CW complex<\/a>\u00a0that is connected and in two dimensions is also spherical. This was named after the man, Whitehead conjecture.<\/p>\n Equation: (EQ4)<\/p>\n This equation is the definition of\u00a0morphism<\/a>\u00a0and is referred to as an assembly map.\u00a0 Check out the\u00a0reduced C*-algebra<\/a>\u00a0for more insight into the concept surrounding this equation.<\/p>\n Equation: y=limn\u2192\u221e(\u2211m=1n1m\u2212log(n))<\/p>\n Find out if y is rational or irrational in the equation above. To fully understand this problem you need to take another look at rational numbers and their concepts.\u00a0 The character y is what is known as the Euler-Mascheroni constant and it has a value of 0.5772.<\/p>\n This equation has been calculated up to almost half of a trillion digits and yet no one has been able to tell if it is a rational number or not.<\/p>\n Equation: \u03c0 + e<\/p>\n Find the sum and determine if it is algebraic or transcendental. To understand this question you need to have an idea of\u00a0algebraic real numbers<\/a>\u00a0and how they operate. The number pi or \u03c0 originated in the 17th century and it is transcendental along with e. but what about their sum? So Far this has never been solved.<\/p>\n 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.<\/p>\n2. The Collatz Conjecture<\/h2>\n
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3. The Erd\u0151s-Strauss Conjecture<\/h2>\n
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4. Equation Four<\/h2>\n
5. Goldbach's Conjecture<\/h2>\n
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6. Equation Six<\/h2>\n
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7. The Whitehead Conjecture<\/h2>\n
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8. Equation Eight<\/h2>\n
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9. The Euler-Mascheroni Constant<\/h2>\n
10. Equation Ten<\/h2>\n
Conclusion<\/h2>\n