hardest math problems

Over the years, in many forms or another, people have been set Maths problems, either by other people or by God. Some of these problems however are infinitely harder than the rest, and The World's Hardest Maths Problems is a collection of these for your enjoyment, or rather the lack of it.[citation needed] History These individual questions were first created by Euclidean Protectorate in order to pose a test for the officers to see if they were fit to join the ranks in the fight against the Non-Euclidean Witchcraft created during World War π. The idea was that there could only be one of three outcomes, each with different decisions made concerning the individual to have provided those answers: The officer attempted to answer the questions in the time allowed, and failed on account of their impossibility. If they did not complain, and merely took it on themselves as failure, then they were counted as having enough faith in the Order to be allowed to fight. However, if the officer complained that the questions were impossible, then whilst their faith was still demonstrated, they were shot for insubordination. In the order there can be no room for such insolence! The third outcome was that the officer would answer all the questions, and worst of all get them right. As this was only possible by practicing Non-Euclidean Magicks, the officer has deemed a Heretic and burned at the stake for witchcraft Objections! Many (i.e. most) historians argue that the above section is utter nonsense, particularly as the whole World War π thing never happened anyway. Instead they hold that the questions are merely the product of a deranged mind that has been spending too much time with Puff the Magic Dragon, if you catch my meaning. The Questions Information required to complete the questions You are given a triangle that has sides of 66cm, 73cm, and 94cm. One of the angles is.
Just when you thought math couldn't get any harder. A TV presenter in Singapore recently brought up a math problem that has been driving the Internet crazy. See also: In Defense of Math: 7 Reasons Numbers RuleAt first, the problem seems impossible to solve. But once you use some logic, the solution is actually rather simple. Rattle your brain — or phone a friend —before you look at the solution below the picture. The solution, courtesy of Singapore's Study Room: First we need to figure out if Albert knows the month or the day. If he knows the day, then there is no chance that Bernard knows the birthday, so it must be that Albert knows the month. From the first statement, we know that Albert is sure that Bernard doesn't know the birthday, so May and June should be ruled out (the day 19 only appears in May and the day 18 only appears in June). In other words, if Albert had May or June, then he cannot be sure that Bernard doesn't know, since Bernard could have had 18 or 19. Following that statement, Bernard knows that May and June are ruled out. Then, Bernard is able to know which month it is. So it must be either July 16, August 15 and August 17 (not 14th as then he can't know). Since Albert subsequently can also be sure of the date, he must know it's July. If it's August, he can't be sure as there is August 15 and 17. So the answer is July 16. The question was originally thought to posed to fifth graders but was later clarified to be for 14-year-olds competing in the Singapore and Asean Schools Math Olympiads (SASMO). It was the first ever recorded leak from the competition's booklets and will be replaced by the time Cambodia runs the competition. Congrats! You are now smarter than a 14-year-old. Have something to add to this story? Share it in the comments.
Since the Renaissance, every century has seen the solution of more mathematical problems than the century before, and yet many mathematical problems, both major and minor, still elude solution.[1] Most graduate students, in order to earn a Ph.D. in mathematics, are expected to produce new, original mathematics. That is, they are expected to solve problems that are not routine, and which cannot be solved by standard methods. An unsolved problem in mathematics does not refer to the kind of problem found as an exercise in a textbook, but rather to the answer to a major question or a general method that provides a solution to an entire class of problems. Prizes are often awarded for the solution to a long-standing problem, and lists of unsolved problems receive considerable attention. This article reiterates the Millennium Prize list of unsolved problems in mathematics as of October 2014, and lists further unsolved problems in algebra, additive and algebraic number theories, analysis, combinatorics, algebraic, discrete, and Euclidean geometries, dynamical systems, partial differential equations, and graph, group, model, number, set and Ramsey theories, as well as miscellaneous unsolved problems. A list of problems solved since 1975 also appears, alongside some sources, general and specific, for the stated problems. Contents 1 Lists of unsolved problems in mathematics 1.1 Millennium Prize Problems 2 Other still-unsolved problems 2.1 Additive number theory 2.2 Algebra 2.3 Algebraic geometry 2.4 Algebraic number theory 2.5 Analysis 2.6 Combinatorics 2.7 Discrete geometry 2.8 Euclidean geometry 2.9 Dynamical systems 2.10 Graph theory 2.11 Group theory 2.12 Model theory 2.13 Number theory (general) 2.14 Number theory (prime numbers) 2.15 Partial differential equations 2.16 Ramsey theory 2.17 Set theory 2.18 Other 3 Problems solved since 1975 4 References 5 Further reading 5.1.
Yang–Mills and Mass GapExperiment and computer simulations suggest the existence of a mass gap in the solution to the quantum versions of the Yang-Mills equations. But no proof of this property is known. Riemann HypothesisThe prime number theorem determines the average distribution of the primes. The Riemann hypothesis tells us about the deviation from the average. Formulated in Riemann's 1859 paper, it asserts that all the 'non-obvious' zeros of the zeta function are complex numbers with real part 1/2. P vs NP ProblemIf it is easy to check that a solution to a problem is correct, is it also easy to solve the problem? This is the essence of the P vs NP question. Typical of the NP problems is that of the Hamiltonian Path Problem: given N cities to visit, how can one do this without visiting a city twice? If you give me a solution, I can easily check that it is correct. But I cannot so easily find a solution. Navier–Stokes EquationThis is the equation which governs the flow of fluids such as water and air. However, there is no proof for the most basic questions one can ask: do solutions exist, and are they unique? Why ask for a proof? Because a proof gives not only certitude, but also understanding. Hodge ConjectureThe answer to this conjecture determines how much of the topology of the solution set of a system of algebraic equations can be defined in terms of further algebraic equations. The Hodge conjecture is known in certain special cases, e.g., when the solution set has dimension less than four. But in dimension four it is unknown. Poincaré Conjecture In 1904 the French mathematician Henri Poincaré asked if the three dimensional sphere is characterized as the unique simply connected three manifold. This question, the Poincaré conjecture, was a special case of Thurston's geometrization conjecture. Perelman's proof tells us that every three manifold is built from a.