Is there anything in mathematics that has not been discovered?
104553
While most 'unsolved' math problems are hard to describe until you get to high levels of mathematics, there are a few unsolved problems which can be explained at a high school level.  For example, the Collatz conjecture:\n\n   Start with a positive integer.\n\n   If it is even, divide by two.\n   Otherwise multiply by three and add one.\n\n   Repeat this process indefinitely.\n\n   The open question is: Does this process always\n   eventually reach one?\n\n   For example:\n\n     Start with 7.\n     Multiply by three and add one to get 22.\n     Divide by 2 to get 11.\n     Multiply by three and add one to get 34.\n     Divide by 2 to get 17.\n     Multiply by three and add one to get 52.\n     Divide by 2 to get 26.\n     Divide by 2 to get 13.\n     Multiply by three and add one to get 40.\n     Divide by 2 to get 20.\n     Divide by 2 to get 10.\n     Divide by 2 to get 5.\n     Multiply by three and add one to get 16.\n     Divide by 2 to get 8.\n     Divide by 2 to get 4.\n     Divide by 2 to get 2.\n     Divide by 2 to get 1.
477417
NO. It is still unsolved.
341730
not so much discovered....more sort of made it
1016930
Not that I have heard.  But anything is possible.
572082
There are many undetermined ( not undefined ) mathematical quantities such as :\ninfinity - infinity\ninfinity / infinity\nzero / zero\nzero ^ zero\nzero * infinity\nas an example : (0^2)^0 = 0^0\n                (0^3)^0 = 0^0\nis that mean that 2=3 ?\nSo 0^0 is an undetermined quantity\nregarding that zero can be considered as the smallest +ve quantity we can ever have or the biggest -ve quantity we can ever have
478296
Fermat's Last Theorem has been solved ashas the Four Color Theorem. The Poincare conjecture has recently been solved. Trisecting a general angle with unmarked straightedge and compass has been shown to be unsolvable (although it is possible with marked straightedge and compass).\n\nHigh on the list of open problems:\n\nRiemann Hypothesis.\nP=NP?\nTwin prime conjecture.\nAre there any odd perfect numbers?\nProof of existence of solutions to Navier-Stokes equations.
61658
This has to do with the idea of mathematical neoplatonism.  This philosophy holds that their are 'universal truths', including mathematical concepts, waiting to be discovered.  If that is the case, then mathematics is not just an invention of humans, and would have also been discovered by any other race in the universe capable of space travel.
659059
No it can never be completely understood there is always something unknown,
807032
Have a read at Steven Hawkings "A Brief History of Time"  There is an on-line version somewhere so you don't have to buy it.  It is a long book but is a good effort at explaining very complex mathematics in lay persons terms.  I'm no genius and even I managed to grasp the majority of it.  \n\nIt runs through the history of mathematics and physics, big bang theory (singularity), dark matter, black holes, the lot.  Just don't let your friends find out.  They'll think you're a dweeb!
472461
Gauss and Euler have so much impacted the whole history and methodology of mathematics that they deserve my top score.\n\nLooking to the other answers, I believe Newton is a bit overvalued as a mathematician (not as a physicist of course): calculus was independently discovered also by Leibniz and received fundamental contributions by many others.\n\nI also want to spend a word about Henri Poincare, a mathematician of great vision, who was ahead his time and with his work on differential equations posed the foundations for modern math branches such as dynamical systems and chaos theory.
258206
There are countless such mathematicians. The major ones are Euler and Gauss. Other significant contributions came from al-Khwarizmi, Evariste Galois, and pretty much every major mathematician. See "Men of Mathematics" by E.T. Bell, although it is a bit biased, and "Mathematics and its History" by John Stillwell.
186463
http://en.wikipedia.org/wiki/Discovery_of_america\nNothing is known for absolute certain, but there are lots of theories
5768
I personally think they don't exist.  Here's what Wikipedia has to say, "It is unknown whether there are any odd perfect numbers. Various results have been obtained, but none that have helped to locate one or otherwise resolve the question of their existence. Recently, Carl Pomerance and Joshua Zelinsky have both presented heuristics which strongly suggest that no odd perfect numbers exist."
959558
Not that I have heard of
1094642
Kurt Gödel, famous for his incompleteness theorems has shown that for any consistent formal theory that proves basic arithmetical truths, it is possible to construct an arithmetical statement that is true but not provable in the theory. That is, any consistent theory of a certain expressive strength is incomplete.\nhttp://en.wikipedia.org/wiki/Goedel\n\nThere are other limits to knowledge most of which do not lend themselves to short answers.\nAlonzo Church's undecidability theorem - there exists no one procedure for deciding the validity of any argument in the system.\nhttp://en.wikipedia.org/wiki/Alonzo_Church\nChaos theory (well never have accurate weather forecasts more than 2 weeks out)\nhttp://en.wikipedia.org/wiki/Chaos_theory\n\nThese limits affect not just science but all human learning. Beyond all of this, humans are simply not capable of knowing all there is to know. There will always be aspects of the universe unknown to us and inaccessible to science or religion because we’re not smart enough to ask the right question and incapable of understanding the answer.
717854
something that cannot be explain
298891
Everything can be mathematically based, so I would have to say the advantages of knowing mathematics totally outweighs the disadvantages of learning it.\n\nHistory\nMain article: History of mathematics \nThe evolution of mathematics might be seen to be an ever-increasing series of abstractions, or alternatively an expansion of subject matter. The first abstraction was probably that of numbers. The realization that two apples and two oranges have something in common, namely that they fill the hands of exactly one person, was a breakthrough in human thought. In addition to recognizing how to count concrete objects, prehistoric peoples also recognized how to count abstract quantities, like time -- days, seasons, years. Arithmetic (e.g., addition, subtraction, multiplication and division), naturally followed. Monolithic monuments testify to a knowledge of geometry.\n\nFurther steps need writing or some other system for recording numbers such as tallies or the knotted strings called khipu used by the Inca empire to store numerical data. Numeral systems have been many and diverse.\n\nFrom the beginnings of recorded history, the major disciplines within mathematics arose out of the need to do calculations on taxation and commerce, to understand the relationships among numbers, to measure land, and to predict astronomical events. These needs can be roughly related to the broad subdivision of mathematics, into the studies of quantity, structure, space, and change.\n\nMathematics since has been much extended, and there has been a fruitful interaction between mathematics and science, to the benefit of both.\n\nMathematical discoveries have been made throughout history and continue to be made today. According to Mikhail B. Sevryuk, in the January 2006 issue of the Bulletin of the American Mathematical Society, "The number of papers and books included in the Mathematical Reviews database since 1940 (the first year of operation of MR) is now more than 1.9 million, and more than 75 thousand items are added to the database each year. The overwhelming majority of works in this ocean contain new mathematical theorems and their proof."