How do mathematicians invent new math? What are the limits?
460235
Well there is still a list of unsolved mathematical problems called Hilbert's 23 challenges.  Most math develops form the need to correlate new equations to streamline comparisons or find new ways to predict observable behavior.  the former being how calculus of founded.\n\nhttp://en.wikipedia.org/wiki/Hilbert's_problems
70438
None, Zero was invented by Indian Mathematician Aryabhata and later Brahmagupta developed its concept
567674
Blaise Pascal? He invented the calculator. Maybe Isaac Newton, the inventor of calculus, or Charles Babbage, the inventor of the computer. Perhaps John Napier, who discovered how to add, subtract, multiply, divide, and even extract square roots simply by moving pieces on a chessboard? Tell you what, pick René Descartes, he's the inventor of coordinate geometry. These are all excellent choices!
412238
Math is a natural extension of human needs to count and measure. Cavemen probably did need to compare groups of things (Which group of stones is larger?) and that leads to comparison words (> < =) in human languages. Then natural numbers are invented to communicate and count quantitatively (1 2 3 ...). More operations, plus, minus, multiply, divide, are invented as needs arise and human societies and technology become more complex. \n\nIt's likely that school math curricula more or less trace such historical progress from basic to complex math knowledge. Starting from comparisons in kindergarten and go through numbers, addition, subtraction, multiplication, division, fractions, decimals, percents, in primary school. Most of these constructs were known millennia ago. Then algebra, geometry, trigonometry--now studied in high school--were invented within the last few thousand years. Analytic geometry and Calculus, the next major advances, were built on algebra & geometry knowledge and matured to today's form in the last few hundred years. Today, they are studied in late high school and university years. \n\nMany, many people throughout history contributed to the advances and accumulation math knowledge. Prominent mathematicians did more than most and three people are often hailed as the most outstanding of mathematicians in history: Archimedes, Newton, and Gauss.\n\nFor more details, see The MacTutor History of Mathematics archive at http://www-groups.dcs.st-and.ac.uk/~history/
88566
http://www.exploratorium.edu/learning_studio/cool/mathematics.html
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Math is used all the time in the engineering sciences.  Many physical phenomena, including fluid flow, heat transport, and diffusion can be described by appropriate partial differential equations.  In order to solve these equations and make predictions, you need to be good at calculus.\n\nIf you limit yourself to addition, subtraction, multiplication, and division, you would be stuck with linear models for everything.  This means that any more complicated relationship between two variables could not be modeled continuously, and you would never be able to extrapolate with any confidence.  Thus development of new technology would be strictly trial and error (and you wouldn't even have a good trial and error system without statistics).\n\nHang in there!  Get through that math.  You don't have to like it, but you will inevitably appreciate the developments that math has enabled.
1186148
There used to be a lot of them, but with computers these days they are being solved by brute force. Examples include Fermat's Last Theorem and the Four Color problem in topology. You can look those up to see what they are, and you will probably find sites listing other unsolved mathematical puzzles.
725561
Oh Dear! lots of dodgy maths out there!\nWelcome to Mr Cantor's infinity paradise hotel!\nWe got infinite rooms, but they're all full just now.\nDon't worry!.. we'll squeeze you in!..I'll just get every guest to move one room along\nNow you can get in room1\nHey there's an infinite stretch limo arrived with an infinite number of guests..no probs just get all our guests to move from room n to 2n!\nYes infinity is an uncountable number, but you can still do mathematical ops with it\nHope that helps, you can work out the rest foor yourselves. PS always agree with your wife- she's right even when she's wrong-now that's a true paradox
800132
how does this fit into mathematics?
219295
Because it has no real form, there are many equations, and new ones being invented every day, Math is the base of life, its more opionion than fact thats its abstract, Math is a mystery just like humans, evolution or space.\n\nIf you really think about it hard and long you will come to the conclution thats its a mystery.
910564
umm none that im aware of, what kind of mathamatics leval are you looking at?
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."
302880
My opinion:\nMathematics, as a formal system, is invented in the sense that one starts\nwith a certain set of elements (usually numbers, but not necessarily so) and\ndefines a set of rules regarding various relationships between, and\noperations of, those elements. And you can invent any rules of the game you\ndesire.\n\nMathematics, as a discipline, may be quite a different process. One may\nperceive a certain pattern, regularity, or whatever word you might want to\ndescribe some insight (usually regarding numbers, but not necessarily so)\nand try to "explain" that insight. This process may be quite circuitous, and\n"illogical".\nThere are any number of observations (conjectures) in mathematics that are\nput forward without any proof. Perhaps "Fermat's Last Theorem" is the most\nfamous, but by no means the only, example of something that was found to be\nempirically true for a long time before it was proven in a formal sense.  If\nyou read any of the popular histories of numbers like 'pi' , 'e' , or 'i' it\nwill be clear that there is much more discovery than invention.
36505
Great question.\n\nI think a maths history project would be wonderful.\n\nSpecifically, I would like to see a paper which explains how the trigonometric functions were calculated in history.\n\nFor example, what angles did the Greeks know trig functions for?\n\nWhat resources did Isaac Newton have for trig functions?\n\nHow were these tables calculated before electronic computers?\n\nThe combination of history and maths would be very interesting.\n\nCheers!
521561
There's nothing like born clever or something like that.There are people who have flair for mathematics but being clever is different thing.However there's absolutely no reason you cannot beat best of these smart people if you train regularly.Training makes all the difference.Above all you must have curiosity a desire to learn experiment .Sadly these things don't matter and only end results are used as a measure of human excellence.Behind 99.99% of all so called big mathematicians is hours of hard work.\nPaul Erdos one of the most prolific mathematician hardly ever slept so involved was he with his work.\nJust try to develop the interest.And remember math is not the end of world.
127
Don't know yet, but lots of wild theories and mathematical approaches being tried (some, via\nhttp://myweb2.search.yahoo.com/search?p=4%208%2015%2016%2023%2042):\n\nhttp://www.d.kth.se/~dicander/lost.html\n\nhttp://www.4815162342.com/forum/viewforum.php?f=3
990013
Mathematical ideas become more exciting, tangible and memorable when you act them out with your whole body.\n   \nFor several examples that treat math and dance as a single creative activity, not as two separate disciplines, go here: