Mathematics

A while back I read that Mochizuki may have solved the abc conjecture but apparently the proof was so complicated that it was challenging for mathematicians to actually understand it. It is probably a bit of a long shot, but has anyone heard more about it from a professional side (i.e. from the actual community rather than blogs)? As a whole I found the whole issue quite an interesting in context of both, cutting edge science and science communication.

I am wondering if something like this N/β=0 , N≠0 has any function? This beta would help us get rid of any left over numbers as in x^2=1 we would have x^2/β(1) The β(1) only tells us what used to be there.

Please help. My attempt to rotate the volume about the x-axis of y=x^2, first by disk method, then by shell method produces two answers - where obviously it should be the same answer. The limits are from 1 to 0. 1. V=Pi int(x^2)^2 dx = Pi int(y^4)dx = Pi/5 = 0.62631 ft cbd. (Disk method using f(x) where y=x^2). 2. V=2Pi int y.(sqrt y) dy = 4xPi/5 = 2.51327 ft cbd. (Shell method using g(y) where x=sq rt y). Couldn't be simpler? I've spent hours trying to see what's wrong.

i have few more dumb questions about some basic stuffs ... is it always possible to plot the graphs of algebraic expressions and equations on the graph ??? i always had these doubts about variables ...how they were going to look like in a graph ?? about expressions , equations ... and how they are represented in the graph ... are they only going to look like simply points on the graph ??? or you can call it a region ? or something like that ??? i have been trying to stare into books at free times... trying to fill the missing parts ... its a bit exhaustive .. sometimes i want to look into the books ... then i get double exhausted after staring into …

I'm doing some PDE exercices and I'm having a rough time finding out on which variable my problem depends on. For example, if I have to solve the Laplace equation (or any homogeneous PDE) over a cylinder (or sphere) with Dirichlet (or Neumann or Robin) boundary conditions that depends on z and r, how I know if the solution depends on the angular coordinate? What I'm doing actually is set the separation of variables and notice that for the angular part I have not any boundary conditions so I can't find a unique solution. Is that a right way to do that? I know that for the cylinder I have periodical conditions psi(0)=psi(2pi) but it isn't enough right? Anyway, is there a…

I'm going to say the conjecture is wrong on the basis that the last three largest prime numbers have an over fifty thousand line gap each with 100 numbers in each therefore there is no way for the largest prime - 1 to be found as the sum of two primes.

From wiki: "ZFC does not assume that, for every property, there is a set of all things satisfying that property. Rather, it asserts that given any set X, any subset of X definable using first-order logic exists. The object R discussed above cannot be constructed in this fashion, and is therefore not a ZFC set. In some extensions of ZFC, objects like R are called proper classes." I was running through possible sets without subsets and started to think of sets containing only explicitly unique objects. The definition of an explicitly unique object being an object which does not share the same value of its properties with any other object. I then thought about quant…

i have this few doubts about taking an initial guess ... i am not sure how to do that when it comes to certain equations for solving them with numerical methods ...i dont know how to do that you are supposed to take an initial guess when it comes to certain equations ... is it about re arranging equations to fit certain formulas ... ??? do i have to take an initial guess of something in the equations when methods like these are involved ... ??? few simple examples .. might look like this ... that is fixed point iteration on a quadratic equation ... they start by re arranging equations to apply the fixed point iteration ... what is the initial gue…

Hi, I am a senior in High school. In only 4 months I have managed to self teach (from paperback books, PDF files and online courses uploaded to various platforms such as youtube)the following during my free time: Calculus 1,2,3, Differential Equations Linear Algebra Abstract Algebra Discrete Mathematics Analysis 1,2 Calculus of Variations (Optimization Calculus) Elementary Number theory Concise Introduction to Mathematical Logic It is clear to me that I am gifted. I can only imagine once I dedicate myself full time to the study of math. I am not clear what exactly to study. I am interested in Complexity Theory, Number Theory and Artificial Intelligence. I…

It appears that the calculoation of the amount of bending of light passing the sun uses the same calculation that is used for a comet passing the sun.. If that is the case there is a problem. The comet accelerates then decelerates while the light maintians a constant velocity. That means it takes longer for the light to pass the sun than it would if it could be accelerated in the forward direction. By allowing for the constant velocity of light the result should match the Special Relativity calculation. Does this reaoning make sense?

This is not as frivolous as the title suggests, but since this subforum seems to have gone into hibernation, try this 1. Take any number at all with more than 1 digit and add the digits. 2. If the result has more than one digit, add again 3. Now subtract this single-digit number from your starting number (not added) 4. Add the resulting digits again. 5. I bet it will be the number 9 Can you see why? Once you do, you will see that the restriction in (1) to more than a single digit is not required. PS If anyone here asks "what is the point of this thread, do I have a question?", the question is already posed, and the "point" is to illustra…

this is a noob question to most of you .. but i would like to have some clarity ... since i am still following computer oriented numerical methods .... last time , i opened up a thread about polynomials and numerical methods ... some of the things got clearer ... and some of the things got lost in the confusion of discussions ... the last thread was mostly a lot of basic questions about linear and non linear polynomial equations ... some of the things got clearer ... some not that clear .... anyway back to the question ... what are simultaneous equation ? what are systems of linear equations ? is it simply a bunch of polynomia…

5 * 17 = 85 Prime Number + Prime Number = Product = N (in RSA) y = ((85/x) * 85 - x^2)/ x = ((85^2/x) + x^2)/ 85 p = ((85/x) * 85 - x^2)/ x * ( 85^2/((85^2/x) + x^2)) - 85; sol = NSolve[p0, x] {{x®-86.893},{x®-7.50438+19.0222 ä},{x®-7.50438-19.0222 ä },{x®16.9017}}

What is the minimum number of properties posessed by members of a set?

I am collecting examples of where maths and the physical sciences differ over something. Examples offered would be gratefully received. For instance cos (z) = 3 has no solution in the real world and this fact is of vital importance in creating transistors. However in the mathematical world the equation has complex solutions.

Do they not exist not only as abstract toys for mathmaticans, but also as tools to describe our "space time" continuum and the realitys and interactions that exist therein. If the space time contiuumn is measured "relatively" speaking from a "perspective". Then should not operations that exist amongst elements and vectors in fields and rings also exist as relative to a perspective? If the idea of all field and rings and the study of infinity in these given fields and rings, is described as "successors and predecessors related by morphisms (functions)," then should not zero, existing as an "element" in fields and rings, not also posses a "successors and predecesso…

I heard the following story: There was a statement made by a teacher that there is no number after ininfity. A student said that he heard there are infinite numbers between 1 and 2. So there is an end to infinity it comes after 1 and before 2. Which made me think that there is real end to infinity the number is 2. Then I tried to compare it to a real example using space/movement. Take an object for example when that object moves from point A to point B it is constantly surpassing infinity. Point A suddenly ends and point B begins. So everytime an object moves it constantly surpasses infinity. The "jump" movement between point A and point B. This brings along several o…

From your post #63: "I do not have the understanding of solid geometry and calculus it would take to figure if the length of the diamond's side is exactly r, when measured on the surface of the sphere, but it would be "neat" if it was, and would have implications as to what Pi is. That is, as to "why" Pi is. Just one of the things I care about figuring out. If it has already been figured out fine, I am just looking for the answer, one way or the other." Pi is an imaginary number. The result of attempting to describe the imaginary circumference of an object by the length of a line used to scribe that circle. The radius may be a real physical construct; a circle won'…

I sincerly wish to only hear out others opnions. I have no desire to re-hash old topics of mine. With the moderators approval I ask the following, with out any intention of further reply. Is there a diffrence between the space of Zero and the value of Zero?

I just need to get this stuff out of my head and this is probably a better place to do it than in(yet another) notebook. A + A' = B f(x) + r(x) = B f(x) != r(x) or f(x) = r(x) - Dependent on base and x. Mixed base series possible consisting of only palindromic numbers. ie. 1, 2, 3, 4, 5, 6, 7, 8, 9, 11, 22, 33... and no, I have no idea what use any of this would ever be. I keep thinking cryptography, but not sure how that would go. Is non-palindrome forming mixed base possible? Unknown at present.

this is a cool idea i found over at xkcd forums. for a number n, if n is composite, break it into its prime factors. if n is prime, place '<' '>' around the number and determine the n'th prime its is. then the first 20 numbers are... 1 <> 2 <<>> 3 <><> 4 <<<>>> 5 <><<>> 6 <<><>> 7 <><><> 8 <<>><<>> 9 <><<<>>> 10 <<<<>>>> 11 <><><<>> 12 <<><<>>> 13 <><<><>> 14 <<>><<<>>> 1…

I'm looking for an algorithm that can help identify abnormal trends in time-series metrics. The best I've been able to find so far is ARIMA (a completely new concept for me). We offer several services which we monitor active usage against, for any given time of day (typically updated once a minute). Here's a example of one of our services: What I'm interested in is gradual degradation that doesn't get noticed until ... well, it gets noticed. For example, if we zoom in to 12/6 we see: So what I'm specifically interested in here is the trend downward `@17:30~`. Likewise another good example would be: Here we can see the abnormalities on 12/1 and 12/4 during peak. Ar…

This article explains why the cardinality of a set must be either Aleph0 or |ℝ|. In "Cardinality of the set of binary-expressed real numbers" I have shown that binary numbers cannot fill the unit real interval in spite of infinity of digits. In general, the members of a discrete set can only occupy isolated points in a continuous space leaving empty intervals behind. So, the fundamental difference between a continuum and a discrete set is the continuity, not the number of elements. Continuity and discreteness are collectively exhaustive and mutually exclusive. The cardinality of discrete set is aleph0, that of cintinuous set is |ℝ|. Because a set must be continuous or d…

i have lot of doubts regarding polynomials and numerical method .. can someone help me understand some basics of it ... ? how do i dissassemble this sofa of polynomial properly ? and how does numerical method help ? can i have an example of a simple problem where i can utilize numerical method ???

Cardinality of the set of binary-expressed real numbers This article gives the cardinal number of the set of all binary numbers by counting its elements, analyses the consequences of the found value and discusses Cantor's diagonal argument, power set and the continuum hypothesis. 1. Counting the fractional binary numbers 2. Fractional binary numbers on the real line 3. Countability of BF 4. Set of all binary numbers, B 5. On Cantor's diagonal argument 6. On Cantor's theorem 7. On infinite digital expansion of irrational number 8. On the continuum hypothesis You can read the article in the pdf below or the link below Cardinality of the set…