There’s a new preprint on arXiv, Counterexample to the Hodge Conjecture, by Kim and Roush, that proposes a counterexample to the Hodge conjecture, one of the Clay Mathematics Institute’s 7 Millenium Problems. It’s a bold claim, and the 12-page paper looks like it would be easy for an expert (which I am not) to follow, so we’ll probably hear a definite verdict relatively soon. Interestingly, part of the argument involves a computer calculation.
Via Peter Woit.
Update. The authors have withdrawn their claim of a counterexample.
Consider many different types of functions like a(x), b(x)……,z(x). Now we know that the highest value of x in all these functions can be n( the last term) i.e
n of a(x)= n of b(x)=……=n of z(x) if we further write it simply it will be
a.n=b.n =………..=z.n
Now let k be a kind of typical operation such that the operation gives minimum value of n therefore,
a.k(n)=b.k(n)=…………….=z.k(n)………………….(1)
Now we conclude that the lowest value of n of a function equals the lowest value of n of any other function.
Consider a function y= p² + b² where p means perpendicular and b means base. Let the triangle which has p and b be inscribed in a circle. Now if we check the relation up to 360º then we will find it to be correct. There are 360 number of degrees in a circle and further the difference between the degrees are so small that if a relation is correct for x number of degrees and if it is also correct for x+1 number of degrees then it will certainly be correct for the values between x and x+1 number of degrees therefore we state that for checking a functional relation 360 can be considered as a nth value. Therefore and again from equation (1) if we consider those functions to be a kind of formula or relation we will conclude that the nth value for those will also be 360.
For a function whose value rotates between some particular values we need to check whether the function decreases or increases for its n =360 because if the function is increasing for its value up to n=360 as from our above discussion we will state it as a increasing or decreasing function and as a result the value will never rotate.
solution of Hodge conjecture ,Riemann hypothesis and others
As hodge conjecture and Riemann hypothesis has already been checked 360 times we will easily state these to be correct. Many other solutions also follow in similar way ….
sorry i dont have my website
please reply fast
please send me feedback
Solution of Hodge Conjecture and Riemann Hypothesis
Consider many different types of functions like a(x), b(x) … z(x). Now the highest value of x is n (the last term) and for every functions it is equal i.e. n of a(x) =n of b(x) = ………… n of z(x).
Writing simply a.n = b.n = …………… = z.n
Let k be a typical operation such that it gives the minimum value of n
Now,
a.k (n) = b.k (n) = ………….. = z.k (n) ………… (1)
Now, it tells us that the minimum nth value for function equals the minimum nth value for any other function.
We know that there are 360 no of degrees in circle. And the difference between them is so small that it can be neglected for checking relations like h2 = p2 + b2 which is Pythagorean Theorem. It means if we just check the relation up to n = 360 degree by inscribing the right angled triangle in the circle then we can identify whether it’s true or false. And from Eqn (1), we can conclude for every function we can check whether a relation is true or not by supposing n = 360.
Solution of Hodge Conjecture, Riemann Hypothesis and many others.
As Hodge Conjecture and Riemann Hypothesis has already been checked for n = 360, we will state that it is correct. Solutions of others can also be done in similar way.
Please, send feedback as soon as possible!