A 53-Year-Old Network Coloring Conjecture Is Disproved

A paper posted online last month has disproved a 53-year-old conjecture about the best way to assign colors to the nodes of a network. The paper shows, in a mere three pages, that there are better ways to color certain networks than many mathematicians had supposed possible.

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Andrew Booker, a Mathematics Professor at the University of Bristol, Just Solved a Deceptively Simple Puzzle That Has Boggled Minds for 64 Years

A mathematician in England has cracked a math puzzle that's stumped computers and humans alike for 64 years: How can the number 33 be expressed as the sum of three cubed numbers?

While it might seem simple on its face, this question is part of an enduring number-theory conundrum that goes back to at least 1955 and may have been mulled over by Greek thinkers as early as the third century. The underlying equation to solve looks like this:

`x^3 + y^3 + z^3 = k`

That answer is:

`(8,866,128,975,287,528)^3 + (–8,778,405,442,862,239)^3 + (–2,736,111,468,807,040)^3 = 33`.

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Riemann Hypothesis Solved By Sir Michael Atiyah After 160 Years, He Says

One of the world's most renowned mathematicians showed how he solved the 160-year-old Riemann hypothesis at a lecture on Monday — and he will be awarded $1 million if his solution is confirmed.

Sir Michael Atiyah, who has won the two biggest prizes in mathematics — the Fields Medal and Abel Prize — took the stage at the Heidelberg Laureate Forum in Germany on Monday to present his work.

To solve the hypothesis you need to find a way to predict the occurrence of every prime number, even though primes have historically been regarded as randomly distributed.

Aityah's solution will need to be checked by other mathematicians and then published before it is fully accepted and he can claim the prize from the Clay Mathematics Institute of Cambridge.

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Every Positive Integer Is A Sum Of Three Palindromes

For integer g ≥ 5, we prove that any positive integer can be written as a sum of three palindromes in base g.

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Mathematicians Deliver Formal Proof Of Kepler Conjecture

A team led by mathematician Thomas Hales has delivered a formal proof of the Kepler Conjecture, which is the definitive resolution of a problem that had gone unsolved for more than 300 years. The paper is now available online through Forum of Mathematics, Pi, an open access journal published by Cambridge University Press. This paper not only settles a centuries-old mathematical problem, but is also a major advance in computer verification of complex mathematical proofs.

The Kepler Conjecture was a famous problem in discrete geometry, which asked for the most efficient way to cram spheres into a given space. The answer, while not difficult to guess (it's exactly how oranges are stacked in a supermarket), had been remarkably difficult to prove. Hales and Ferguson originally announced a proof in 1998, but the solution was so long and complicated that a team of a dozen referees spent years working on checking it before giving up..

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Two-hundred-terabyte maths proof is largest ever

A computer cracks the Boolean Pythagorean triples problem — but is it really maths?

Three computer scientists have announced the largest-ever mathematics proof: a file that comes in at a whopping 200 terabytes, roughly equivalent to all the digitized text held by the US Library of Congress. The researchers have created a 68-gigabyte compressed version of their solution — which would allow anyone with about 30,000 hours of spare processor time to download, reconstruct and verify it — but a human could never hope to read through it.

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Proof Claimed For Deep Connection Between Primes

The usually quiet world of mathematics is abuzz with a claim that one of the most important problems in number theory has been solved.

Mathematician Shinichi Mochizuki of Kyoto University in Japan has released a 500-page proof of the abc conjecture, which proposes a relationship between whole numbers — a 'Diophantine' problem.

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Extended Midy's Theorem

This is my proof, and an extension, of Midy's Theorem. Someone had referenced this in Wikipedia almost six years ago, but it was recently removed (still in the history) to make Wikipedia more official. Since this blog came about after my proof, I never went back and added it.

P vs. NP

According to Vinay Deolalikar a research scientist at HP Labs, P is not equal to NP.

His preliminary manuscript can be found here.

Proof of the Existence of God

Click here for the explanation.

Metamath Proof Explorer

Inspired by Whitehead and Russell's monumental Principia Mathematica, the Metamath Proof Explorer has over 6,000 completely worked out proofs in logic and set theory, interconnected with over a million hyperlinked cross-references. Each proof is pieced together with razor-sharp precision using a simple substitution rule that practically anyone can follow, not just mathematicians. Every step can be drilled down deeper and deeper into the labyrinth until axioms of set theory—the starting point for all of mathematics—will ultimately be found at the bottom. You could spend literally days exploring the astonishing tangle of logic leading, say, from 2+2=4 back to the axioms.

The Coq Proof Assistant

Coq is a formal proof management system: a proof done with Coq is mechanically checked by the machine. In particular, Coq allows:

• to define functions or predicates,
• to state mathematical theorems and software specifications,
• to develop interactively formal proofs of these theorems,
• to check these proofs by a relatively small certification "kernel".

Math Forum

My Math Forum: for a better understanding of mathematics.

Goldbach Conjecture: Proved?

The Goldbach Conjecture states that all positive, even integers ≥ 4 can be expressed as the sum of two primes.

Several papers have recently surfaced at arXiv.org claiming to have proved this. However, none of these methods have been verified yet.

• A Proof of Goldbach Conjecture


• From the Goldbach Conjecture to the Theorem

Proof Without Words

1³ + 2³ + … + n³ = (1 + 2 … + n)².
Mathematically, $\sum_{i=1}^{n} i^3 = (\sum_{i=1}^{n} i)^2$.

Proof Without Words

Area(Parallelogram) = ad - bc.

Proof Without Words

Law of Cosines: $\a^2 +b^2 - 2ab\cos\theta = c^2$.

Proof Without Words

1 + 4 + 9 + … + n² = n(n + 1)(2n + 1)/6.
Mathematically, $\sum_{i=1}^{n} i^2 = \frac{n(n+1)(2n+1)}{6}$.

Proof Without Words

$AB + AX = AD$.

Proof Without Words

Pythagorean Theorem: For a right triangle with legs a and b and hypotenuse c,
$a^2 + b^2 = c^2$.