# General issues: what is the longest math proof?

Contents

As of 2011, the longest mathematical proof, measured by the number of published journal pages, is the classification of finite simple groups, with well over 10,000 pages. However, there is another proof that would be far longer if the details of the computer calculations it depends on were published in full. In 2016, researchers used computers to create the world’s longest proof, solving a mathematical problem that had remained open for 35 years. The proof has a size of 200 terabytes, and it would take 10 billion years for a human being to read it.

## So let’s look at the request more closely

Mathematics is a field that has produced many long and complex proofs, some of which have taken decades or even centuries to develop. The length of a proof can be measured in various ways, including the number of pages in a published journal article, the amount of time it takes to read the proof, or the amount of data required to store the proof digitally.

The longest math proof to date is the proof of the classification of finite simple groups, which was developed over a period of several decades by hundreds of mathematicians and comprises over 10,000 pages of published journal articles. This proof is considered to be one of the most important achievements in modern mathematics, as it provides a complete and rigorous classification of all finite simple groups, which are fundamental objects in algebra and group theory.

However, there have been several other long and complex mathematical proofs developed in recent years. In 2016, three computer scientists 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. This proof concerns a specific problem in the field of algebraic geometry, and its development required advanced computer algorithms and massive amounts of data storage.

In addition to these examples, there are many other long and complex mathematical proofs that have been developed over the years. These proofs cover a wide range of fields and subfields within mathematics, and are often the result of decades or even centuries of work by generations of mathematicians. Some of the most famous long proofs in mathematics include:

Proof Field Length
Classification of Finite Simple Groups Group Theory Over 10,000 pages
Kepler Conjecture Geometry 300 pages
Four Color Theorem Graph Theory 200 pages
Poincaré Conjecture Topology 100 pages
Feit-Thompson Theorem Group Theory 255 pages
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It is worth noting that the length of a proof is not necessarily a measure of its significance or complexity. Some important mathematical results, such as Fermat’s Last Theorem, have relatively short and elegant proofs, while others, such as the classification of finite simple groups, require massive amounts of technical detail and computation. In either case, the development of a new mathematical proof is a major achievement in the field, and often requires significant collaboration and innovation from mathematicians around the world.

## On the Internet, there are additional viewpoints

Three computer scientists have announced the largest-ever mathematics proof: a file that comes in at a whopping 200 terabytes 1, roughly equivalent to all the digitized text held by the US Library of Congress.

Two-hundred-terabyte maths proof is largest ever
The University of Texas’s Stampede supercomputer, on which the 200-terabyte maths proof was solved. …
The numbers 1 to 7,824 can be coloured either red or blue so that no trio a, b and c that satisfies a2 +b2 = c2 is all the same colour.

This is a list of unusually long mathematical proofs. Such proofs often use computational proof methods and may be considered non-surveyable. As of 2011, the longest mathematical proof, measured by number of published journal pages, is the classification of finite simple groups with well over 10000 pages. There are several proofs that would be far longer than this if the details of the computer calculations they depend on were published in full.

It took two days and only 800 of the many processors of the Stampede supercalculator at the University of Texas to review all of these possibilities and provide the long-awaited proof, generating 200 terabytes in the process. “The researchers then verified the proof, which is too long to be read by a human, by using another independent software program,” Simon adds. Computers have now become indispensable allies for mathematicians in resolving this type of combinatorial problem. Already in 2014, computers were used to build a proof measuring 13 gigabytes—the previous record—that made it possible to end an enigma similar to that of Pythagorean triples.

The longest mathematical proof is 15000 pages long, involved more than 100 mathematicians and took 30 years just to complete it. how to write a mathematical proof? About Graham’s number which is largest number ever used in a serious mathematical proof and it is bigger than the googolplex. It’s so big, the Universe does not contain enough stuff on which to write its digits: it’s literally too big to write. … The mathematical proof for “1+1=2” took well over a hundred pages to write, in a book titled “Principia Mathematica”. Mathematician Kurt Gödel wrote a formal mathematical proof for the existence of God. There exists a mathematical proof that shows if only one sex asks the other sex out, only the sex doing the asking will get an optimal pairing.

This is a list of unusually long mathematical proofs. Such proofs often use computational proof methods and may be considered non-surveyable. As of 2011[update], the longest mathematical proof, measured by number of published journal pages, is the classification of finite simple groups with well over 10000 pages. … And so we can try this out with a few things, we can take S of 3, this is going to be equal to 1 plus 2 plus 3, which is equal to 6. We could take S of 4, which is going to be 1 plus 2 plus 3 plus 4, which is going to be equal to 10. Now what I want to do in this video is prove to you that I can write this as a function of N, that the sum of all positive integers up to and including N is equal to n times n plus one, all of that over 2. And the way I’m going to prove it to you is by induction.

The Rolf Schock Award in Mathematics will go to Michael Aschbacher for helping figure out the longest proof ever made by mathematicians. In 2004, he plugged a hole in the Enormous Theorem, a proof that began in 1971 and has only recently been completed. The Enormous Theorem has taken over three decades, a hundred different people working on it, and 15,000 pages of calculations, not including the 1200 page guide that Aschbacher published to plug the hole in the proof in the first place. What could be worth all this mathematical effort? Symmetry. Hey, if it’s good enough for a supermodel’s face, it’s good enough for the longest proof in the world. Some shapes are symmetrical, and if you rotate them enough, they recreate the original shape.

In this manner: what is the most extensive proof in mathematics? The most extensive “proof” in mathematics – essentially, a series of mathematical steps, leading to a result – was completed in 2004. The proof, which concerns the classification of mathematical symmetry groups – a concept aptly known as the “Enormous Theorem” – took 100 mathematicians three decades and some 15,000 pages of workings to pin down.

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What is a mathematical proof?
A mathematical proof is an explanation acceptable to other mathematicians that a theorem logically must be true. In the law, a person can only be convicted if the proof is beyond reasonable doubt. In a mathematical proof, proof must be beyond all doubt, no exception. Proof is the main function of all mathematics.

Likewise: how long is an unusually long proof? The length of unusually long proofs has increased with time. As a rough rule of thumb, 100 pages in 1900, or 200 pages in 1950, or 500 pages in 2000 is unusually long for a proof.

How long did it take to prove the enormous theorem?
The proof, which concerns the classification of mathematical symmetry groups – a concept aptly known as the “Enormous Theorem” – took 100 mathematicians three decades and some 15,000 pages of workings to pin down. All records listed on our website are current and up-to-date.

Moreover: what is the longest proof of 1 1 2? It’s all done in formal logic, and must surely be one of the longest proofs relative to the length and complexity of the statement it’s proving.

What is a 15000 page proof?
The “proof’ was to be found scattered across hun- dreds of journal articles. Collectively, they run about 15,000 pages! The “proof’ is essentially the tying together of 100 or so theorems obtained be- tween the early 1950s and 1980.

Regarding this: has 3X 1 been solved? The 3X + 1 problem (Collatz conjecture) has been proposed for many years, however no major breakthrough has been made so far.

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What is the hardest proof in math?
Today’s mathematicians would probably agree that the Riemann Hypothesis is the most significant open problem in all of math. It’s one of the seven Millennium Prize Problems, with \$1 million reward for its solution.

Accordingly: what are the 7 unsolved maths problems? Clay “to increase and disseminate mathematical knowledge.” The seven problems, which were announced in 2000, are the Riemann hypothesis, P versus NP problem, Birch and Swinnerton-Dyer conjecture, Hodge conjecture, Navier-Stokes equation, Yang-Mills theory, and Poincaré conjecture.

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