Identity wrote:JaneFairfax wrote:Is this the most difficult proof ever?

No. That would probably be, "Classify all finite simple groups." That spanned thousands of papers and hundreds of mathematicians. Another good one is "Prove that any group of odd order is solvable." That one was 255 pages.

I believe we have a new contender for the record:

Baffling ABC maths proof now has impenetrable 300-page ‘summary’.

A summary of a massive mathematical proof that has baffled mathematicians for the past five years may help a few more people get to get grips with the key ideas. How long is the explainer? A mere 300 pages.

And that is only the summary: the original work – Shinichi Mochizuki’s proof of the ABC conjecture published in 2012, using a radical new theory developed over two decades – contained over 500 pages.

]]>Here is an interesting example:

]]>Anis a topological subspace of such that given any pointn-dimensional (real) manifoldxin there exists a real number (depending onx) such that the open ball is homeomorphic to .

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Monox D. I-Fly wrote:a nickel is a tenth of a dollar and a dime is a twentieth of a dollar.

Are you sure?

That's what Google said.

]]>Inherent love for numbers!

]]>Lucas,

you mention that pi divided by 10000..... million is proof. However, then its not pi. The value of pi is changed. You are dealing with the unaltered value of Pi, that is in the order of 3.14159......

so I do not think your disproof is correct

The disproof is correct (as long as he divides by 10^(10^6) rather than 10^6). The product of a (non-zero) rational number with an irrational number is always irrational, and the statement in question was about irrational numbers, not π.

]]>ganesh wrote:Whats so special about the TN

1.444667861..................??????Is it known if this number (i.e. e^(1/e)) is transcendental?

It has not been proven to be transcendental, I don't think.

]]>Better yet, "the rest is left as an exercise for the reader".

]]>For example, isomorphisms are easy, they are what you use to say that two groups are equal. But is there a way we can use that kind of language with homomorphisms?

Aside from preserving an algebraic structure, there are ways in which such algebraic structures can be visualised. One of my favourite examples includes homomorphisms of directed graphs.

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