Does Combinatorics qualify as an "advanced topic" here?

[Note: It is taught is in high school level(enumerative)]

I learnt long time back approximate value of 100! is 9.332622e+157, checked today for accuracy.

]]>I have fixed your LaTeX.

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Sir Michael Francis Atiyah… is a British-Lebanese mathematician specialising in geometry.

At a hotly-anticipated talk at the Heidelberg Laureate Forum today [Monday 24 September 2018], retired mathematician Michael Atiyah delivered what he claimed was a proof of the Riemann hypothesis, a challenge that has eluded his peers for nearly 160 years.

I used to share the same idea than you -- the fact that the manifold and curved space answers most of all the cosmogony. But I hit a snag.

Let's say that what they say about the light emissions is real. That means : the further you look, the older the time. That explains amongst other the cosmic microwave background.

That implies then that if the universe was at a time incredibly small, I should see that point at 14 billion light years away, everywhere around me. In my perception, I'm in a sphere centered around me whose borders are reduced into a single dot. Just like I was in a hyper-droplet (to continue with 2D perception, as If I were in a piriform (tear-droplet) shape).

Problem : this assumption is true for every point of the universe. How is it possible geometrically ?

]]>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:

]]>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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