Oldest Unsolved Math Problems Solved After Eons

Thanks for watching.

Subscribe to my newsletter for occasional updates, and discoveries that make math come alive.

Timestamps

0:00 Squaring the Circle
2:42 Euler’s Sum of Powers Conjecture
5:17 Four Color Map Theorem
6:57 Legendre’s Constant
9:38 Fermat’s Last Theorem

— DISCLAIMER —

This video is intended for entertainment and educational purposes only. It should not be your sole source of information. Some details may be oversimplified or inaccurate. My goal is to spark your curiosity and encourage you to conduct your own research on these topics.

[robinvanleeuwen]

Fermat be like: the proof is trivial and is left as an exercise for the reader

[alabamaal]

It is actually possible to "square the circle" employing a compass and straightedge, using the following procedure:
1) Mark a point on a circle's perimeter.
2) Rotate the circle 360 degrees (one full turn), tracing out a straight line segment. The resulting line segment is equal to the circumference of the original circle. (Imagine a can rolling on its side.)
3) Using the compass and straightedge, bisect the line segment into a half segment.
4) Bisect a half segment into a quarter segment.
5) Again using the compass and straightedge, construct a square with each of the sides equal to the quarter segment.

The resulting square will have a perimeter equal to the original circle's. It won't be possible to state the exact length of the side of the square except as a ratio of Pi since Pi, which defines the circle's perimeter (circumference), is an irrational number. Nevertheless, the constructed square is a valid geometric representation of the squared circle.

Neat, huh? Except for one problem: I cheated. You see, I didn't use just the two instruments, a compass and a straightedge, but also used a rotating marked circle. The rotating marked circle qualifies as a third "instrument", which is against the rules.

Pi is not only an irrational number, but is also a transcendental number, meaning that it cannot be a solution of an equation involving only finite sums, products, powers, and integers. Because the transcendence of Pi is involved, it would take an infinite number of steps to "square the circle" using only a compass and straightedge, making such a solution impossible. Sorry.

[SeanSkyhawk]

Legendre's actual appearance is also considered an unsolved math problem, the watercolor caricature by Julien-Léopold Boilly shown in the video is LITERALLY the only surviving portrait of the famous mathematician.

[coopa_troopa]

how does this guy not have millions of subs! this channel has crazy good quality

[lumbersnackenterprises]

144 is one of the coolest numbers in all the ways it tends to show up

[DKDexter]

In a way, isn't Euler's sum of power's conjecture, and Fermat's last theorem ... "sort of" the same?

[e-pluszak]

8:12, yeah, but if for one value of B this ratio approaches 1 so it does for any other as lim x→∞ (x / (ln(x) - B_1)) / (x / (ln(x) - B_2)) = 1, to make any sense of "optimal value of B" you need to define some more strict way of comparing π(x) with x/(ln(x) + B)

[CalBruin]

The name is _Noam_ Elkies not "Noah"

[systemchris]

Even a star trek episode refers to Fermat's last theorem not being solved... It's weird to see in a sci fi lol

[romanbykov]

you have a problem saying the nationality of Chebyshev for the same reason?

[dan-usnk]

What if a country is surrounded by more than 4 countries? How would 4 colors suffice?

[Robi]

5:35 - gotta ask: why that map in the background is in Polish :D?

[Liquid_Pain]

ooo cool, i like learning about maths :P

[romanbykov]

Euler is not a "swiss" mathematician

[dfih]

I like this channel, but you’re really loose about names. For example in this video your pronunciation of Fermat or your misspelling and misnaming of Noam Elkies as “Noah Elkies”

[LeoStaley]

The way you keep mispronouncing fermat's name