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I "discovered" Mersenne primes on my own when I was about 15 years old. Imagine my disappointment when I learned that some French guy beat me by four centuries.
Homey I have no idea what the hell hes talking about myself. I don’t Evan know why I watch this stuff like I’m gonna be sitting there in a sweater vest in a library with a tall ceiling and all of a sudden grab chalk and wright equations
You also made a mistake. He should have swapped (0, 1) by (1, 0) (not (1,1)). Also he marked the graph Y-X instead of X-Y (horizontal Y, vertical X) which is not the common Cartesian system.
The ramsay theory problem is very hard to understand. In your picture, the edges are not all the same color. They're red, blue, and black. Problem solved. 2 dimensions. It's a square.
a very small nitpick at 4:40 : there is a proven bijection between mersenne prime and EVEN perfect number. it excludes if odd perfect numbers... if any exist, as stated before
about Ramsey problem, the problem itself is much more general and actually explaining the general case would be easier because it is not related to hyper dimensional squares at all
4:28 Correction: There exists a bijection between EVEN perfect numbers and Mersenne primes. If there exist infinite odd perfect numbers, this doesn't necessarily mean that an infinite amount of Mersenne primes exist.
5:31, this is not the common cartesian coordinate system, you have the x and y axes the wrong way round, y nornally goes on the vertical axis and x on the horizontal
But it is still a Cartesian coordinate system, and not a polar, cylindrical, or spherical coordinate system. The labeling of the axis is arbitrary, x being the vertical axis and y being the horizontal is just as valid as the other way around.
2^(2y+1)-2^y where y=0,1,2,3... can be use to find perfect numbers, Not all numbers produced by this formula are perfect but all perfect numbers (so far) fit this formula.
Whoopsies! In the rational distance problem, there are 2 (0, 1)s. One of those is supposed to be (1, 0) Also everything is horrendously off grid But interest video nonetheless
How about the fact that odd numbers are female/feminine and even numbers are male/masculine Like 8 is masculine, but if 8 were odd I’d consider it feminine. Idk it’s my brain Also because I feel like O is a feminine Letter E is masculine letter, and Odd has 3 letters which 3 is feminine and Even has 4 letters and 4 looks masculine, 24 looks like a cool slick boy 31 looks like a cheerful girl
TREE(3) has surpassed it, although it's creator, Harvey Friedman, has devised many functions that allegedly grow much faster than TREE, but never proved anything about them. And his papers look like they've been printed on some fax paper.
Well since I'm not studying in mathematics. Can someone explain why is it important that we understand this type of questions? Like what does it solves?
The methods we use for solving these problems might also apply to solving other problems in the future. For example, any new methods we find for solving problems about primes can influence cryptography - giving us new methods of securing and encrypting data. The more abstract a problem is the wider the possible fields and problems its solution can be applied to.
@@HopUpOutDaBed I can see the moving sofa problem (besides the obvious y'know, moving of sofas) relating to implants like artery stents; finding a maximum workable area for a device that can still navigate the body without risking bruising or other damage. It's hard to defend the value of some of these, but I'm sure across the many many professions and sciences, one of them likely has some creative (but also probably very niche) application
1. Knowledge is good for knowledge's sake. 2. The tools you develop to solve logical puzzels and problems like these come in handy elsewhere. Ring theory was invented to solve number theory and algebra problems that seemed meaningless and now it's being used for computer graphics. Everything you see on display on a computer, unless it's bitmap, including every letter typed, is an algebraic variety carved out by polynomials that the computer is graphing in real time. And of course, it is STILL being used for number theory and algebra problems. Group theory and complex numbers were really doubted but are now an indispensable part of physics and complex numbers come into anything that has to do with electricity of fluid flow. 3. The distribution of primes is useful for cryptography. The sofa problem is a calculus of variations problem, which comes up everywhere in engineering and physics. Optimisation problems' usefulness should be obvious. Ramsey theory helps us understand general graph theory better, which is crucial for computer code. Something like queing, sorting algorithms and Google Maps wouldn't work without graph theory. The inscribed rectangle problem is solved topologically. The solution for the square problem would probably require some breakthrough in real analysis, algebraic topology or analytic geometry, which needless to say would send ripples everywhere else in math and science. The rational distance one will probably be solved with algebraic geometry, given that that is how the problems of rational points on elliptic curves get solved. I already explained why algebraic geometry is important.
I know what the "double arrow" in the giant number at the end of the video means. But can someone tell me the meaning of the "double less-than" symbol?
@@cloudy28 true, but technically considering the largest we have is the largest it is. Also the question arise. How do we know we haven't reach the limit? But let's say we haven't found it yet.
@@asagiai4965 the largest shape we know doesnt have to be the largest shape possible. We don't know If we reached the limit because no one was able to proof it.
Great! Now you can publish your work and totally clown on all of those dumb professional mathematicians! Who needs to study prime spectra of ideals of polynomial rings for affine schemes and moduli spaces for years if a random commenter says it's easy and can be done in one sitting!
