The Mathematical Proof That Ended in Murder

[@EllieSleightholm]

brilliant.org/EllieSleightholm - Try everything Brilliant has to offer for FREE for a full 30 days! The first 200 of you that click on the link will get 20% off Brilliant's Annual Premium subscription 👀

[@alberteinstein3612]

I’m glad that we can now advance our understanding of mathematics and science without fear of execution or blasphemy. It’s very sad that these revolutionary people were punished for accepting the truth

[@davidplanet3919]

Excellent. You can use “Proof by contradiction” to show the nth root of 2 is irrational for n>2. First assume the nth root of 2 is rational and write it p/q. Then 2 = p^n / q^n. Hence p^n = 2 q^n = q^n + q^n. But this contradicts Format’s Last Theorem. Therefore the nth root of 2 must be irrational.

[@johnmaguire2185]

The history of mathematics is as dark and twisted as any of Shakespeare’s plays.

[@epikherolol8189]

Everything was dark in the early days. Even today it is and we don't realise it

[@AbigailRoseFoster]

This is so amazing. You make it all seem so simple.

[@hubertorhant8884]

Clearly and neatly stated ! The reminders of basic arithmetic is nicely put. Those highlights set the context and prepare the mind to receive the logical argument by contradiction. Loved it. PS: One could say the Cartesian way.

[@MousumiMondal-n3j]

In 4th step, we can say, p and q are coprime, also.

[@VIMALKUMAR-dy3xz]

Hello maam ...im vimal prakash from india...im teaching Mathematics jee main and advanced student ..your teaching process is very bell....im inspired your teaching....love and light from India 🎉🎉🎉🎉❤❤❤❤😊

[@sourabhsoni2930]

M always waiting for your videos😊

[@alexmai7816]

Great video!

[@KhaledIseed]

Really I love Mathematics in real life, When I saw your channel give me more encourage Thank you so much !!

[@SurajSingh-nx7yj]

thank you 🙏

[@luisakehau1398]

A classic :) ... Nice video I enjoyed so much. It's a nice question to ask: how many cultures in the world knew about irrational numbers?

[@VarunAstro]

Ellie, can you upload something related to physics also once in a week!!

[@armanavagyan1876]

Thanks PROF so much for UR VIDEOS THEY just awesome)

[@eartphoze]

The square root of two is irrational since on february 1st of year 2020, the tangent p to q showed March 1st on the same day of week, but to account for leap year if 2Pi is 1 year then 5.25 is the new year where for another 4 years , february 1st and march 1st arent at the tangent vector of zero , Plot these coordinates y= | 0.1 - 2 | + 9 To denote the reimann zeta function triviality, where in this case the year 2019, is the +9, and x is 2 of [2]019, and 0.1 is the same root as the square root but not from two as in the triangles that derive the root from tetris game pieces in tesselation, as in the trianlge, but of a square from one single side rubiks cube partition, since tirning any cube side will use Log, so 0.1/sqrt 3, until totaling 0.1-0.9 pieces, and by year 2027 it have been |0.8-2| + 7 ---> 0.8 - 2027, LRC circuits

[@jrb0580]

There is something missing from the proof. At 16:30 you say that if p^2 is even, by (2) p is even. But in (2) you only show that if p is even then p^2 is even. To show the converse we need a short proof by contradiction: suppose p^2 is even and p is odd. But if p is odd, then by (2) we have p^2 is odd, contradicting the assumption that p^2 is even.

[@benbrook469]

yesss I love the new intro music

[@ArjanvanVught]

Thank you

[@deepanikarunaratne2075]

New introduction song is great :)

[@ariannavalli9052]

Hozier + math = perfection

[@HunzolEv]

I love your videos young woman!

[@salahadinmahmud6217]

But what if p/q is not a fraction in lowest terms?

[@dragonfractal6361]

If p/q is not in its lowest terms already, then p and q will share additional common factors, but the common factor of 2 pointed out in the video is there whether p/q is in its lowest terms or not. Every rational number can be written as a completely reduced fraction, so specifying that p/q is in its lowest terms shows the contradiction.

[@jamesjohn2537]

❤❤❤nice dear, love love always wins!!

[@samuelmayna]

Bro. No fishing on youtube.

[@Sarojini-l9d]

Thanks, please do some applied maths videos.

[@lousleightholm]

Very clear - thanks very much!

[@YogendraSingh-ir6dh]

INDIAN NCERT 10 TH BOOK

[@eartphoze]

In a gesture of symbolic memory, language plays the teeth in the game of evolution, and de evolution. You've heard the expression "kicked in the teeth" or bat the ball, or bat sh***, to imply empty, void, or falsity. In philosophical terms, stuck. To be at a moment where I liked it better when things could have been unchanging, and dynamic. I was left shipwrecked, literally and figuratively. Is east west or west east? If square roots of 2 imply irrational that 3 points make a face in euclidean geometry, the slope would be the brain of Godzilla trying to code, or program. Because your proof in a right triangle 📐 provides short comings, in one direction towards a fraction lowest terms. You can deduce from lowest terms, if the right triangle is a sun dial, or if the shadow is the direction of time with respect to a vector ray, steming from the 90 edge of that triangle , pointing at the top of the triangle at angle theta divided by many vector rays. For the equation of time. Now if you'd assume that a program like PHP, for (i= 0; I< 5; I++); a few things here, tye right triangle accounts for velocity in linear and direction tangent to C squared , a 2 d circle rolling off the top of triangle crosses any vector ray inside the square root of two, implied by the second condition of I5 , to define those rays as the If's and the height or Sin in trig, as the While's loop. So three points make a face but the rest is short of reason, don't forget to add a second triangle over the first with a 2D circle at center, the rotate that new figure 180 in either direction, you'd see the integral curve by triangles and Einstein's or newtons path to space-time fabric of the cosmos with Brian green, and yes the aether is at best the interloping of virtual reality with irrational numbers, because if you take the Google exam with a race of 5 horses then you'd have to add parameters for each horse unless it wss a quantum computation, you'd be back to the bezier curve or Solomon codes in parity check for NPN, PNP while the world's figures out of visual models are better that intuitive ones,

[@eartphoze]

Or where Analog in A/C is converted to D/C and reed Solomon codes from bezier curves , Virtual Memory or Reality in syntaxt alone like ROMs Emulations

[@reu.mathematicsacademy8566]

My favorite 💝

[@julianwilson9919]

Great video! One small problem unless I'm mistaken is that you showed that p even implies p squared is even but later on you used the converse without proof (that p squared even implies p even).

[@silver6054]

Right. I think you need to show that every integer is either odd or even. Otherwise an even square could result from an even number or maybe from some other kind. Ignoring this, the converses are easy to prove more or less by inspection (as squaring an odd results in an odd, if you have a square that is even it must have come from an even number). There are some other small gaps which are fine for this level of presentation. You would need to mention that p^2 and q^2 are always integers, vital for saying 2q^2 is even for example. But these are nitpicks. This is a very well-known proof though so maybe Ellie's talents would be better used on something more novel!

[@ksksvsisnsnis]

Do you know Malayalam

[@jhawar-ji]

What the fuck?

[@Zetaishere]

I know .. iam a malayali...Malayalam, is the language spoken in Kerala,india

[@jhawar-ji]

@@Zetaishere Bruh, I know what Malayalam is. My distress is, what's the point of asking that here.