How do mathematicians prove things? An introduction to basic proofs

Outro:
"Lateralus" as performed by Sakis Strigas
Originally by Tool

My current equipment for making videos (affiliate links):

[EpicMathTime]

Next video will be delayed due to me recording the whole thing with a broken microphone.

[shangxu]

What they teach: write everything down in precise and well defined manner.

What they do: "the proof is trivial and is left as an exercise"

[crashplague]

Toga, Marcus Aurelius in thumbnail, Seneca quote at the end. You are quickly becoming my favorite internet man.

[MrCmon]

Being rigorous and having a good feeling for logic is most important when reading proofs. But when finding proofs, creativity and pattern recognition is most important.

[yousifkhalil]

Zora's domain music makes this proof a chilling side quest

[einekonsequenz]

I really like this video, I'd like seeing some videos on proof strategies. I personally really like proof by induction.

[BrainGainzOfficial]

Great introduction and an even better costume! 🧠💪🏼

[kikosilva]

Another great one! Keep 'em coming! This is very important even at early stages (High school and below), writing down an answer where you identify the objects being treated, the intermediate 'goals' being reached, and the results being used, goes a long way in mastering the ""beast"" that is mathematics.

[MrHowbout]

Omg the Eric Andre "we'll be right back" before the proof killed me. You rock man.

[hamiltonianpathondodecahed]

instead of Q.E.D 🔳
we should use " *BADA BOOM BADA BANG* " [i.e 3b1b style of QED]


some of u might recognise it from the matt parker's comment section

[noir]

Hands down the most attractive mathematician I have ever seen. Woah!

[jhawk]

Are you writing normally and then just flipping the pixels horizontally in the editing or are you just really good at writing backwards?

[JustAlex]

1:54 that's a real mathematician. People like to assume that I am good at doing calculations in my head, "because you're a mathematician, dude!"
Well, but I'm no computer xD

[wayneyam]

I thought mathematicians always left their proof as an exercise to the reader.

[jarrodanderson]

I just finished my 1st Discrete Maths class at Uni. It changed my love for the stuff immensely. Great video bro. More proofs!

[lightningblade]

The 38 part made me subscribe to your channel, a little bit of humour in mathematics and other quantitative fields doesn't hurt and makes the video more enjoyable to watch.

[noname_whatsoever]

Awesome! I would love to see more videos on proofs from you, I think it's an underexplored area in youtube mathematics--yet so fundamental to the subject at large.

What fascinates me is how much is implicitly assumed in the simple proofs you introduced: the notation as true representation of the natural language statements, the algebraic rules about addition and multiplication, and so on. All proofs rely on a multiplicity of rules that are accepted as true (either as axioms or by other proofs) that are combined in ways that make us see that new rules can be deduced from them, or that some rules contradict them and should thus be considered false and excluded from the set of true rules.

There is something strange and mysterious about the whole process of proving things. We don't really need to grasp the details of what we do when we prove things to prove them, as do some mathematically gifted children when they readily grasp poofs but cannot explain to you what they do.

[enemyofthethrone]

I subbed before the Lateralus riff at the end. Bravo.

[caleblott]

I'm waiting for him to wear that toga and then yell: "THIS. IS. MATHEMATICA!" and then kick some bad proofs into a bottomless pit.

[angelmendez-rivera]

I really appreciate that you used Zora's Domain soundtrack from Breath of the Wild for the video. You have great taste