The Heart of Fermat's Last Theorem - Numberphile

Modularity... Simon Pampena gets to the heart of proving Fermat's Last Theorem.
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NUMBERPHILE

Videos by Brady Haran

[EugeneKhutoryansky]

Now that we have the heart of Fermat's last theorem, we just need its liver, kidneys, gallbladder, etc...

[pime]

*whispers* My attempt at a circle.
-Yea it's not bad.
-Thanks man.
i lol'd

[jerome]

"That's my attempt at a circle" - "its not that bad" ... "Thanks man" idk why I laughed so much at this ffs😂😂

[bentoth]

I love how excited Brady sounds when he says "it's like a slinky."

[ArjunBahuguna]

One of my favourite Numberphile videos now. With visual intuition, it really makes modular elliptic curves accessible.

[sams.]

I know there is a lot more to it, but this is the single best explanation of the Taniyama–Shimura conjecture I’ve ever seen! “modular forms with many symmetries are actually elliptic curves in disguise”. I never really could wrap my head around modular forms until now.

[phyein]

This is exactly the kind of math vid I look for - I'm a long way from being able to understand advanced math but I love attempts to paint an intuitive analog (difficult as it may be on it's own as well) to extremely technical stuff that seems so alien. Nobody can just look at a wikipedia summary of modular forms and elliptic curves and even begin to get an idea like one that is conveyed here for example. This is the kind of thing I want to get out of learning more and more advanced math.

[Joeobrown]

this all goes way over my head (and probably most of our heads), but i think we can all agree that's a pretty great shirt

[colebutler]

"That's not bad"
"Thanks man"

[fSateQ]

fisrt numberphile video i understand nothing

[owenlever]

This is a truly marvellous demonstration of Fermat's last theorem.

[recklessroges]

The "infinite plane" animation: ICWYDT and laughed, (so thanks), but I wondered if that might confuse newer students that don't play as comfortably with math. My second thought was that I love Dr Pampena's calmed-mania style of presentation, and the irony of describing a helix with his fingers while we are looking at many lovely examples attached to his head.

[RoflZack]

The infinite plane joke at 1:40 hahaha

[onlygiga]

This video is just great. I'm tempted to say it's my favorite video of all numberphile videos so far (although the coin flip ones are a strong contestant for my favorite video as well). I've watched all videos on this channel and all your other channels Brady and ever since I saw your videos on Fermat's Last Theorem wondered how the conjecture works. Great stuff, keep up the good work!

[randyzeitman]

Severely well explained ... to get the core of the idea of modularity and whole numbers.

[dominiclohry]

what an absolutely amazingly elegant basic explanation. Thank you!

[shivtekoriginal]

just came home from a royal society lecture on ramanujan where his work on modular mathematics came up. Was reading Fermat's Last Theorem on the train and planned to search up about modular forms. Then this happens... love you guys

[jazzsoul]

He’s so passionate that’s beautiful to see

[PetraKann]

This presentation is like trying to give a person a taste of what "calculus" is about by introducing them to the addition of fractions. I personally dont see the point. It would have been better to post this video as a description of what modular forms were (and perhaps make a reference at the end to how it was useful in the early work carried out to develop a proof of Fermat's Last theorem)

[bernardofitzpatrick]

Like Simon's way of teaching and he seems a really cool, chilled dude.