Birch and Swinnerton-Dyer conjecture by 
Ciro Santilli 35 Updated 2025-03-28 +Created 1970-01-01
Ciro Santilli 35 Updated 2025-03-28 +Created 1970-01-01The BSD conjecture states that if your name is long enough, it will always count as two letters on a famous conjecture.
Maybe also insert a joke about BSD Operating Systems if you're into that kind of stuff.
The conjecture states that Equation 1. "BSD conjecture" holds for every elliptic curve over the rational numbers (which is defined by its constants and )
Equation 1. . Where the following numbers are defined for the elliptic curve we are currently considering, defined by its constants and :
- : number of elements of the elliptic curve over the finite field, where the finite field comes from the reduction of an elliptic curve from to . can be calculated algorithmically with Schoof's algorithm in polynomial time
- : rank of the elliptic curve over the rational numbers. We don't really have a good general way to calculate this besides this conjecture (?).
- : a constant
The conjecture, if true, provides a (possibly inefficient) way to calculate the rank of an elliptic curve over the rational numbers, since we can calculate the number of elements of an elliptic curve over a finite field by Schoof's algorithm in polynomial time. So it is just a matter of calculating like that up to some point at which we are quite certain about .
The Wikipedia page of the this conecture is the perfect example of why it is not possible to teach natural sciences on Wikipedia. A million dollar problem, and the page is thoroughly incomprehensible unless you already know everything!
Birch and Swinnerton-Dyer conjecture by Kinertia (2020)
Source. The $1,000,000 Birch and Swinnerton-Dyer conjecture by Absolutely Uniformly Confused (2022)
Source. A respectable 1 minute attempt. But will be too fast for most people. The sweet spot is likely 2 minutes.Mechanics before quantum mechanics and special relativity.
Written mostly by Eric W. Weisstein.
Ciro once saw a printed version of the CRC "concise" encyclopedia of mathematics. It is about 12 cm thick. Imagine if it wasn't concise!!!
Infinite Napkin is the one-person open source replacemente we needed for it! And OurBigBook.com will be the final multi-person replacement.
If a product of a big company has a catchy name it came from an acquisition by Ciro Santilli 35 Updated 2025-03-28 +Created 1970-01-01
Ciro Santilli 35 Updated 2025-03-28 +Created 1970-01-01If a Big Company makes a product that Does Something, they just call it Big Company Does Something.
If a product is called "Big Company Catchy Name Does Something", then it came from an acquisition, and they wanted to keep the name due to its prestige and to not confuse users.
TODO what's the point of it.
Bibliography:
- www.youtube.com/watch?v=j1PAxNKB_Zc Manifolds #6 - Tangent Space (Detail) by WHYB maths (2020). This is worth looking into.
- www.youtube.com/watch?v=oxB4aH8h5j4 actually gives a more concrete example. Basically, the vectors are defined by saying "we are doing the Directional derivative of any function along this direction".One thing to remember is that of course, the most convenient way to define a function and to specify a direction, is by using one of the coordinate charts.We can then just switch between charts by change of basis.
- jakobschwichtenberg.com/lie-algebra-able-describe-group/ by Jakob Schwichtenberg
- math.stackexchange.com/questions/1388144/what-exactly-is-a-tangent-vector/2714944 What exactly is a tangent vector? on Stack Exchange
Everybody Was Kung-Fu Fighting (trope) by Ciro Santilli 35 Updated 2025-03-28 +Created 1970-01-01
Ciro Santilli 35 Updated 2025-03-28 +Created 1970-01-01By the Open University. "Open" I mean.
Some/all courses expire in 4 weeks: www.futurelearn.com/courses/intro-to-quantum-computing. Ludicrous.
There are unlisted articles, also show them or only show them.