Hello! Thanks for sharing your hot take. Your opinion is Wrong and I am going to tell you Why.
“Hot take” should be reserved for statements which are conjectured or hypothesized but not proven. Despite not being proven, a statement should have some evidence in its favor before being presented as a hot take.
On the other hand, once something is proven, it is tea. To prove something is to spill the tea. A proof is an effortpost. Proper format for spilling the tea is to write the statement of the tea, followed by “in this essay I will,” and then the effortpost, beginning with statement of assumptions. A proper effortpost ends with “thank you for coming to my TED talk,” or “TED” for short. Allow me to demonstrate.
Fermat’s Little Tea.
For p, a ∈ ℤ, if p is a prime which does not divide a, then a^(p-1) = 1 (mod p).
In this essay I will let p, a ∈ ℤ, such that p is a prime which does not divide a. Lagrange’s theorem indicates that ℤ/pℤ* is a cyclic group under multiplication. As such the order of any element of ℤ/pℤ* is the order of the group, p-1. Since p does not divide a, a is an element of ℤ/pℤ*, and as such, its order in the group is p-1. Therefore a^(p-1) = 1 (mod p). TED.
The Four Color Tea is notable for being the first major tea spilled by computer. The Four Color Tea, then the Four Color Hot Take, was first proposed by Francis Guthrie in 1852. The tea was notoriously difficult to spill, but over a century later, in 1976, Wolfgang Haken and Kenneth Appel presented an effortpost using a very advanced (for the time) computer at the University of Illinois.
The first person to spill the tea on the Riemann Hot Take with an effortpost accepted by experts will be the recipient of a million dollar prize.
this is a niche post
Tea: √2 is irrational.
Efforpost:
In this essay I will let r = √2 and spill by oh no that r ∉ ℚ
First, we need to spill a lemonade:
Lemonade 1: For all q ∈ ℚ, there exist relatively prime a,b ∈ ℤ such that q=a/b. Effortpost: By definition, q ∈ ℚ ⇒ ∃ x, y ∈ ℤ | q=x/y. If x and y are not relatively prime, then let z = gcd(x,y) be the greatest common divisor of the x and y, and let x’=x/z and y’=y/z. Then q = x/y = x’z / y’z = x’/y’. Since z was the greatest common divisor of x and y, x’ and y’ must be relatively prime, so we take a=x’ and b=y’. LED.
Like, what if r were rational? Then by lemonade 1, there exist relatively prime p, q ∈ ℤ such that r = p/q. Squaring both sides gives us 2 = p²/q² -> p² = 2q², so p² is even. However, this is only possible if p itself is even, in which case p² = 2q² is divisible by four. This further implies that q² is even, and so q must be as well. If p and q are both even, then they have a common factor of 2; but by definition they are relatively prime.
oh no.
Thus, r = √2 ∉ ℚ by oh no. TED.
Every generation coming up with new names for things might just save math. Before spilling my tea, let me lay out these three lemonades… it’s just more inviting.
The big thing in my area in grad school was the Baum Connes conjecture, and Paul would have loved having the Baum Connes Hot Take. Alain… probably depends on the french for hot take.
I think needed is a word for Theory. Like K Theory, Homotopy Theory…
Bullshit. It’s bullshit. K bullshit, graph bullshit, homotopy bullshit, Galois bullshit, number bullshit, category bullshit. It’s all bullshit.
Katherine Crighton 