Notation Memes

Newton's derivative notation strikes again with maximum chaos energy. The equation shows d q ω/dt q = ω̇ (omega with dots above it), and honestly, this is the most Newton thing ever. While Leibniz was out here inventing clean, logical notation that clearly shows what you're differentiating with respect to what, Newton was like "nah, I'll just slap some dots on top and call it a day." The joke here is that Newton's dot notation (those dots floating above the ω) looks suspiciously like he just... kept adding dots for higher-order derivatives. Need a second derivative? Two dots. Third? Three dots. It's the mathematical equivalent of naming your variables x, xx, xxx. The "q" superscripts on the left side suggest this is a q-th order derivative, which would require q dots stacked vertically in Newton's notation—basically turning into a dotted line ascending to the heavens. Plot twist: Newton probably chose this notation specifically because it was easier to write by hand in the 1600s. But looking at it now? It's like he designed it to confuse physics students three centuries later. Mission accomplished, Isaac.

When you're working with complex numbers and someone's still out here using ℜ and ℑ like it's 1897. Meanwhile, Re() and Im() gang is living in the 21st century with proper function notation that doesn't require digging through LaTeX symbol tables. The real vs imaginary part notation debate is apparently the mathematical equivalent of a turf war, and honestly, the Re()/Im() crew has cleaner syntax and better readability. Your move, blackletter enthusiasts. Fun fact: Those fancy ℜ and ℑ symbols are called "blackletter" or "Fraktur" letters, originally from German typography. They look cool on a chalkboard but are an absolute nightmare to type on a keyboard without memorizing obscure Unicode codes.

This is the mathematical equivalent of saying "the floor here is made of floor." The equation literally states that the real numbers (ℝ) are defined as the set of all x such that x is a real number. It's beautifully, hilariously circular! Set builder notation is supposed to construct or define sets using properties, but this definition just... assumes you already know what real numbers are. It's like defining a cat as "an animal that is a cat" – technically true, but spectacularly unhelpful. Mathematicians actually construct the reals through rigorous methods like Dedekind cuts or Cauchy sequences, so this lazy circular definition gets the sarcastic "thank you Mr. Helpful" treatment it deserves. Perfect example of when formalism meets maximum laziness.

This is basically the Crips vs Bloods of mathematics. On the red side, we've got Leibniz with his dy/dx notation for derivatives—smooth, elegant, and looks like actual fractions (even though they're not, but shhhh). On the blue side, there's Newton rocking the dot notation for derivatives, keeping it simple and clean. The funny thing? These two literally invented calculus independently around the same time and got into one of history's pettiest academic beefs about who did it first. Their rivalry was so intense it split European mathematics for generations. Leibniz's notation won the popularity contest though—most of us learn dy/dx in school because it's way more intuitive for showing what's actually happening. Newton's dot notation still shows up in physics for time derivatives, so both gangs are still repping to this day. Choose your fighter wisely—your calculus professor is judging you.

Someone plotted cos x (1) and the graph is having an identity crisis. That superscript x could mean "cosine to the power of x" or it could mean "cosine applied x times" (like iterating the function). The result? A Frankenstein curve that looks like it's trying to be both an exponential decay AND a periodic function while also having a nervous breakdown near x = -1. This is what happens when mathematical notation refuses to commit. In trigonometry, cos²(x) usually means (cos(x))², but cos⁻¹(x) means arccos(x), not 1/cos(x). Pick a lane, math. The chaos here is real—somewhere between -1 and -1.5, the function apparently encounters a singularity and decides to just... teleport. Beautiful. Every math student has stared at notation like this wondering if they're solving the problem correctly or summoning an eldritch horror. Turns out it's both.

Look at this mathematical rebel! Instead of writing x 0 = 1 like every textbook since Newton's day, they've gone full circle with O 0 = 1. It's the mathematical equivalent of showing up to a black-tie event in a neon jumpsuit! Zero raised to zero power has sparked more heated debates in math departments than the proper pronunciation of "gif." The expression is technically an indeterminate form, but mathematicians generally define it as 1 by convention. Kinda like how we all agree traffic lights are red-yellow-green even though colorblind people might beg to differ!

Mathematicians inventing increasingly absurd ways to write "multiply this number by all smaller positive integers" is peak academic efficiency. First we had n! (factorial), then n!! (double factorial), and apparently someone thought "why stop there?" So now we've got Roman numerals joining the party! Next semester's homework: Calculate 42!^MCMXCIX. Your calculator's already sweating.