The 7 Levels of Math

Discussing the 7 levels of Math.
What was your favorite and least favorite level of math?

00:00 - Intro
00:50 - Counting
01:42 - Mental math
03:02 - Speedy math
03:51 - Adding letters
04:54 - Triangle
06:09 - Calculus
07:25 - Quit or Finish

[sergioespana]

I love how calculus is seen as an end or a final boss, but if you actually get to study Maths in an University it's literally just the beginning, and realize it's just an specific case of some really, really abstract topics.

[AniketKumar-lwsu]

I once heard someone say that once a kid in his class asked the teacher "Where will we use these in real life"
The teacher said "You won't but one of the smart kids might"

[lamalamalex]

As a scientist, all of my frustrations and blunders had one single source: I didn’t know enough math.

[michaelsipos]

As a senior math major I have to say: Calculus is only the beginning of your brain being forcibly re-wired. Calculus is still relatively computational (i.e. you can still learn an algorithm or equation and just run some values through it), just wait until you get into Abstract Algebra (Group Theory really) or Proofs and Analysis, THAT'S when the training wheels come off and you have to actually learn on your own how to derive and understand the world of concepts and logic that Mathematics is comprised of.

[cphVlwYa]

Hate to break it to you, but calculus is the start of math, not the end. Also, an understanding of math allows you to learn science much faster. There's too much science to learn and you'll never learn fast enough without math. If you hate it, you likely just didn't have good enough teachers and so you warped your frustration into anger so you didn't have to feel bad about yourself even though it probably wasn't your fault anyway. Nevertheless, if you see something like calculus as inapplicable to everyday life, that simply means you don't understand it well enough to apply it.

[HaramGuys]

I have taken over 40 mathematics courses past calculus 3, and what you described as level 7 is where real math starts.

[christophersoo]

Bro really said "Calculus is the final boss of maths 😭😭".

[louisrobitaille]

5:33 Fun fact: sine, cosine, and tangent are actually way more relevant in circles than triangles 👀. After all, when you're measuring the sine of an angle, what you're really measuring is the value on the y-axis of the point at the intersection of the circle's circumference and a linear function going through the origin, where the origin is the point of the angle. The cosine is that point's value on the x-axis. This is used *way more often* especially in physics.

[ignacio]

Math isn't just about numbers and that's the reason why so many people hate it, instead it is all about logical reasoning, results that conduct to other results and if we keep teaching kids only to multiply or divide faster instead of making them actually think, they are bounded to hate math.

[SerbAtheist]

Here are the actual 7 levels of math:

1) Arithmetic: counting, adding, subtracting, multiplying and dividing, up to and including multiplying and dividing multi-digit numbers.

2) Basic Algebra: solving basic linear equations, solving systems of linear equations, basic algebraic manupilation including applying the distributive law, fractions, negative numbers, square roots and exponents, along with appropriate topics in other areas such as Pythagora's theorem and basic divisibility

3) High School Algebra: basic polynomials, quadratic equations, trigonometry, congruences, functions, linear algebra, basic group theory, basic combinatorics: permutation, variation and combination

4) Basic Calculus: limits, single and multivariable calculus, basic differential equations, basic topology, more advanced group theory.

5) Advanced Calculus: Fourier and other transforms, Green's functions, Stoke's theorem, manifolds, Lie groups, tangent spaces. Most scientists outside of math and physics will stop here.

6) Advanced Undergrad Math: Noether's theorem, gauge theory, Galois theory, vector bundles, differential forms, de Rham coholomogy, Dynkin diagrams and a bunch of other stuff that is already extremely esoteric. This is usually where physicists, except certain types of mathematical phycisists, jump ship.

7) Graduate and Research Math: Incredibly technical to the point where only specialists in that particular field can read and understand papers. The jump from Level 6 to Level 7 is probably the biggest jump of them all as it requires a lot of adjustment. The concepts are incredibly difficult, to the point of being barely understandable, due to them incorporating a ridiculous amount of mathematical ideas inside.

[paulvictor]

I loved math so much as a kid, then for years after my Adhd got bad I thought I was bad at it and thought my passion left, and only in the last year since I've been diagnosed and treated for it I found out that I do still have that passion and love for it, and I'm now retaking my precal and statistic 1st year course and building up my skills to where they were meant to be, and I must say, I think that the love of math is something that can be deep in us and present itself as long as you're under the right circumstances.

[anno_nym]

Ironically, I think the best part of math is when it gets abstracted from actual calculations and is more of a hypothetical collection of thoughts than anything instantly applicable (e.g. multiplying numbers). I wasn't very good at doing the simple stuff, when it was all about learning and practice and in my personal opinion, thinking really about abstract logic and going deeply into the "why and how?" made it interesting in the first place.

[alemon]

this sounds a lot like a "school made me hate math" problem, once you start to study math alone it's much much more easy and fulfilling

[racool]

We've known the 'why' for millennia, and we've used math to advance our society to where it is today. Every single topic you learn in math, especially calculus, has hundreds of applications used in a variety of fields. If schools stop teaching math society will eventually crumble, which is why nations strive to teach it to everyone.

[reidflemingworldstoughestm]

Sounds as if you didn't like math, but you liked arithmetic. Math really starts around algebra, trig, and calculus, where you reach a point from which you can begin to apply your skills to interesting questions in the real world. Questions like finding the center of mass of a tapered rod, or locating the source of a gunshot based on the exact moment three different microphones detected the sound.

[markgross]

It's kinda funny cause in reality the math you learn up to high school is just prerequisite. Math pretty much begins at calc 1 and linear algebra. My partial differential equations professor used to joke that whenever we had a problem that would simplify down to something with just vector calculus or below that the rest of the problem was just "stuff you learned in kindergarten." The truth is that it takes a lot of math to understand what math is really useful for.

Something that I think would help with the "why am I learning this" problem is making linear algebra the first university math class rather than calculus. I use linear algebra much more compared to how much I use calculus. Calculus is largely a tool for dealing with physics; the most use I've gotten out of calculus so far is fourier analysis and the sturm-liouville problem.

Also, I believe people have a fundamental misunderstanding of what math really is--math is logical reasoning. Numbers are a small part of math, and the ability to do calculations fast is just "technical ability." Being good at math is being able to craft logical arguments and perform logical reasoning. I've had a few proof-based math classes, and it's essentially like writing essays.

In fact, guidelines for writing proofs (that I remember) are the following:
1. Use words when possible and not symbols
2. Never start a sentence with a symbol
3. End each thought with a "."
4. Be clear

In other words, its a formal argument.

[harrygoesgaming]

Currently in Calculus 2 struggling with different methods of integration... BUT I am having the time of my life because I have people around me and good professors that have taught me to not give up. I wanna be a civil engineer one day and hopefully I'll apply this stuff in my future job

[fabriziobrown]

I think the why is to let a few people into highly mathematical subjects, in the first grades of school I struggled alot with math, then I gradually became better, this led me to choose a stem university. If it wasn't for the initial pain, I would have never taken this path

[ThomasMeeson]

I'm the other way around. I never liked maths between ages 3-12 but then trigonometry got me interested and when I was 15/16 I had decided to learn the entire A-level course before I'd even taken it because I was so fascinated. I'm now studying it in university and it gets more interesting every day

[kingarthr]

Level 1: High school math and calculus
Level 2: Undergrad degree
Level 3: Masters degree/Early grad school
Level 4: Phd
Level 5: Postdoc/industry researcher
Level 6: Associate professor, established researcher
Level 7: Full professor
Level 9: Terrance Tao and co. (The elites of math)