Mathematicians vs. Engineering Classes be like... 

To quote my professor "We don't solve integrals, that's what mathematicians are for."

"Actually this is what we called proof by shut the hell up"

To the Engineer, close enough is perfect. To the Artist/designer, there's no such thing as perfect. To The Mathematician, there's nothing except perfection.

“I literally hate engineering, it’s the worst shit ever.” Hey he’s an engineering student

"approximately is the same as equals. well, approximately. " This was glorious.

A mathematician, an engineer, and a statistician were out hunting in the woods. They crested the top of a hill, and saw a deer standing in the distance. Not wanting to get the shot wrong, the mathematician took some readings of the ambient air temperature, pressure, and wind speed, did a couple pages of calculations, and finally arrived at a number. Then he lifted the rifle to his shoulder, aimed to the precise angle that would hit the deer, and fired. The bullet missed, about 10 meters to the left. The engineer scoffed "Oh geez, gimme that." And he took the gun, removed the scope, bolted it back on crooked, then handed it back to the mathematician. "There." He said. "That should account for your error. Now take that exact same shot again." The mathematician fired again. The bullet landed 10 meters to the right. "We got him!" Cried the statistician.

Don’t get me started on Physicists and Mathematicians. I remember a moment in my Quantum Mechanics class in grad school the instructor paused, turned to the class and asked “are there any mathematicians in here?”. No one raised their hand. He then sighed relief and said “good, I didn’t want to have to justify what I’m about to do”. He then pulled a differential through an integral sign.

“but why do I have to know how to integrate by hand?” “you won't walk around with MATLAB in your pocket all the time.” Wolfram Alpha:

Engineering majors be like "what real world usage or application does this hypercomplex mathematical equation have?". Mathematicians say "None whatsoever. But aren't maths beautiful?"

This integral is hard because its on the back of our table of integrals. That had me dying.

If engineers wasted their time proving everything and being accurate, we would have stuck with technology from 18th century.

What I've learned in Engineering focused math classes about the approximately equal sign, is that it just means "close enough".

*≈ = =* such extremely important formula this is

“Why be right when you can approximate” ~Engineers Still trying to recover

There is a joke my father told me once when I was child. He had dropped out from Physics, and is now a great carpenter. I'm now a Mathematics student. In a certain town, once was promoted a competition for the construction of bridges. One engineer, one physicist, and one mathematician were asked to make the best bridge possible, the perfect bridge. The engineer worked like he always did. He made the project, and in a few months the bridge was up. The bridge was good enough. The physicist took longer to make his bridge. By the end of the year, his bridge was up too. It was also good. The mathematician still had to hand in his project, though, so the competition was still not over. People waited for him for a long time. Days, months, years passed, and nothing from the mathematician. The people kind of just forgot about the competition, and it was left without conclusion. The town had two new bridges, and people used them in their daily lives, and they eventually payed no mind anymore to the competition that originated those bridges. Decades later, however, a student found out about the competition, and wondered "What about the mathematician?". The student went to the university, looking for the mathematician, and found his office. The student knocked on the door. A raspy voice responded "Come in.". The office was small and cluttered with paper, in piles, covering the desk, bursting out of drawers, and even piled over a couple of chairs. Sitting behind the desk, was a very old man. The student greeted him, and questioned him about the competition. "Why didn't you hand in your project? Did you forget about it? Did you give up?". The mathematician looked up to the student. "No. I've been working on it this whole time.". "And... do you already have an idea of how the bridge is going to be?", the student asked. To which the mathematician responded, excited, "No. But I know now, that the perfect bridge, it exists and it's unique!".

Engineers: Makes reasonable assumptions and approximations to make their calculations easier and more useful Mathematicians: *And we took that personally.*

The difference between theory and practice is that in theory, theory and practice are the same thing but in practice, theory and practice are not.

Mathematicians: "Do...do you approximate and round everything?" Engineers: "You get used to it."

Sometimes I am in awe how people figured out the theorems where engineering stands so proudly of and then I hear a mathematician explain it and then I remember why I never bothered looking deeper into the foundations.

Got my BChE (Bachelor of Chemical Engineering) University of Delaware (1986), worked 2 years in Rohm & Haas Chemical Research, got my Masters (1991) in Math + PhD (2000) in Math in differential algebra. Worked my ass / brain off for all of them. But, the pure abstract math was just orders more difficult than anything I ever did in engineering, as hard as engineering was. I was not prepared for the level of abstraction for graduate level math. Ended up taking undergraduate math courses in graduate school, in spite of having taken a year of Abstract Algebra (1987-1988) at Villanova University, and one semester of Advanced Calculus (spring 1987) at Drexel University. Fell into a deep depression in first semester of graduate school (fall 1988) due to being way in over my head. I still have no idea what most professional-level mathematics is proving or saying, in spite of having seen and heard the terminology over and over. 99% of all the professional-level mathematics I see is defining spaces (of functions or maps) and maps between those spaces. Maps & spaces. Maps & spaces. Maps & spaces. The math I work on now is much more combinatorial. On an off-topic, I wish people who know NOTHING about either math or computer programming, who have done neither (I've done a LOT of math, and a LITTLE programming) would stop IDIOTICALLY equating or comparing the two. THEY ARE TWO COMPLETELY DIFFERENT ACTIVITIES! Yes, BOTH are all about MANAGING COMPLEXITY. Yes, BOTH use/apply logic formally. But computer programming is all about GETTING A COMPUTER TO DO SOMETHING. Mathematics is all about PROVING THEOREMS: STATEMENTS ABOUT WHAT IS. STATIC PROPERTIES. Even the most computational math and formula-finding does that or is that.

"Is this an engineering joke I'm too sophisticated to understand." So this is the mathematician's version of the rich meme.

Gawd, I never thought I'd encounter a context where the engineers would become viewed as the jocks. Everything is relative.

I can confirm the words "lookup table," "approximately," and "assume" are quite frequent in engineering classes

>Instantly leaves at “Real World Applications.” It’s adorable.

“This one is pretty tricky, yep the solution is on the back of the table of integrals”

My math teacher once said: "Math is a strong, independent subject that ain't need no applications!"

I love that you and Andrew make videos in which you take stabs at each other, all in good fun. It is important to point out the frustrating differences that scholars encounter between these disciplines; more importantly, that these differences should not be allowed to be polarizing lines of division between fields that are so intrinsically cooperative. Great job guys! Please keep the content coming :)

1:20 I thought he said " we found the virgin already" LMAO

Let's get a moment of silence for the engineers who just realized they chose epsilon < 0 on their pre-lab.

My professors were never like that, usually when someone asks for where an equation comes from they just put it as an exercise on the homework

'Proof by shut the hell up' is definitely going to be a groundbreaking invention.

4:10 Mathematician: „A calculator for sure doesn’t have that much *overcalculation*“ CS and CE students: „pfffft“

“Hey we found the virgin, already! That was pretty quick” -anyone who hears someone ask to do actual integration in ENGR

As an engineering student, the thing I can't stand the most in my classes is when the professor says the solution to a complex integral is "trivial". Like maybe it is to you and maybe for some students, but it'd be nice to get a reminder on how to do some calculus every now and again.

I'm not sure if this was part of the joke, but the fact that pi² ≈ g is a historical artifact which pretty much depends on the "fundamental theorem of engineering". Namely, the meter was originally defined by the French to be the length of a pendulum of period T=2 seconds. The exact formula involves pi and g, and is derived using the small-angle approximation sin(x) ≈ x. Props to these guys, if this was thought out in advance.

"I don't even have a calculator here." I felt that one, as a math minor.

Welcome to Electrical Engineering, where numbers are imaginary and so are the women. 😭 Especially in the Black Magic (radio frequency) specialization

The fundamental theorem of engineering is actually π = e = 2.

I've never seen a derivative or integral lookup table in engineering school. It was derive it by hand every time.

Pi squared = g is close enough in most applications. If I worked it out properly it's about a 1% error. Now all I need is for a company to bring enough mass to Earth so I can use g=10 m/s²

I still remember my first math 1 class. The professor literally said "We use exact numbers here, not like those physics ones, they like to approximate everything".

Like where it is derived from. . . This textbook😂

From being a (computational) math major for undergrad that went to grad school for EE ~30 years ago, this definitely brought back some memories. 😊 I don’t remember my profs taking quite the same shortcuts….but I seemed more comfortable following the derivations than others who were the engineering undergrads. 😏

4:20 I prefer calling it proof by approximation

When a mathematician sees a formula which was obtained not through derivation, but rather through rigorous testing and analysis of data to create a model for a given property of a substance:

And then the computer scientist is like "Can I just program my math homework away?"

I'm an engineering student and in my school, the professors will explain and show the derivation of each formulas before we can move on to the actual problem... In this way, we can understand where did it came from and it's really helpful and fun knowing how go derive the formulas rather than memorizing it hahahaha

As an engineer, they taught me like a mathematician and after that we were allowed to use look up tables,just because it's faster,and about most of the "complaints" of the mathematician if not all were addressed in my classes

"Real-world applications" *leaves the class* HAHA, extremely relate-able.

2:49 420 points for 69% real smooth 😂

As physics student, i have an existential crisis because i have to adopt both these mentalities

This video illustrates the big difference between engineering at a German university and engineering in the US. In Germany you do exactly what the "mathematician" asks, to a degree that makes you want to vomit after 4-6 semesters of engineering math. At one point, unfortunately, many people shut down and just push through the torture with a switched off brain :D because from semster 1 onwards it's all tailored to Dr.-Ing. (Ph.D) level and Dr.-Ing. habil. levels just like the programs for lawyers are still aiming for the high office of becoming a judge. German eduction can be very 19th-century-brutal in that regard.

One reason civil engineers are always approximate is cause the small numbers don't really matter as we will always times the required amount by a safety factor anywhere between 1.5 - 2x then use the next size up for standard construction sizes.

"OH is this an engineering joke I'm too sophisticated to understand?" I'm dead 😂😂

When I came across this video this morning it reminded me of something I have seen some time ago concerning Mathematics and Physics. It of course will be applicable to engineering as well.... A quote from a book on Path integral Quantum Mechanics by Richard Feynman, “the mathematically rigorous solution may not be physically rigorous”.

As an engineer I find it funny how mathematicians get so worked up. Most of the approximation formulas are simply the first (few) terms of Taylor expansions. If you're going to build something, and your manufacturing skill isn't infinitely precise, infinite precise results are meaningless. Those approximations are 'good enough'. Also you cannot calculate exact results anyway. Or are you doing a complete solve of the motion equations for all air particles in your lab to see how the air affects your experiment exactly?

“Why be right when you can approximate?” I love it, that’s it...that’s engineering

I remember being being caught by the approximation thing in university. In my pure math class we'd been looking at a formula with first order and second order terms. Most of the lesson was spent proving that the first order term approached zero. Then I walked into my physics class and the prof had the same equation on the board. "The first degree term will be swamped out by the second degree term, so we can just ignore it," he said, and simply crossed out the troublesome term.

LOL. In my last semester in EE Grad school, the one thing I learned myself to do was to find a way to solve all the math topics that I ever learned using a TI Nspire CX CAS Graphing Calculator. Whether it was finding the limit of some cockeyed function or something else, I taught myself how to use the Calculator to find the answer. This way I could forget ALL the different techniques/theorems/proofs etc. needed to solve that problem while letting the calculator do all the grunt work. All I needed to know was how to use the calculator for my specific problem. LOL

I was both but I was an engineer first. I remember in an math analysis class, no mathematician could calculate a simple Fourier transform because they were first trying to determine whether it existed. That’s pretty much the difference: engineers prove existence through calculation, possibly wasting time because it can’t be done, whereas; mathematicians don’t waste time calculating things that can’t be done. They just waste time proving existence that could have been done through calculation.

Like my chem eng proffessor says. A scientist and a mathematician would spend weeks on one thing. While an engineer would have moved on to something more interesting.

I really love how everyone uses Dotson last name 😂

The formula on the whiteboard at the start is hilarious, nice touch!

I was studying the use of Laplace Transform in AC circuits for my Circuits and Systems course and it stated, "The inverse of Laplace Transform gives you the function itself. For now, we just assume that the statement is true since its proof is beyond the scope of this book". And I was like great!. This is something I love about engineering. You never bother about proving complex mathematical stuff.

I once solved an exam question, but I was off by a factor of 2. Couldn't find where that came from for the hell of me. Then I found a cool approximation: We know that n = n+1 for large values of n. Substituting 1 in that expression teaches us that 1 = 2 for large values of 1.

Are we seriously going to ignore this legendary Nintendo Mii lobby music?

As an engineering teacher, I can say that this fundamental theorem of engineering is glorious

I was a "pure mathematician" (well, math major, theoretical track) in Accounting 101. I completely disrespected that class, cut it all the time, the works. Got my ass handed to me on the first exam. Dropped the class with my tail between my legs. Folks, Accounting isn't Math. It's procedure. And if you don't respect it, it'll own you.

I know this is a joke on the competition between mathematicians and engineers, but a lot of this isn't true, in my experience. In my Engineering mathematics classes at University (aerospace systems engineering), we always had to understand the derivations of equations, and why they worked. Even in fluid mechanics modules, we had to be able to derive bernoullis equation from first principles in an exam. Not a very mathematical example I know. But engineering mathematics classes were basically pure maths, with barely any actual real world uses. The one area I remember using lookup tables was Control engineering, where we used lookup tables for Laplace transformations. We had separately, previously learned the maths in the engineering mathematics module, but you don't want to be fannying about with maths when you've got a complex system to model, when you can easier and quicker just move between domains using a table.

“Anyone else confused by *Andrew’s* question?” Lmfao you guys are like the 3 Musketeers

1:42 we do sometimes use convolution to get the value of that integral

Oh that "New Years' Resolutions" part got me 😆. Oh, you sweet summer child.

Meanwhile in programming: And now we make Pi equal to 3.14 as a double and go from there. lol

lol "here approximately equals equal well.... approximately

Way back in the mists of time, and across the ocean in England, I took a year of a math degree and then switched to engineering in my second year. This video is a perfect representation of my second year at university. A near constant anxiety attack.

Very odd question but where did you get that grey book case thingy from (the thing you held your books in and entered with at the start of the class) I have to know 😅

"Where does this equation come from?" >The textbook -Every math teacher I have ever had

Engineers are a special kind of people. Last day I found an old friend and we had the following dialogue: -It's been year since I don't see you mate. What are you up to? -Well, I'm in business engineering -That sounds cool, is it like economics or something like that? -iTs EnnGinEeeRinG!!!!!!!!!!! And he left, I'm still wondering what the fuck is business engineering.

"That's the bayesic idea of where we're headed" That's smart shit right there.

This is very true, love the vids.

"and by small, I mean equal to zero" LMFAO 😭😭

"Why be right when you can approximate" - every programmer when they notice 0.1 does not equal 0.1 thanking engineers

"Why be right when you can approximate" LOL Im dead!

The lab counting more towards your final grade than the exam is the most accurate part.

Wait, you can use LaTeX for spreadsheets? My whole life was a lie...

“That’s what we call proof by shut the hell up” I give this response 420/69 stars, which is exactly equal to 6.1 stars.

My entire goal after leaving chemical engineering & going on to higher math in graduate school was to spend 5 years in graduate schoo, return to bioengineering and become a Dr Frankenstein type of bioengineer. But, 33 years later, and I am still stuck on the math.

Yeah, i feel like thats only in certain countries, because i'm in Italy, and the professors here demand on nearly all the exams, the appropriat demonatration of various formulas, some times we pass like 2 hours just to get to that specific formula that we need

π²=g Laughed everytime I see that

You should do mathematician in a philosophy class next.

Engineer here. I love seeing the derivation of certain equations. Usually the ones that aren't clear as to how they are applied.

Somebody described it really well. "Mathematicians try to put everything into variables, applicable to any virtual situation but they don't have much concentration on a "real world" problem. Engineers work with a specific case to sole a specific problem, instead of virtualising everything for substitution."

"Is Anyone else confused by Andrew's Question?" Had me dying of laughter! Awesome work!

I switched from pure math to mech engineering and holy shit I thought these were just jokes but they are actually so true. Engineering math course is so dumbed down it's hilarious.

I've been taught about numerical integration and math people has a way to make simple things seems harder to comprehend. they made it seems so difficult it amazes me

4:42 IS LITERALLY SO FREAKING TRUE OVERLEAF MY LOVE

If you use Latex, Maple and Mathematica, you're a theorist. If you use Matlab and Latex, you're an experimentalist. If you use excel and word, you're a pleb.

4:40 I feel this so hard, I'm the only engineering student who regularly uses LaTeX on all my assignments 😅

I remember materials class. Every material has a 1D elastic modulus and a 3D bulk modulus. Changes in volume under pressure are as linear as changes in length under tension. The overuse of linear approx. was hilarious.

Great video! great idea for a collab, I liked the engineer in a maths class you were in as well 4:15 proof by shut the hell up ah yes, my RCL Analysis teacher's favorite phrase