What is the point of higher mathematics if very few can understand it?

Question

I've been out of school for 2 years now and found out that many of my math major friends have gone into teaching. The very few who went on to doctorate programs dropped out due to academic and research difficulties. I have an idea of what they went through -abstract formalism and proof writing over fields and ring theory and real analysis, all of which have zero applications

Answer 1

What's the purpose of this cupcake in front of me, if I'm the only one who can eat it?



Seriously, it's about ideas. They always seem distant and esoteric at first, but they often eventually find links to other parts of mathematics, and *their* ideas.



Case in point: Fermat's last theorem.

It's an algebraic problem in integers, that any junior-high algebra student can understand, but that a parade of great mathematicians over the course of 2+ centuries failed to resolve.

In the end, the proof was achieved using the seemingly totally irrelevant field of elliptic curves.



And what real-world application has Fermat's last theorem got? None.

So far.

But it's interesting to a lot more people than can understand the proof.



When it was being developed in the early-to-mid 19th century, non-Euclidean geometry seemed about as removed from reality as you could get. But when Einstein had an idea for a theory of gravitation that would be compatible with his special relativity, it sure came in handy!



How many understand Riemann tensors and Christoffel symbols? Not many. But these things are essential in the advancement of some very important fields of science, as we saw last Thursday, with the announcement of the first detection of gravitational radiation.



If Gauss, Riemann, and Lobachevsky hadn't pioneered that field of mathematics, Einstein wouldn't have had the basis needed for the theory of gravitation we know as General Relativity; and that team of scientists wouldn't have thought to build a device that could now open a new window on the universe, and some of its most exotic behavior.

Answer 2

You typed your question on a machine built by people who understood those higher mathematics. They're the people who wrote the algorithms that are encrypting your wifi connection, doing the data processing when you play a blu-ray, or shoving millions of tessellated polygons onto the screen when you're playing a videogame.



Almost every aspect of our modern lives is built upon higher mathematics. Your phone is calculating your position based on complex maths involved in GPS. When you adjust your photos, you're applying complex matrix calculations or Fourier Transforms. When you have a product delivered to you, the carrier might well have applied complex algorithms to route the vans in such a way as to minimise delivery times and fuel costs. When you buy something, the factory that manufactured it could well be running complex control systems to maximise yield, minimise materials, and minimise costs.



The point is, our society is great at hiding the complexity that lies behind it. But that complexity exists and without it, our modern society couldn't function.

Answer 3

I am also experiencing that difficulty, because I am now studying modern geometry as a secondary teacher courser in mathematics. However, my teacher in that subject told us it is good to study higher mathematics because there are questions which concern the validity of theorems in fundamental maths but require knowledge of higher maths in order to be answered satisfactorily. Examples would include fundamental theorem of algebra and the reason why there are no general formulas involving radicals for solving polynomial equatons of degree five or beyond. It could also spark the interest of some students to pursue a mathematics degree in higher education and they would become professionals in engineering or other applied aspects of maths, or they could also become future math teachers themselves.

Answer 4

Mathematics is used extensively throughout the world.

It is used in:-

Electrical Engineering

Electronics

Mechanical Engineering

Civil Engineering

Chemical Engineering

Physics

Finance and Insurance

to name a few.

Answer 5

What has zero application today will be a hot topic of tomorrow. Gravity waves might be an example of that. Who would have thought these things could actually be detected?



How about string theory? You think anyone cared decades ago? I doubt it. Of course I would admit in a 1/2 life second that you know much more about this than I do -- much much more. But not everything we study does have immediate applications. It's sort of like Field of Dreams: if you think it, they will come.

Answer 6

Much of mathematics beyond algebra and trigonometry is impractical and useless, except to get a degree. Foreign language is also a waste of time and money. A college student might waste a semester and $10,000 learning French and never meet anyone who speaks French.

Answer 7

Nobody is forced to take higher mathematics. If you don't like it, do something else. There are many subjects which I do not understand and have zero interest in, but that does not mean they should be scrapped just to please me.

Answer 8

I like math just for fun of it as you are correct as most of it useless but I am okay with it as math should never have a purpose but just form of enlightenment as Indiana Jones Sr just want wanted to find the Holy Grail just for

enlightenment. As a math major I just wanted knowledge as that is all I am looking for as may never use it but their an enjoyment.

Answer 9

Very few can understand it - that's the point.

Answer 10

Some of it seems useless except when you try to shoot a satellite to Pluto and beyond.

Answer 11

that IS the point



they dont want idiots trying to study it wasting everybody elses time

Answer 12

I don't believe you troll.