What is the greatest contribution of the subject of Mathematics? What are the most beneficial branches and how have we benefited?

The greatest contribution of Mathematics is that we have an objective way to understand much of our world.

I hope you are not asking this for your homework.

@zenvelo

Careful.

This is purely for discussion purposes as I felt it would bring about good conversation. Besides that, what course would ask such a question for homework?

I dunno, how about the concept of zero?

“The introduction of numbers as coordinates is an act of violence.” – Hermann Weyl

I’m pretty sure Weyl would have thought singling out one branch from the unity of mathematics and calling it the greatest would be an “act of violence” as well. ;)

Lemme quote the man again:
“The question of the ultimate foundations and the ultimate meaning of mathematics remains open; we do not know in what direction it will find its final solution or even whether a final objective answer can be expected at all. ‘Mathematizing’ may well be a creative activity of man, like language or music, of primary originality, whose historical decisions defy complete objective rationalization.”

Answering a question in mathematics usually brings up several new questions. It has always enticed those who practice it in the “pure” (non-applied, theoretical or absolute) sense to keep forging ahead. Time and again, physicists have found models in pure mathematics waiting for them, as-if ideally tailored – often a century or more in advance – for application to their problems. As eminent a figure in that field as Eugene Wigner thought that this was ‘unreasonable’.

Mathematics helps us
understand the solar system
is a universal language
let’s us plot land for ownershop
analyze data related medicine, marketing, etc., etc.
predict outcomes
it’s endless
I mean practically everything is intertwined with math.

The greatest contribution? I’ll say using it for medical science if I have to choose one, but I hate to choose only one.

All of technology uses mathematics, whether it is a car, radio, rocket or toaster. As @hiphiphopflipflapflop pointed out, the physicist Eugene Wigner spoke of the unreasonable effectiveness of mathematics. Mathematics is more than just numbers, but think of all the things that can be measured using numbers. We use them to count, find probabilities, and measure length, time, mass and electrical charge. Why should numbers be applicable to all these things?

My vote for most useful branch of math would be analysis, which includes calculus. I don’t think there is a branch of mathematics that does not have some practical use. The mathematician George Hardy took pride in saying that his area of expertise, number theory (the study of whole numbers), had no practical application. He has been proven wrong on this. There are several uses, notably public key encryption.

Apart from its practical uses, mathematics can stand on its own and, for those of us who appreciate it, can be quite beautiful.

No math. No enlightenment. No prediction of solar eclipses. No replacement of superstition with reason.

No math. No quantum physics. No transistor. No computer. No web browser. No Fluther.

No math. No good weather forecast. No tornado watches. No hurricane evacuations.