The Greatest Mathematical technique-tell me

[lewis198]

Hey Guys, question:

In your opinion, what mathematical technique stretches the limit of human reasoning, or simply is the most fascinating?

 

[bit188]

I don't know about "techniques," but I've recently started into real analysis -- I find aleph numbers and the concepts of countability and uncountability to be fascinating.

 

[ice109]

literally? infinity

 

[mathwonk]

i like deformation theory, the differential calculus of moduli spaces. This often involves sheaf cohomology, another of my favorite tools.

I also like the tools of algebraic and differential topology. and galois theory is pretty brilliant, but I find it less generally useful.

the most useful, and hence important mathematical tools are almost universally agreed to be calculus and linear algebra, hence those are the ones "EVERYONE" should study.

 

[prasannapakkiam]

Well, in my oponion Equation theory is the basic and fundamental theory that nearly all of mathematics including Algebra, Calculus Trigonometry etc. This logic creates all of mathematics. So my say is that Equation Theory is by far the mist useful and important technique..

 

[Nancarrow]

Not so much a technique as a notation for me. Specifically, positional notation with zeroes, for representing numbers and doing basic arithmetic with them.

What do you get if you multiply XXXVII by LXIV? I don't know, and I'm sure as hell not going to find out!

Also as I've started learning about the foundations of maths (purely in my spare time, for my own enjoyment), I've been very impressed by the way that all those disparate bits of maths that I learned, can be given a common foundation in axiomatic set theory.

 

[matt grime]

An inquisitive mind is the most important tool a mathematician may possess.

 

[CRGreathouse]

Not so much a technique as a notation for me. Specifically, positional notation with zeroes, for representing numbers and doing basic arithmetic with them.

What do you get if you multiply XXXVII by LXIV? I don't know, and I'm sure as hell not going to find out!

Just make a doubling table!

LXIV      I
CXXVIII   II
CCLVI     IV
DXII      VIII
MXXIV     XVI
MMXLXIII  XXXII

LXIV      I

CCLVI     IV


MMXLXIII  XXXII

Collecting symbols, we get MMCCLXLXXVIVIIII. Simplifying, we have MMCCCXXIII.

Whew!

 

[Office_Shredder]

Let $$\epsilon > 0$$

 

[Invictious]

Not necessarily a technique, but calculus was what made me love math and now, we are happily married (we still get arguments when we get to logarithms and probability/permutations/combinatorics though)

Seriously, how did Newton do that? Creating something that made humanity advance so much further forwards, only with the mathematics available at that time?