What is 'beautiful about mathematics' (1 Viewer)

[Sy123]

Following on from this (which is an interesting read to say the least):

http://www.reddit.com/r/AskReddit/comments/1prbm7/mathematicians_of_reddit_what_is_beautiful_about/

What do you find beautiful about mathematics?


For me as a 'laymathstudent', I find things like infinite series and weird things in number theory quite beautiful, such as:





Or the fact that the probability of picking 2 coprime natural numbers is which is the reciprocal of the first series.....

Other things like the infinite series of e, alternating one of pi/4, and pi coming up in random places all the time such as how:

 

[anomalousdecay]

I find that the way Mathematics is interconnected into everything. God's ultimate language for the universe.

 

[Menomaths]

Maths is very interesting and beautiful!

 

[anomalousdecay]

inb4menomakeanomalousdecaysy123matics

 

[seanieg89]

Haha I commented on this reddit post earlier today.

For me it is because there is this unique duality between abstraction and applicability. From the pure perspective, we can list any collection of axioms we like, and study the perfect world governed by these axioms. Some might be more interesting than others, and some might not make much sense, but there is absolute freedom in our choice.
On the other hand, if we choose our axioms and definitions in a way that mirror concepts we have a vague intuitive grasp of from our human experiece (eg notions of distance leading to the axiomatisation of metric spaces), we can construct a system, a language, that is completely abstract (All we are doing is manipulating formal strings of symbols), yet tells us more about the world we live in.
In addition to this, ignoring applicability for now, these abstract symbols seem to take on a life of their own once we have defined them. There are so many results that seem almost magical, yet we can say exactly why they are true. This certainty, and the notion of rigorous proof is a large part of what has drawn me to pure mathematical research over any of the natural sciences.

(There are far more more eloquent responses on the reddit link, I highly recommend a read.)

Also, I highly recommend one of my favourite short interviews regarding this question: http://www.youtube.com/watch?v=dToui7IVwBY. (One of the greatest mathematicians of the last century, specialising in geometry.)

 

[seanieg89]

And to be more specific, one of the most marked examples of beauty in mathematics is the prime numbers. Here you have objects which you could define to an intelligent primary school kid, and yet there are questions about them that have been asked for THOUSANDS of years but not answered. (For example, can we write every even number that is at least 6 as the sum of two primes?).

That such a simple definition leads to such bizarre, seemingly random patterns is pretty amazing.

 

[rumbleroar]

I think its beautiful how everything is intertwined and it explains so much of our world...like damn complex number vectors just shapes together the basis of geometry rules and everything is clicking and its just so wonderful

and the logic
its just
mindblowing

 

[anomalousdecay]

I think its beautiful how everything is intertwined and it explains so much of our world...like damn complex number vectors just shapes together the basis of geometry rules and everything is clicking and its just so wonderful

and the logic
its just
mindblowing

Similar to me.

Anyone remember Spiral's quote:

"I wish I had a machine that could turn maths books into friends"

or something like that?

 

[Sy123]

The fact that you can think logically and it's structured is really what causes me to find maths beautiful. Also, I like how there's always a concrete answer compared to English where there are hundreds which I really don't like.

Its not just English either

Pretty much every discipline bar Mathematics, Logic and its derivatives (Computer Science and so on) are the only subjects where ambiguity is eliminated completely I think

Even with sciences, no matter how 'rigorous' we are in areas such as Physics, its always up to discrepancies and reformations, i.e. Quantum Physics vs Classical Physics. Who knows, maybe in 200 years everything we know in science will be debunked, but what makes Maths awesome is that it is true no matter where you live, what time you live, or what area of the universe you live, provided the same base axioms are kept.

 

[anomalousdecay]

Its not just English either

Pretty much every discipline bar Mathematics, Logic and its derivatives (Computer Science and so on) are the only subjects where ambiguity is eliminated completely I think

Even with sciences, no matter how 'rigorous' we are in areas such as Physics, its always up to discrepancies and reformations, i.e. Quantum Physics vs Classical Physics. Who knows, maybe in 200 years everything we know in science will be debunked, but what makes Maths awesome is that it is true no matter where you live, what time you live, or what area of the universe you live, provided the same base axioms are kept.

Yes. That's why I'm sticking to engineering.

 

[JT145]

Makematics
Menomaths
Memomaths
Menomatics
anomalousdecay
Sy123

 

[anomalousdecay]

Makematics
Menomaths
Memomaths
Menomatics
anomalousdecay
Sy123

Thank you for the compliment. By the way, join our menomaticmania.

But I must say you have forgotten some great mathematicians here: seanieg89, rumbleroar, hawkrider and yourself.

 

[JT145]

But I must say you have forgotten some great mathematicians here: seanieg89, rumbleroar, hawkrider and yourself.

you what

 

[Ikki]

3dtronics lol