The different systems such as the notation and the axiomatic systems are invented but the patterns and the logic which we used is discovered. The logic is already existent, we just have to discover how to apply that knowledge into different rules.

What is it in Math's that ensures 100% certainty 

There is not 100% certainty in mathematics since there is room for human error and there might be exceptions to these rules (anomalies). There is no 100% certainty in terms of human understanding rather than the already undiscovered mathematical principles.

We could rephrase this question to "to what extent is science a math's". Math is a science because all of the sciences are parts of math since math is required in all the different sciences hence, the sciences would not exist without math since they would not be able to describe any properties of the physical reality.

Pure mathematics tries to make proofs easier to understand in order to pave the way for humanity to understand more complex ideas, as it mainly studies abstract ideas.

In mathematics, the proof is completely absolute. Once there has been a rule/law established it isn't questioned since in order to prove that this part of mathematics works we are attempting to prove a theory rather than disproving your theories.

The golden ratio is a large part of the beauty of mathematics since it has inspired many artists to create different paintings using this mathematical principles. There is also human beauty in terms of symmetry since humans like the look of more symmetrical faces.

Intuition and imagination in mathematics helps us discover new rules and principles which further on answers the question of whether mathematics is invented and discovered.

Opened ended question. I don’t think you can find a direct answer. Maths is a language that describes natural laws. Would maths exist without consciousness? If there are no people would maths exist? 

What is it in Maths that ensures 100% certainty? 

Math is an exact science, but there are certain areas in math that do not really completely valid, such as theory of chaos. Math tries to identify those natural laws and describe them exactly

To what extent is Maths a science? 

Both you can have pure math, which is simply for the benefit of mathematics, but has no use in real life, so no scientific uses. Maybe in the future that pure math could be used for something. 

What is the value of pure mathematics? 

Too keep your brain active, to exercise it. 

How does proof in mathematics differ from proof in the natural sciences? 

No comment 

He does not really know how to prove it natural sciences...

What is the relation between mathematics and beauty? 

Math is everywhere even in music. Certain tones are better than the others, Number of petals in the flowers, math is everything...

E^(Pii) -1 = 0

beauty ratios, mathematical tones, tessellations, fibonacci 

What is the role of intuition and imagination in Mathematics?

To be a mathematician you need imagination, geometry needs it as there are different objects rotated in space. To discover something mathematicians had to do a leap of fate, to discover something with their imagination, The best example would be imaginary numbers or numbers you can square root with number 1. With the help of those imaginary numbers you can get concrete results. They are widely used in telescopes, etc. 

I think math was discovered because the laws that were invented were already there but it something that scientists discovered that proved the theory that was correct.

What is it in Math’s that ensures 100% certainty?
We use math that proves a hundred percent because scientific proof is what is commonly accepted in our time. This is because prior to our century no believed in evolution.

What is the value of pure mathematics?
“It gives us a way of describing everything that possibly exists. It gives structure. Without mathematics, science wouldn’t be able to do the things that it does” - Teacher

How does proof in mathematic differ from proof in the natural sciences?
We use math that proves a hundred percent because scientific proof is what is commonly accepted in our time. This is because prior to our century no believed in evolution. 

What is the relation between mathematics and beauty?
All art is mathematical such as Steph curry making a 3 pointer but do they know the fully know the math technique? However that doesn't mean the math is less beautiful.

What is the role of intuition and imagination in Mathematics?
I think imagination does have a role in mathematics which goes easier for some however its more practicing that allows people to be good in math. 

Depends if you’re talking about the processes of math or the language of math. The world seems to be organised but the language of math allows us to explore this organised world. 

 

No such thing as 100% certainty, better yet, mathematics seems to put on restraints on real life situations and capture uncertainty.

 

All science is based on math.

 

One might argue there is no value, since the answers to mathematical questions (which are usually solved through ‘pure mathematics’ = done in the absence of real world correlations) are usually not necessarily relevant.

 

Proof in natural sciences is usually inductive, and proof in math is usually deductive proof.

 

No right answer, since the answer is personal… Although examples could be Fibonacci, fractals, etc.

 

Much larger than people think it is. Intuition doesn’t necessarily exist, simply a recollection of facts. Imagination however is very important, since one is then able to ‘see’ certain outcomes of mathematical problems before an answer is provided.

 

 

I think math was discovered because the everyday mathematicians are finding links, and as students teachers always want us to find links.

What is it in Math’s that ensures 100% certainty?
Nowadays, we see maths as a logical way of thinking and is accepted nowadays. But in the past and prior to our century no even believed in evolution and that the world was round.

What is the value of pure mathematics?
“It gives us a way of describing everything that possibly exists. It gives structure. Without mathematics, science wouldn’t be able to do the things that it does” - My maths teacher

How does proof in mathematic differ from proof in the natural sciences?
Nowadays, we see maths as a logical way of thinking and is accepted nowadays. But in the past and prior to our century no even believed in evolution and that the world was round.

What is the relation between mathematics and beauty?
All art is mathematical as paintings and factors involving that is scale etc but David Beckham kicking free kicks is beautiful but they do not know the mathematical technique. Although, behind that there are angles and strategies, they do not know it is present however that doesn't mean the math is less beautiful.

What is the role of intuition and imagination in Mathematics?
I think intuition is a part of logic but imagination is even more important mathematics develops through links. Those are not possible without the human brain and using intuition, logic and our imagination.

I think math was discovered because the everyday mathematicians are finding links.

What is it in maths that ensures 100% certainty? 
Maths recently has been seen now as something logical. Before it used to be a evolution. It has believed that this has changed into logical thinking.

What is the value of pure mathematics? 
¨Mathematics is seen as giving structure to a different language of communications.¨

How does proof in mathematics differ from proof in the natural sciences? 
Proof is being able to find the answer to an mathematics equation. This will lead to having the correct answer proving that something is wrong.

What is the relation between mathematics and beauty?
Some people saying that getting the correct answer to a long equation is the beauty of maths.

What is the role of intuition and imagination in mathematics?
I believe that imagination is a key role in the art of mathematics due to its design of creating a new formula and to work on the knowledge of answering a question.