[T]he different branches of Arithmetic - Ambition [G]eometry is not true, it is advantageous.
Logic doesn't apply to the real world.
...from the same principles, I now demonstrate the frame of the System of the World.
In any case, do you really think kids even want something that is relevant to their daily lives? You think something practical like compound interest is going to get them excited? People enjoy fantasy, and that is just what mathematics can provide - a relief from daily life, an anodyne to the practical workaday world.
...a consistency proof for [any] system ... can be carried out only by means of modes of inference that are not formalized in the system ... itself.
Why do we believe that in all matters the odd numbers are more powerful?
Mathematics is a body of knowledge, but it contains no truths.
Number was the substance of all things.
The question you raise, 'How can such a formulation lead to computations?' doesn't bother me in the least! Throughout my whole life as a mathematician, the possibility of making explicit, elegant computations has always come out by itself, as a byproduct of a thorough conceptual understanding of what was going on. Thus I never bothered about whether what would come out would be suitable for this or that, but just tried to understand - and it always turned out that understanding was all that mattered.
Science is what we understand well enough to explain to a computer. Art is everything else we do.
No human investigation can be called real science if it cannot be demonstrated mathematically.
I had a feeling once about mathematics - that I saw it all... but it was after dinner and I let it go.
There are two ways to do great mathematics. The first is to be smarter than everybody else. The second way is to be stupider than everybody else - but persistent.
Mathematics is the queen of science, and arithmetic the queen of mathematics.
It is not certain that everything is uncertain.
Math is the only place where truth and beauty mean the same thing.
Mathematics is the abstract key which turns the lock of the physical universe.
If anyone tells you it's impossible to be fabulous and smart and make a ton of money using math, well, they can just get in line behind you - and kiss your math.
We use only 10% of our brains... Imagine how smart we would be if we used the other 60%!
But in the new (math) approach, the important thing is to understand what you're doing, rather than to get the right answer.
The mathematician is entirely free, within the limits of the imagination, to construct what worlds he pleases.
There is nothing strange in the circle being the origin of any and every marvel.
I think, therefore I laugh.
... mathematics is absolutely necessary and useful to the other sciences.
Every new body of discovery is mathematical in form, because there is no other guidance we can have.
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