...from the same principles, I now demonstrate the frame of the System of the World.
Geometry enlightlens the intellect and sets one's mind right
Why do we believe that in all matters the odd numbers are more powerful?
The full beauty of the subject of generating functions emerges only from tuning in on both channels: the discrete and the continuous.
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.
Although I am not stupid, the mathematical side of my brain is like dumb notes upon a damaged piano.
[T]he different branches of Arithmetic - Ambition [G]eometry is not true, it is advantageous.
The object of mathematics is the honor of the human spirit.
Number was the substance of all things.
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.
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.
Yes, we now have to divide up our time like that, between politics and our equations. But to me our equations are far more important, for politics are only a matter of present concern. A mathematical equation stands forever.
Math is the only place where truth and beauty mean the same thing.
Mathematics is the queen of science, and arithmetic the queen of mathematics.
It is not certain that everything is uncertain.
Mathematics is the abstract key which turns the lock of the physical universe.
But in the new (math) approach, the important thing is to understand what you're doing, rather than to get the right answer.
We use only 10% of our brains... Imagine how smart we would be if we used the other 60%!
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.
Every new body of discovery is mathematical in form, because there is no other guidance we can have.
When things get too complicated, it sometimes makes sense to stop and wonder: Have I asked the right question?
So how does one go about proving something like this? It's not like being a lawyer, where the goal is to persuade other people; nor is it like a scientist testing a theory. This is a unique art form within the world of rational science. We are trying to craft a "poem of reason" that explains fully and clearly and satisfies the pickiest demands of logic, while at the same time giving us goosebumps.
Give me extension and motion and I will construct the universe.
... mathematics is absolutely necessary and useful to the other sciences.
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