Ideas - Quotes
Having lots of ideas doesn`t mean you`re clever, any more than having lots of soldiers means you`re a good general.
In the development of mathematical ideas, one important initial driving force has always been to find mathematical structures that accurately mirror the behaviour of the physical world. But it is normally not possible to examine the physical world itself in such precise detail that appropriately clear-cut mathematical notions can be abstracted directly from it. Instead, progress is made because mathematical notions tend to have a "momentum" of their own that appears to spring almost entirely from within the subject itself. Mathematical ideas develop, and various kinds of problem seem to arise naturally.
If your private life conflicts with your intellectual opinion, it cancels your intellectual ideas, not your private life.
Most of the fundamental ideas of science are essentially simple, and may, as a rule, be expressed in a language comprehensible to everyone.
If you genuinely loved God, wouldn`t you want to understand him as best you can? When faced with different ideas about God, wouldn`t you want to ask some questions, and look at the supporting evidence for the different views, and try to figure out which one is probably true? Doesn`t it seem insulting to God to treat that question as if it didn`t matter? There are profound differences between religions. They are not trivial. And the different religions cannot all be right. (Although, as atheists like to point out, they can all be wrong.)
If a `religion` is defined to be a system of ideas that contains unprovable statements, then Gödel taught us that mathematics is not only a religion, it is the only religion that can prove itself to be one.
Don`t take your intuitions and ideas to be "natural": they are often the products of the ideas of audacious thinkers who came before us.
Great minds discuss ideas; average minds discuss events; small minds discuss people.
If an idea is not taken up and used as a solution to a problem it has no value. It becomes a non-idea. Lying in a drawer it is useless. Worse than useless, it’s a complete waste of space. Ideas have to be applied before they are recognized as good ideas. Even a bad idea executed Is better than a good idea undone. The longer it is used the better the idea is considered to be. That is why the wheel is reckoned to be the best idea ever.
Having too many ideas is not always a good thing. It’s too easy to move on to the next one, and the next one. If you don’t have many ideas, you have to make those you do have
work for you.
We all appreciate music, even if we can’t compose or perform it. Likewise, the ideas of science can be accessed and marveled at by everyone.
Having ideas is not the same thing as being creative. Creation is execution, not inspiration. Many people have ideas; few take the steps to make the thing they imagine.