The efficient use of plausible reasoning is a practical skill and it is learned… by imitation and practice.
Mathematics succeeds in dealing with tangible reality by being conceptual. We cannot cope with the full physical complexity; we must idealize.
Mathematics is the cheapest science. Unlike physics or chemistry, it does not require any expensive equipment. All one needs for mathematics is a pencil and paper.
Возможно, не существует открытий ни в элементарной, ни в высшей математике, ни даже, пожалуй, в любой другой области, которые могли бы быть сделаны… без аналогии.
Anything new that we learn about the world involves plausible reasoning