Mathematics deals exclusively with the relations of concepts to each other without consideration of their relation to experience.
Interpretation
Mathematics is a study of abstract concepts and their relationships, independent of real-world applications.
In this quote, Albert Einstein emphasizes that mathematics is fundamentally about the relationships and structures formed by concepts, rather than being tied to practical experiences or empirical evidence. This suggests that the essence of mathematics lies in its own internal logic and reasoning, which can exist independently of the physical world.
In practice
In a lecture about the importance of mathematics in theoretical physics.
I cannot then believe in this concept of an anthropomorphic God who has the powers of interfering with these natural laws. As I said before, the most beautiful and most profound religious emotion that we can experience is the sensation of the mystical. And this mysticality is the power of all true science.
If I would follow your advice and Jesus could perceive it, he, as a Jewish teacher, surely would not approve of such behavior.
I want to know all Gods thoughts; all the rest are just details.
In the middle of adversity there is great opportunity.
I do not believe that civilization will be wiped out in a war fought with the atomic bomb. Perhaps two-thirds of the people of the earth will be killed.
To me the worst thing seems to be a school principally to work with methods of fear, force and artificial authority. Such treatment destroys the sound sentiments, the sincerity and the self-confidence of pupils and produces a subservient subject.
One can think of any given axiom system as being like a computer with a certain limited amount of memory or processing power. One could switch to a computer with even more storage, but no matter how large an amount of storage space the computer has, there will still exist some tasks that are beyond its ability.
The brain is the most complicated organ in the universe. We have learned a lot about other human organs. We know how the heart pumps and how the kidney does what it does. To a certain degree, we have read the letters of the human genome. But the brain has 100 billion neurons. Each one of those has about 10,000 connections.
During the century after Newton, it was still possible for a man of unusual attainments to master all fields of scientific knowledge. But by 1800, this had become entirely impracticable.
It is generally believed that our science is empirical and that we draw our concepts and our mathematical constructs from the empirical data. If this were the whole truth, we should, when entering into a new field, introduce only such quantities as can directly be observed, and formulate natural laws only by means of these quantities.
As mechanistic biologists, we are hoping that by understanding how the virus works at the molecular level, we will be able to predict with more accuracy how it will evolve.
The history of the universe is, in effect, a huge and ongoing quantum computation. The universe is a quantum computer.
Subscribe for the occasional hand-picked quote. No noise.