In order to solve this differential equation you look at it until a solution occurs to you.
The mathematical sciences particularly exhibit order symmetry and limitations; and these are the greatest forms of the beautiful.
It seems that if one is working from the point of view of getting beauty in one's equations, and if one has really a sound insight, one is on a sure line of progress.
It is more important to have beauty in one's equations than to have them fit experiment... It seems that if one is working from the point of view of getting beauty in one's equations, and if one has really a sound insight, one is on a sure line of progress. If there is not complete agreement between the results of one's work and experiment, one should not allow oneself to be too discouraged, because the discrepancy may well be due to minor features that are not properly taken into account and that will get cleared up with further developments of the theory.
One nonabsolute number is the given time of arrival, which is now known to be one of the most bizarre of mathematical concepts, a number whose existence can only be defined as being anything other than itself. In other words, the given time of arrival is the one moment of time at which it is impossible that any member of the party will arrive.
The laws of nature are but the mathematical thoughts of God.
I think it is a peculiarity of myself that I like to play about with equations, just looking for beautiful mathematical relations which maybe don't have any physical meaning at all. Sometimes they do. At age 60.
Today's scientists have substituted mathematics for experiments, and they wander off through equation after equation, and eventually build a structure which has no relation to reality.
The fundamental laws necessary for the mathematical treatment of a large part of physics and the whole of chemistry are thus completely known, and the difficulty lies only in the fact that application of these laws leads to equations that are too complex to be solved.
The universe is governed by science. But science tells us that we can't solve the equations, directly in the abstract.
I regard it in fact as the great advantage of the mathematical technique that it allows us to describe, by means of algebraic equations, the general character of a pattern even where we are ignorant of the numerical values which will determine its particular manifestation.
If others would but reflect on mathematical truths as deeply and as continuously as I have, they would make my discoveries.
It is more important to have beauty in one's equations than to have them fit experiment.
A good deal of my research in physics has consisted in not setting out to solve some particular problem, but simply examining mathematical equations of a kind that physicists use and trying to fit them together in an interesting way, regardless of any application that the work may have. It is simply a search for pretty mathematics. It may turn out later to have an application. Then one has good luck. At age 78.
The world looks like a multiplication-table, or a mathematical equation, which, turn it how you will, balances itself.
My intention here is to make it clear that not a single cell of my composition, here in regard to The Raven, is found by chance or intuition, that the composition moved towards perfection with the precision and inevitability of a mathematical equation.
It [the depression] was not accidental. It was a carefully contrived occurrence worked out as one works out a mathematical equation. The international bankers sought to bring about a condition of despair here so that they might emerge as the rulers of us all.
Under the federal reserve act, panics are scientifically created. The present panic is the first scientifically created one, worked out as we figured, a mathematical equation.
The thing that got me started on the science that I've been building now for about 20 years or so was the question of okay, if mathematical equations can't make progress in understanding complex phenomena in the natural world, how might we make progress?
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.
or simply:
