Top 1002 Quotes & Sayings by Famous Mathematicians - Page 17

My father was the most rational and the most dispassionate of men.

Man has always learned from the past. After all, you can't learn history in reverse!

Self-love is always the mainspring, more or less concealed, of our actions; it is the wind which swells the sails, without which the ship could not go.

Eugene Wigner wrote a famous essay on the unreasonable effectiveness of mathematics in natural sciences. He meant physics, of course. There is only one thing which is more unreasonable than the unreasonable effectiveness of mathematics in physics, and this is the unreasonable ineffectiveness of mathematics in biology.

Namely, we have no right to believe a thing true because everybody says so unless there are good grounds for believing that some one person at least has the means of knowing what is true, and is speaking the truth so far as he knows it.

No weather forecaster can tell you for sure when to wear a rain slicker, stock up on canned goods, or evacuate a city that's in a cyclone's path. All forecasters can offer is their best guess at the atmosphere of the future, whispered by the simulated blue marble and wrapped up in uncertainty.

Pure mathematicians just love to try unsolved problems - they love a challenge.

The interaction between math and physics is a two-way process, with each of the two subjects drawing from and inspiring the other. At different times, one of them may take the lead in developing a particular idea, only to yield to the other subject as focus shifts. But altogether, the two interact in a virtuous circle of mutual influence.

A god whose creation is so imperfect that he must be continually adjusting it to make it work properly seems to me a god of relatively low order, hardly worthy of any worship.

There are three signs of senility. The first sign is that a man forgets his theorems. The second sign is that he forgets to zip up. The third sign is that he forgets to zip down.

Now ... the basic principle of modern mathematics is to achieve a complete fusion [of] 'geometric' and 'analytic' ideas.

Try a hard problem. You may not solve it, but you will prove something else.

It may be said that the conceptions of differential quotient and integral, which in their origin certainly go back to Archimedes, were introduced into science by the investigations of Kepler, Descartes, Cavalieri, Fermat and Wallis. . . .

Although the prime numbers are rigidly determined, they somehow feel like experimental data.

The infinite in mathematics is always unruly unless it is properly treated.

The first object of my endeavours was the means to become perfect and happy.

... mathematics is very much like poetry ... what makes a good poem -- a great poem -- is that there is a large amount of thought expressed in very few words. In this sense formulas like or are poems.

Mathematical Analysis is as extensive as nature herself.

Mathematics, however, is, as it were, its own explanation; this, although it may seem hard to accept, is nevertheless true, for the recognition that a fact is so is the cause upon which we base the proof.

Those arts which are, to be sure, not finite, as geometry and arithmetic, do not suffer adornment; others, contrarily, are rather subject to division and embellishment, such as astronomy and jurisprudence.

Mathematics is often defined as the science of space and number . . . it was not until the recent resonance of computers and mathematics that a more apt definition became fully evident: mathematics is the science of patterns.

I've learned to distinguish between the greatness of God and the inexcusable evil that has been done by those professing his name. And so I do not deduce [as Christopher Hitchens does] that God is not great, and that religion poisons everything. After all, if I failed to distinguish between the genius of Einstein and the abuse of his science to create weapons of mass destruction, I might be tempted to say science is not great, and technology poisons everything.

I like crossing the imaginary boundaries people set up between different fields - it's very refreshing.

Throughout his life Newton must have devoted at least as much attention to chemistry and theology as to mathematics.

We know the past but cannot control it. We control the future but cannot know it.

Civilization advances by extending the number of important operations which we can perform without thinking of them.

Men pass away, but their deeds abide. [His last words.]

Only dead mathematics can be taught where the attitude of competition prevails: living mathematics must always be a communal possession.

When the time is ripe for certain things, these things appear in different places in the manner of violets coming to light in the early spring.

For most problems found in mathematics textbooks, mathematical reasoning is quite useful. But how often do people find textbook problems in real life? At work or in daily life, factors other than strict reasoning are often more important. Sometimes intuition and instinct provide better guides; sometimes computer simulations are more convenient or more reliable; sometimes rules of thumb or back-of-the-envelope estimates are all that is needed.

I know how to control the Universe. Why would I run to get a million, tell me?

No Victor, you got it backwards, you should evaluate these integrals non-rigorously if you can, and rigorously if you must.

But 'the physical level of rigor' is higher on certainty than the logical one, since reproducible experiments are more reliable than anybody's, be it Hilbert's, Einstein's or Gödel's intuition.

It wasn't until my second year that I got to actually work with Church.

Bombieri's Law: of Finance: Profits are on paper, losses are in cash

How did Biot arrive at the partial differential equation? [the heat conduction equation] . . . Perhaps Laplace gave Biot the equation and left him to sink or swim for a few years in trying to derive it. That would have been merely an instance of the way great mathematicians since the very beginnings of mathematical research have effortlessly maintained their superiority over ordinary mortals.

The idea that information can be stored in a changing world without an overwhelming depreciation of its value is false. It is scarcely less false than the more plausible claim that after a war we may take our existing weapons, fill their barrels with information.

I find it fascinating that you can look at the same problem from different perspectives and approach it using different methods.

There is one place left in which open racism can be practiced institutionally in the U.S. today, that is through this diversity/equity movement, in which it appears to be that you can be openly anti-white, openly anti-straight, openly anti-male, and this is considered progressive.

The topdog may win the game of force. But not the moral issue - and when that dawns upon him and his allies, change of consciousness sets in, and demoralization starts thawing the frozen heart. The game is over.

However impenetrable it seems, if you don't try it, then you can never do it.

Algebra is but written geometry and geometry is but figured algebra.