<p>All Richard P. Feynman. (Posted here because he is, among other things, a Caltech icon.)</p>
<p>"The theoretical broadening which comes from having many humanities subjects on the campus is offset by the general dopiness of the people who study these things."</p>
<p>"You can know the name of a bird in all the languages of the world, but when you're finished, you'll know absolutely nothing whatever about the bird... So let's look at the bird and see what it's doing -- that's what counts. I learned very early the difference between knowing the name of something and knowing something."</p>
<p>"We cannot define anything precisely! If we attempt to, we get into that paralysis of thought that comes to philosophers, who sit opposite each other, one saying to the other, 'You don't know what you are talking about!' The second one says 'What do you mean by know? What do you mean by talking? What do you mean by you?', and so on."</p>
<p>"...far more marvelous is the truth than any artists of the past imagined it. Why do the poets of the present not speak of it? What men are poets who can speak of Jupiter if he were a man, but if he is an immense spinning sphere of methane and ammonia must be silent?"</p>
<p>"We cannot define anything precisely! If we attempt to, we get into that paralysis of thought that comes to philosophers, who sit opposite each other, one saying to the other, 'You don't know what you are talking about!' The second one says 'What do you mean by know? What do you mean by talking? What do you mean by you?', and so on."</p>
<p>Seems like he encounterd some typical skeptics.</p>
<p>: ). the analogy is flawed. most people would agree that sex is more enjoyable having tried both, but the same is probably not true of math and physics. less banally: to the extent that sex is deeper and more transcendent than more solitary activities, it is more like math than physics.</p>
<p>feynman, of course, meant only that physics is useful whereas math is fun with no purpose. but, much as they'd like to think otherwise, it is pretty improbable that physicists could have invented all the math they use.</p>
<p>"it is pretty improbable that physicists could have invented all the math they use."</p>
<p>Ben, I can hardly tolerate such an insult, regardless of how true it is.</p>
<p>I believe in physicists who can invent any math they want, and I resent your implication that they can't. In fact, I will have you know that I am a USWFI-certified wishful thinker; my beliefs are stronger and more deep-seated than 97.31% of the United States population (and we're talking a pretty competitive playing field here).</p>
<p>I like both math and physics..Though in math, I think mathmaticians' efforts are putting into too many useless things in the real world. For example, Many mathmaticians put their efforts into Fermat's last theory for 250 years until Wiles proved it. Goldbach's conjecture is still going on. But the sad thing is they are almost completely useless in real world. Actually they are trying to prove them either because they are curious about it or they want a reputation. It's not for entire human nor for the world development. That's why I like differential equation in math and I like physics more. They are more likely to be based on real world. Actually math is made up mostly by human, while physics is made up by God or nature and physicist try to find the facts in there.</p>
<p>one of the amazing things about math is that those "useless" facts discovered in the course of trying to prove Fermat's Last Theorem and Goldbach's conjecture are now absolutely key ingredients in the cryptography used by the NSA every day to send crucial military communications. How's that for relevance?</p>
<p>Nothing is more shocking than the way mathematical truths discovered for their own sake keep finding applications.</p>
<p>Think about this, also: most of the math used in "real" physics -- that is to say, in quantum mechanics, atomic theory, information theory, etc., was invented for "useless" purposes by mathematicians before physicists saw that these structures actually described something deep in the real world. The physicists probably never would have had these insights without the mathematical edifice that the mathematicians had built. </p>
<p>To say it again, and briefly: mathematicians built the conceptual structure we use to describe the physical world. Without knowing it!</p>
<p>This is a deep mystery -- how nature seemingly follows axiomatic mathematics that was discovered without reference to the natural world. How these useless theorems keep describing things we can touch and taste.</p>
<p>To say that math lives in its own useless world that doesn't apply to physics or other aspects of nature is just to say that you know fairly little yet of science :)</p>
<p>Of course Ben is right, but I'd like to point that actually figuring out which math to apply to various physical problems is hardly trivial. Really, that's <em>all</em> Einstein did in order to formulate general relativity.</p>