26 MAR 2013 by ideonexus
Mathematics Lies Outside Ourselves
I believe that mathematical reality lies outside us, that our
function is to discover or observe it, and that the theorems which we
prove, and which we describe grandiloquently as our "creations," are
simply the notes of our observations.
* * *
Let us suppose that I am giving a lecture on some system of
geometry, such as the ordinary Euclidean geometry, and that I draw figures
on the blackboard to stimulate the imagination of my audience, rough
drawings of straight lines or ... 1 
notes
notesWhen teaching mathematics, it does not matter how nice the drawings or the teaching space, the ideas are what's important and they are independent of the teaching method.
26 APR 2012 by ideonexus
Science Cannot have Creeds
Religious creeds are a great obstacle to any full sympathy between the outlook of the scientist and the outlook which religion is so often supposed to require ... The spirit of seeking which animates us refuses to regard any kind of creed as its goal. It would be a shock to come across a university where it was the practice of the students to recite adherence to Newton's laws of motion, to Maxwell's equations and to the electromagnetic theory of light. We should not deplore it the less if our...
1 
1 We should not force students to blindly recite laws and theorems because that would reduce it to religion.
31 JAN 2012 by ideonexus
Courses That Appealed to Steven Chu
I approached the bulk of my schoolwork as a chore rather than an intellectual adventure. The tedium was relieved by a few courses that seem to be qualitatively different. Geometry was the first exciting course I remember. Instead of memorizing facts, we were asked to think in clear, logical steps. Beginning from a few intuitive postulates, far reaching consequences could be derived, and I took immediately to the sport of proving theorems.Folksonomies: education
Folksonomies: education
1 notes
notesHe enjoyed Geometry for the process rather than the boring memorization of facts.
16 DEC 2011 by ideonexus
The Temperament of the Mathematician
It may be observed of mathematicians that they only meddle with such things as are certain, passing by those that are doubtful and unknown. They profess not to know all things, neither do they affect to speak of all things. What they know to be true, and can make good by invincible arguments, that they publish and insert among their theorems. Of other things they are silent and pass no judgment at all, chusing [choosing] rather to acknowledge their ignorance, than affirm anything rashly. They...Folksonomies: mathematics
Folksonomies: mathematics
1 notes
notesAlways to acknowledge their ignorance and only indulge in those pursuits in which total certainty may be achieved.
19 MAY 2011 by ideonexus
Conjecture versus Theorem
Mathematicians use the idea of proof to make a distinction between a 'conjecture' and a
'theorem', which bears a superficial resemblance to the OED's distinction between the two senses of
'theory'. A conjecture is a proposition that looks true but has never been proved. It will become a
theorem when it has been proved. A famous example is the Goldbach Conjecture, which states that
any even integer can be expressed as the sum of two primes. Mathematicians have failed to
disprove it for all eve... 1 notes
notesin mathematics and how it applies to scientific "theory".
