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Blog on Wordpress containing related math links: Shadows of Simplicity
Go forward, faith will follow. -- d'Alembert
Mathematics compares the most diverse phenomena and discovers the secret analogies that unite them. -- Jean Baptiste Joseph Fourier (1768–1830)
Mathematics/physics is "imagination in a straitjacket." -- to borrow from Feynman
It is not possible to be a mathematician without being a poet at heart. -- Sophia Kovalevskaya (1850--1891)
A romance of many dimensions. -- Edwin Abbott (on loan as an apt description in general of the play of mathematicians whose inner-child has not been extinguished)
The most exciting and significant moments in mathematics occur when we discover that seemingly unrelated phenomena are shadows cast by the same beast. -- Terry Gannon (from Moonshine Beyond the Monster)
“Should you just be an algebraist or a geometer?” is like saying “Would you rather be deaf or blind?” — M. Atiyah
Education lights a fire. -- Yulia Zdanovska (Mathematician/teacher, died at age 21 in RU shelling in Kharkiv, Ukraine, while distributing aid. This was on her t-shirt from Yeats: “Education is not the filling of a pail, but the lighting of a fire.”)
Caveat emptor: As explicitly stated by one moderator to me, the number of likes is an indication of appreciation rather than necessarily the validity of a comment or answer. This perhaps accounts for the fact that sometimes responses on MO by Fields medalists (all wonderful contributors) that are disputable subjective claims or patently, objectively wrong have been highly upvoted. Thoroughly check everything that you may need to use (no self-exemption warranted) and don't take opinions here too seriously--blurting, politicking, and the full spectrum of personality traits, good and bad, can be found here as well as in pretty much any large group of people. As always, encourage the facilitators and discourage the obstructionists.
The best approach to mathematics or pretty much anything for which you have a passion: practice, continually develop a repertoire of moves, and enjoy sharing and interacting with the right people--always in motion.
Meditations by William Thurston on mathematics that resonates with me.
The mathematicians that rub me the wrong way suffer from Linnean inanity--"Oh, that's just a member of the animal kingdom." Just a group, just a category--a level of abstraction that bleeds all the spice of life from a topic.