Richard Jernigan -> RE: Learn everything (Dec. 20 2011 9:13:03)
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ORIGINAL: Deniz Other than that i agree what you wrote, and also with Richard, though i have to say that this method Moore had, is something that is practiced among alot of professors. Normally, here in Germany you have lectures and practicing courses. Often the lectures are mandatory, the practicing courses are obligatory. I'm still failing to make myself clear. In Moore's method, the students are absolutely on their own, except for the sequence of axioms, definitions, theorems to prove and problems to solve that were presented by Moore. There is no lecture. None. Zip. Nada. Students may not collaborate. I repeat, the students are absolutely on their own, no lecture, no reading. Reading is almost unerringly detectable. When students must come up with their own proofs of important theorems and solutions to challenging problems, they are remarkably original. They almost never look like the ones in books. For a different prof who used Moore's method, I wrote a term paper giving an existence proof for Fredholm integral equations, one of the fundamental mathematical results used in quantum mechanics. The paper was about 12 pages. It took at least six weeks of almost daily struggle to come up with the ideas that led to the proof. In Courant and Hilbert the same work takes about a page and a half. My prof said the proof was valid, only six students had given a proof in more than 20 years, but he had never seen one remotely like mine. He asked how I came up with it. In a couple of hour-long sessions in his office, I tried to explain the multi-dimensional geometric analogy that motivated the proof. The professor, a grand-student of Hilbert, a noted research mathematician and a former member of the Institute for Advanced Study, just shook his head and said he wasn't sure he followed my intuitive motivation, though the proof itself was clear. I'm by no means anywhere remotely near the front rank of research mathematicians. My originality was a routine occurrence. After the course my prof gave me an autographed copy of the two weighty volumes of Courant and Hilbert's "Methods of Mathematical Physics." He said he thought some of Hilbert's students wasted too much time polishing up short and elegant proofs. He was a gentle and kind hearted man. What was the point? Though my path was far more crooked than Courant and Hilbert's, I learned a hell of a lot wandering in the mathematical wilderness. I stumbled down some very informative paths that happened not to lead to my destination. I had a further six weeks of experience criticizing my ideas, recognizing errors of logic and returning to the fray. And I gained a significant amount of self-confidence through single-handedly winning a battle where few others had succeeded. It was an experience I shared with hundreds of others throughout the middle half of the twentieth century, a few of whom went on to advance the frontiers of mathematics. Moore's method was and is utterly radical in putting the students entirely on their own. It is probably impractical for a discipline like physics or chemistry where experimental results and experimental experience are necessary, though I know a few physicists who have used a modified form of Moore's paradigm. But for mathematics it produced a body of 50 PhDs by Moore, and around 70 by his collaborators. About half of these students, along with Moore himself dominated research in topology and analysis throughout the last 75 years of the 20th century in America and elsewhere...a couple of them my good friends. Moore was not just a teacher, though he taught two undergraduate courses including freshman calculus, and three graduate courses every year until he retired at age 83. He was a prolific and highly influential research mathematician, strongly active up into his late seventies. He was vice president and president of the American Mathematical Society. He wrote one of the Society's distinguished Colloquium Publications, and revised and brought it up to date in his late seventies. He gave the invited Colloquium Address, a high honor for an American mathematician. He was a member of the National Academy of Sciences. He was also a difficult, demanding and dictatorial personality. I never really became friends with him like I did some of my professors. Mary Ellen Estill Rudin, one of Moore's distinguished students, said she would never send one of her children to Moore for fear he would damage them. But I admired him for his accomplishments, and I'm grateful for the significant role he played in making me a self reliant and persistent solver of scientific, technological and managerial problems. University was good for me... ..and I am still the only graduate of the University of Texas at Austin to be both a member of Phi Beta Kappa (an academic honorary fraternity dating back to the 18th century) and to have three consecutive semesters on scholastic probation for making only A's and F's. You see, I was distracted....but that's another story. RNJ
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