Blackboard Technique Two points. Make sure the blackboard is spotless. It is particularly important to erase those distracting whirls that are left when we run the eraser over the blackboard in a nonuniform fashion. By starting with a spotless blackboard you will subtly convey the impression that the lecture they are about to hear is equally spotless. Start writing on the top left-hand corner. What we write on the blackboard should correspond to what we want an attentive listener to take down in his notebook.
It is preferable to write slowly and in a large handwriting, with no abbreviations. Those members of the audience who are taking notes are doing us a favor, and it is up to us to help them with their copying. When slides are used instead of the blackboard, the speaker should spend some time explaining each slide, preferably by adding sentences that are inessential, repetitive, or superfluous, so as to allow any member of the audience time to copy our slide.
We all fall prey to the illusion that a listener will find the time to read the copy of the slides we hand them after the lecture. This is wishful thinking. I bought a copy of Frederick Riesz's Collected Papers as soon as the big, thick, heavy, oversize volume was published. However, as I began to leaf through, I could not help but notice that the pages were extra thick, almost like cardboard. Strangely, each of Riesz's publications had been reset in exceptionally large type. I was fond of Riesz's papers, which were invariably beautifully written and gave the reader a feeling of definitiveness.
As I looked through his Collected Papers , however, another picture emerged. The editors had gone out of their way to publish every little scrap Riesz had ever published. It was clear that Riesz's publications were few. What is more surprising is that the papers had been published several times.
Riesz would publish the first rough version of an idea in some obscure Hungarian journal. A few years later he would send a series of notes to the French Academy's Comptes Rendus in which the same material was further elaborated. A few more years would pass, and he would publish the definitive paper, either in French or in English.
Adam Koranyi, who took courses with Frederick Riesz, told me that Riesz would lecture on the same subject year after year while meditating on the definitive version to be written. No wonder the final version was perfect. Riesz's example is worth following. The mathematical community is split into small groups, each one with its own customs, notation, and terminology.
It may soon be indispensable to present the same result in several versions, each one accessible to a specific group; the price one might have to pay otherwise is to have our work rediscovered by someone who uses a different language and notation and who will rightly claim it as his own. When we think of Hilbert, we think of a few of his great theorems, like his basis theorem.
But Hilbert's name is more often remembered for his work in number theory, his Zahlbericht , his book Foundations of Geometry , and for his text on integral equations. Hilbert's textbook on integral equations is in large part expository, leaning on the work of Hellinger and several other mathematicians whose names are now forgotten. Similarly, Hilbert's Foundations of Geometry , the book that made Hilbert's name a household word among mathematicians, contains little original work and reaps the harvest of the work of several geometers, such as Kohn, Schur not the Schur you have heard of , Wiener another Wiener , Pasch, Pieri, and several other Italians.
Again, Hilbert's Zahlbericht , a fundamental contribution that revolutionized the field of number theory, was originally a survey that Hilbert was commissioned to write for publication in the Bulletin of the German Mathematical Society. William Feller is another example. Feller is remembered as the author of the most successful treatise on probability ever written. Few probabilists of our day are able to cite more than a couple of Feller's research papers; most mathematicians are not even aware that Feller had a previous life in convex geometry.
Allow me to digress with a personal reminiscence. I sometimes publish in a branch of philosophy called phenomenology. After publishing my first paper in this subject, I felt deeply hurt when, at a meeting of the Society for Phenomenology and Existential Philosophy, I was rudely told in no uncertain terms that everything I wrote in my paper was well known. This scenario occurred more than once, and I was eventually forced to reconsider my publishing standards in phenomenology.
It so happens that the fundamental treatises of phenomenology are written in thick, heavy, philosophical German. Tradition demands that no examples ever be given of what one is talking about. One day I decided, not without serious misgivings, to publish a paper that was essentially an updating of some paragraphs from a book by Edmund Husserl, with a few examples added.
Gian-Carlo Rota Quotes
While I was waiting for the worst at the next meeting of the Society for Phenomenology and Existential Philosophy, a prominent phenomenologist rushed towards me with a smile on his face. He was full of praise for my paper, and he strongly encouraged me to further develop the novel and original ideas presented in it. What the number theorist did not realize is that other mathematicians, even the very best, also rely on a few tricks which they use over and over.
Take Hilbert. What he is great at is exposing the "human" side of math and research in general.
The usual histories typically present researchers as perfect abstract beings marching in a linear order from one success to another, all the while harmoniously developing their theories in a glorious show of unity and cooperation. Rota cuts through all that BS and shows how math like any other human activity is influenced by rivalries, fads, fashions, jealousy, pettiness and just plain normal human messiness.
The descriptions of Emil Artin and William Feller of probability fame are also pretty interesting. The large chapter on "Mathematical Gossip" is interesting as it clearly describes how ideas tend to be discovered and forgotten, only to be rediscovered anew by each generation.
Swipe to navigate through the chapters of this book
Are we doomed to basically rediscover the same ideas over and over and over? He makes a great point that the way math is taught is very different from the way it is practiced and that the axiomatic presentation favored by many researchers when writing text books is not necessarily the most effective. Basically: Yes, rigorous proof is necessary as a check to our intuition but its not really the whole story.
To the extent that I can form an opinion on the matter being a simple CS code monkey and all : I find myself very sympathetic to his views. Jan 30, Giorgio rated it it was amazing Shelves: Interesting view on phenomenology, a good explaination of the concept of Fundierung, Husserl. Nice tips for mathematicians such as: treat Engegneeejkfkfjckd as people. Well described biography of Stanislaw Ulam's life and works. Aug 30, Joseph Carrabis rated it it was amazing.
Mircea Pitici, ed. The Best Writing on Mathematics | Philosophia Mathematica | Oxford Academic
Indiscrete Thoughts is a must read for those of us who have modern day mathematical heros. It makes them human and accessible, something all heros should remember when meeting those who put them on pedestals. One of the most important books for any aspiring mathematician, philosopher, or phenomenologist to read. Oct 07, Name rated it it was amazing. If there's anything a Mathematician likes to engage in it's academic gossip, and Rota delivers.
The first few chapters he bares all on some of the great figures in Mathematics, commenting that just because someone is revered as a researcher we should not assume that they were good men. He lays out bigotry, psychosis, and all the flaws of mortal men. An incredibly honest review. He presents some incites in later chapters about his career and his research. He leaves us with not a few bits of wisdo If there's anything a Mathematician likes to engage in it's academic gossip, and Rota delivers.
He leaves us with not a few bits of wisdom in hopes we might become better Mathematicians and perhaps better people. My favorite bit of advice is from a particularly obtuse lecture he attended at MIT where at the end Professor Struik asked, "Give us something to take home!
I have incorporated this pedagogical technique into all of my talks where I am sure to sum up my main points in simple, not simpler, terms so that the listener can always walk away with concrete ideas in their head instead of a jumble of notes.
Even for the non-mathematician this is an entertaining account of academia from an observant and open mind. We could all do well to integrate some of the simple wisdoms displayed by Rota in his writings.
Gian-Carlo Rota – Ten Lessons I Wish I Had Been Taught
Feb 15, Aneel rated it liked it. Rota was my favorite professor. This is a collection of fairly random writings of his. There are short biographies of mathematicians that Rota knew, some writings on Phenomenology that are well beyond my understanding, and musings on what Mathematics is and how its practitioners actually work. The biographies seem to be somewhere between gossipy and irreverent and flat-out mean. Rota seems to be trying to show that a great mathematician needn't be a good person.
Perhaps unintentionally, he seems Rota was my favorite professor. Perhaps unintentionally, he seems to be underscoring the point by being unpleasant himself. The Phenomenology is well outside my ken. I tried to make sense of it, but I'm failing on basic vocabulary. I wish I'd read the afterword first. It warns that almost nobody understands the distinctions Rota is making in these passages. The musings on Mathematics were very interesting. Rota hits the nail on the head a number of times.
Dec 25, Craig Citro rated it it was amazing Shelves: you-cant-take-the-math-from-me. Shubhendu Trivedi rated it it was amazing Jan 12, Paul Vittay rated it it was amazing Feb 22, Xing Shi rated it it was amazing Dec 08, Joshua Galloway rated it it was amazing Feb 02, Pham rated it really liked it Mar 03, David rated it it was amazing Jan 24, Scott Mckuen rated it it was amazing Sep 23, Shery rated it liked it May 13, William rated it really liked it Apr 22, A Probability Path Sidney I.
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Plane Algebraic Curves Egbert Brieskorn. Number Theory Andre Weil. Bernhard Riemann Detleff Laugwitz. Discrete Thoughts Mark Kac. Linear Algebraic Groups Tonny A. Theory of Function Spaces Hans Triebel. Mathematics for the Analysis of Algorithms Daniel H. Notes on Introductory Combinatorics Georg Polya. Simplicial Homotopy Theory Paul G. Back cover copy Indiscrete Thoughts gives a glimpse into a world that has seldom been described, that of science and technology as seen through the eyes of a mathematician.
The era covered by this book, to , was surely one of the golden ages of science as well as of the American university. Cherished myths are debunked along the way as Gian-Carlo Rota takes pleasure in portraying, warts and all, some of the great scientific personalities of the period --Stanislav Ulam who, together with Edward Teller, signed the patent application for the hydrogen bomb , Solomon Lefschetz Chairman in the s of the Princeton mathematics department , William Feller one of the founders of modern probability theory , Jack Schwartz one of the founders of computer science , and many others.
After the publication of the essay "The Pernicious Influence of Mathematics upon Philosophy" reprinted six times in five languages the author was blacklisted in analytical philosophy circles. Indiscrete Thoughts should become an instant classic and the subject of debate for decades to come. It is pages of Rota calling it like he sees it Readers are bound to find his observations amusing if not insightful.
Gian-Carlo Rota has written the sort of book that few mathematicians could write. What will appeal immediately to anyone with an interest in research mathematics are the stories he tells about the practice of modern mathematics. Table of contents Foreward by Reuben Hersh. Review Text From the reviews: "Read Indiscrete Thoughts for its account of the way we were and what we have become; for its sensible advice and its exuberant rhetoric. It has aged very well, and richly deserves its inclusion in this series. Review quote From the reviews: "Read Indiscrete Thoughts for its account of the way we were and what we have become; for its sensible advice and its exuberant rhetoric.