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Indiscrete Thoughts

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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, 1950 to 1990, was surely one of the golden ages of science and 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. Rota is not afraid of controversy. Some readers may even consider these essays indiscreet. This beautifully written book is destined to become an instant classic and the subject of debate for decades to come.

280 pages, Hardcover

First published December 18, 1996

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Displaying 1 - 18 of 18 reviews
Profile Image for David.
259 reviews31 followers
December 22, 2007
In the foreword to the book, Reuben Hersh quotes Peter Lax (with an apology for inaccuracy) as saying "A lecture by Rota is like a double martini!" That sounds about right -- and if true, the olive is certainly in Chapter 20, "A Mathematician's Gossip." I think Rota is almost completely sincere in this little gem, for example: "Milan has succeeded in overtaking Paris in women's fashions, but Paris retains the title for intellectual ellegance. The finest presentations of today's mathematics are heard in the halls of the Institut Henri Poincare, where polite insultes are elegantly exchanged with jewels of mathematical definitiveness." Or what of this little aside, which feels so much pointed to me after a semester of teaching probability theory: "Writers of probability texts are laboring under the illusion nurtured by the late Willy Feller that discrete probability is easier than continuous probability."

And what of the book reviews? I quote one review in its entirety (a review of Passmore's Recent Philosophers): "When pygmies cast such long shadows, it must be very late in the day."

Priceless, I tell you. Priceless.
Profile Image for Wendelle.
2,046 reviews66 followers
January 22, 2020
Five stars for hilarity and earnestness. This book is the mathematician Gian-Carlo Rota's seized chance to share spicy gossip on the traits and absurdities of his fellow geniuses, and of the cranks who sent him hate fanmail. Sandwiched in between are his recollections of the delectably lax collegial atmosphere of Yale during his years of study, his incisive conclusions about the personalities of his peers, and his verdicts brought to bear on the different philosophical schools that speculate about the nature of mathematics.

This book is very quotable.

"He secretly considered himself to be one of the lowest ranking members of the Princeton mathematics department, probably the second lowest after the colleague who had brought him there,"

"Feller was working in his garden pruning some bushes, and Velikovsky rushed out of his house screaming, "Stop! You are killing your father!" Soon afterward they were close friends"

"He became a crusader for any cause which he thought to be right, no matter how orthogonal to the facts"

"Suddenly he found himself in the middle of an asphalt jungle, teaching calculus to morons"

"No other period of civilization has been so dependent for survivalon hypocrisy as the belle epoque, the late post-Victorian age. It has bequeathed us a heritage of lies that we are now painfullycharged witherasing, like a huge national debt. "

"After Stan died life seemed to go on as if nothing had happened, as if his daily phone calls to me were being delayed for some accidental reason (he used to make a round of phone calls to his friends every day in the late morning to relieve boredom), as if at any minute we would meet again and resume our discussions. Three years went by. One day I found the courage to unlock that drawer. The void I had felt for pretending he was still alive had become overwhelming. As I looked
at the monocle, I was struck by the horror of feeling alone. From now on I would be faced with the terror of his absence."

Superbly written, with the clarity of vocabulary that comes from the exactness of a mathematician.
Profile Image for Benjamin.
412 reviews1 follower
August 3, 2015
It's brash and, at times, contradictory, but it's intensely thought-provoking.

In particular, I found it invigorating to read an account that tackles some of the myths that mathematicians tell each other (like the idea that proofs provide unassailable veracity, despite the fact that invalid proofs do trip people up and that some people do not follow valid arguments) without degrading the subject falling back to some relative concept of "truth". He staunchly defends the axiomatic method while fearlessly critiquing it.

His version of phenomenology was presented clearly and is worth dwelling upon.

His complaint that the presentation of mathematics as definition-theorem-proof completely obscures how mathematicians actually work is also worth dwelling upon.

Some of the stories about mathematicians were amusing, but they are not what my mind will retain from this book.

my favorite quote: "Since we erroneously believe that whatever matters must be real, we demand that functions should be reduced to something real."
Profile Image for Andrew Foote.
33 reviews8 followers
February 15, 2020
Rota is a very good writer, and he succeeded in keeping my attention to the extent that I read the whole book in one night. This is surely due mostly to the power of Rota's writing. For a mathematician, he has considerable literary flair. Sentences which could be extracted as aphorisms are frequent. There is an overall tone of "everything you know is wrong, and I am telling you the shocking secrets about how things really are", an attention-seeking technique which many writers use, which can be annoying when you find the writer's supposed insights disappointingly mundane; nevertheless, for me, I found this tone was a reasonable one to take with the subject matter.

The various chapters of the book are somewhat disparate in subject; it's basically a collection of essays.

The first part is biographical in nature (or "gossip", in Rota's own words), and discusses the lives and personalities of various mathematicians of Rota's generation (and a couple of earlier ones, such as Gibbs and Grassmann). I found it readable enough but somebody primarily interested in what intellectual insights Rota has to offer might be bored by it. It requires a more emotionally attuned kind of reading. The chapter about Stanislaw Ulam is particularly compelling, if read this way, and arguably is the peak of the book. I particularly like this paragraph, from the same chapter, which I will probably quote from now on to anybody who asks what appeal there is in mathematics:

Of all escapes from reality, mathematics is the most successful ever. It is a fantasy that becomes all the more addictive because it works back to improve the same reality we are trying to evade. All other escapes—sex, drugs, hobbies, whatever—are ephemeral by comparison. The mathematician's feeling of triumph, as he forces the world to obey the laws his imagination has freely created, feeds on its own success. The world is permanently changed by the workings of his mind and the certainty that his creations will endure renews his confidence as no other pursuit. The mathematician becomes totally committed, a monster, like Nabokov's chess player who eventually sees all life as subordinate to the game of chess.


The second part delves into Rota's thoughts on philosophy of mathematics. I can't say I read this with the greatest deal of attention, but it generally seemed quite reasonable and I would be inclined to take a closer look at it some time when I felt more like doing intensive philosophy. He describes his philosophy as phenomenological in nature, and mostly references Husserl (Heidegger not so much). To give an example of one of his positions, he dissolves the concepts of "truth" and "existence", saying we should instead talk about "evidence" and "identity", respectively.

As for the last part of the book, this is just another miscellany of stuff that Rota wanted to write down but didn't fit in with the themes of mathematical biography and philosophy from the earlier parts. The "Ten Lessons I Wish I Had Taught" essay (a very famous one, which I had already read in independent form) is here, then there is essentially a collection of 1996-era tweets, i.e. punchy little statements that invite the reader to try to figure out the details, and then there are some book reviews. There's not much to remark on here as a reviewer, it's just bonus Rota content, basically.
Profile Image for Fredrik.
224 reviews13 followers
July 9, 2018
Han skriver veldig bra.

Første del av boka er matematikkultur: anekdoter og tanker fra Yale (og andre steder Rota har jobbet). Han krydrer med mange tanker om hva matematikk er, og hvordan matematikk ofte blir feilaktig framstilt i skole og media.

(formalisering har gått for langt: matematikk handler om ideer, ikke bevis. Bevisets eneste rolle i matematikken er for å ha en felles grunnmur - forståelse er mye viktigere, og da er ikke nødvendigvis bevis veien å gå.)

Del to handler om fenomenologi. Mye matematikk, men også ganske hard filosofi (hans favorittfilosof er tydeligvis Husserl, som jeg egentlig bare har hørt om). Mye interessant - dette har jeg lyst å lese igjen. For tidlig å gi en god oppsummering av disse kapitlene, men veldig lærerikt.

Del tre er lettere igjen: for eksempel heter et av kapitlene "Ten Lessons for Survival of a Mathematics Department". Boken avsluttes med en del bokanmeldelser.
Profile Image for Aneel.
330 reviews8 followers
February 15, 2010
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 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.
Profile Image for Rafaela.
31 reviews14 followers
November 15, 2024
Rota is quite a character lol

I know nothing about mathematics, even though it was my favorite subject in school and I sometimes wish I was smart enough to learn it more deeply (my adult brain problem can't even handle 4th grade math 😬). But I do enjoy reading about mathematicians and I find them very inspiring (André Weil is the one who interests me the most and who has made me want to learn more about them).

Anyway, back to the book!

I've never heard of Rota before reading Stan Ulam's Adventures of a Mathematician (which I recommend to everyone), but his character kind of shines through the pages. He doesn't hold any punches and is very frank about his colleagues, which I appreciate, even though he doesn't seem like an easy person to deal with either. I was actually surprised when he said that he angered a lot of people because of this section, since (in my mind) scientists tend to be very thick-skinned and disagreeable.

The first third of the book is about Rota's peers, including a very moving, emotional chapter about his friend Stan Ulam. Not gonna lie, but I didn't expect that level of sentimentality from a mathematician (no offense lol I'm not sentimental either), and I thought it was a very nice surprise and the strongest part the book. It's not just "gossip", though, because Rota also talks about how mathematicians get to know each other and want to know their bottom lines, for example. Despite being clueless about math, I enjoyed those discussions a lot and was able to get something out of them.

[I thought it was a bit funny that Rota said Ulam was self-centered, had an overpowering personality etc., while Ulam said, in his own autobiography, that he liked Rota because they had very similar personalities 😆]

The second part of the book focus on philosophical discussions. I had to skip and skim through most of it, because apparently they bore me *a lot* more than reading about math I don't understand. That said, some parts of it were interesting, like the topics about truth, triviality, mathematical beauty etc. I lack the intellectual baggage, mathematical knowledge and philosophical inclination to appreciate it properly, but I can't say it doesn't have any merit. In this regard, this book is unlike other mathematicians' (auto) biographies, such as Weil's "The Apprenticeship of a Mathematician" (which I love) or "A Beautiful Mind" about John Nash, which most people can read and enjoy despite having no mathematical background.

The third and final part of Indiscrete Thoughts becomes readable again. It focus on advice about lectures (which I liked), book reviews, and a collection of some random thoughts about math.

Overall, I enjoyed the book, but not as much as I had expected. It's too heavy on mathematics for me, but since it's not the book's (or the author's) fault, I don't think it's fair do give it a low rating or anything. Still, I really recommend the first part of the book for everyone interested in mathematicians.
1,621 reviews23 followers
February 18, 2019
(NOTE: I actually originally posted this review on my old blog on August 31, 2005, and I when I reread a decade later I was pleased to realize that I still agreed with everything and I could repost it verbatim):

This is a really funny book.

It is essentially a collection of essay by the late great MIT combinatorialist who passed away only a few years ago.

He is a very amusing and stylish writer, I actually laughed out loud more than a few times(fairly rare for a math book).

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.

Most interesting are his essays on Alonzo Church and Stanislaw Ulam (of Borsuk-Ulam, Hydrogen Bomb and Metropolis algorithm fame). 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.

Are we doomed to basically rediscover the same ideas over and over and over? *HORROR*

He also has several essays on "philosophy of math." His views tended towards phenomenology(Husserl, Heidegger et. al.) and he was violently opposed to the excesses of reductionism and rationalism that is very prevalent in American (& British) philosophy (For us non philosophy majors: He's "Continental" the people he is opposed to are "Analytic").

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.
140 reviews7 followers
July 13, 2020
This is a fascinating book. I was torn between giving it 4 and 5 stars. Had I known more math and philosophy I probably would have given it 5 stars. The greater your knowledge of mathematics and philosophy the greater your appreciation for this book will be. I don't think you'll get much out of it if you don't have at least some exposure to higher mathematics (beyond calculus/differential equations). The sketches of various mathematicians he knew were a highlight for me (particularly the ones on Artin, Ulam, and Feller) as was the section "Mathematical Gossip" that contained some great jumping off points on mathematical areas to learn more about.

The philosophical parts were at times obtuse to me. My knowledge of philosophy (particularly of phenomenology, which Rota is fond of) is not as strong as my knowledge of mathematics, so I did not understand everything in these sections. But the parts I did understand were fascinating.
Profile Image for Joseph Carrabis.
Author 57 books119 followers
August 30, 2017
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.
Profile Image for Kantor.
27 reviews
March 26, 2024
Un libro que se disfruta de principio a fin. Tiene tres partes: una autobiografía matemática, una recopilación de observaciones filosóficas y una final de comentarios variopintos. Cotilleos, matemáticas y fenomenología... ¿qué más se quiere?
Profile Image for CR.
87 reviews2 followers
August 27, 2017
One of the most important books for any aspiring mathematician, philosopher, or phenomenologist to read.
Profile Image for Marshall Müller.
51 reviews4 followers
February 14, 2020
Fun collection of essays and stories written in a way that you don’t need to understand the math to enjoy or get something out of.
Profile Image for Cameron.
78 reviews6 followers
August 1, 2024
A goodread, though I'm not sure I would like to have Rota as a colleague.
18 reviews
October 7, 2016
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 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!" The speaker, Eugenio Calabi, obliged and summed up his lecture in simple points that could be understood by everyone. 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.
87 reviews4 followers
December 26, 2014
first up, i'll admit i'm a cheater -- i skimmed or skipped pretty much all of the second section. this is sacrilege in many ways, but so it goes.

i bought and read this for the mathematical reminisces, and i wasn't the disappointed in the least. rota was witness to such an incredible section of history, so this is a delightful read on that front.

where it shines and earns the 5 stars, though, is the honesty (which was apparently one of rota's trademarks). as rota confronts head-on in the book, it's too easy to fall into the halo effect, failing to see our mathematical heroes as real people. in some sense, it's almost nicer to find out that these legends had their own issues, too -- real people are so much more interesting than 2d ones.
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