Two suggestions by Rota and Feynman on how to do science and math

Giancarlo Rota (1932-1999) was an Italian-born, then naturalized American, mathematician and philosopher. As happens to outstanding thinkers, in his late years he was often invited to give a speech on more or less everything he wanted. At the Rotafest organized in his honour at MIT he spelled out a list of suggestions for scientists1:

A speaker should try to give his audience something they can take home. But what? I have been collecting some random bits of advice that I keep repeating to myself, do’s and don’ts of which I have been and will always be guilty. […] The advice we give others is the advice that we ourselves need.

There would be a lot to say on both the content of those suggestions and wheter the same pieces of advice that are valid for masters are also of great interest for all scientists. But for a change, let me cut this short and just present the two among them that I found the most interesting (one of which is in fact by the physicist Richard Feynman), leaving to the readers all extra-thinking.

5. Every mathematician has only a few tricks. A long time ago an older and well known number theorist made some disparaging remarks about Paul Erdös’ work. You admire Erdös contributions to mathematics as much as I do, and I felt annoyed when  the older mathematician flatly and definitively stated that all of Erdös work could be “reduced” to a few tricks which Erdös repeatedly relied on in his proofs. 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. The second volume of Hilbert’s collected papers contains Hilbert’s papers in invariant theory. I have made a point of reading some of these papers with care. It is sad to note that some of Hilbert’s beautiful results have been completely forgotten.  But on reading the proofs of Hilbert’s striking and deep theorems in  invariant theory, it was surprising to verify that Hilbert’s proofs relied  on the same few tricks. Even Hilbert had only a few tricks!

7. Use the Feynman method. Richard Feynman was fond of giving the following advice on how to be a genius. You have to keep a dozen of your favorite problems constantly present in your mind, although by and large they will lay in a dormant state. Every time you hear or read a new trick or a new result, test it against each of your twelve problems to see whether it helps. Every once in a while there will be a hit, and people will say: “How did he do it? He must be a genius!”


1. This and following citations are taken from: Ten lessons I wish I had been thaught (presented at MIT on April 20, 1996, on the occasion of the Rotafest), in Giancarlo Rota, Indiscrete Thoughts,  Modern Birkhäuser Classics (1997), pages 195–203.

Visiting the Collection de l’Art Brut in Lausanne

The Collection de l’Art Brut is a museum in Lausanne, Switzerland, of a very rare kind. It displays art that is not aware of being art – created by people at the margin of society or of the art world, mostly for they own pleasure or just for expressing themselves.

With the words of Jean Dubuffet, who invented the name Art Brut (the English version comes below):

Nous entendons par là [Art Brut] des ouvrages exécutés par des personnes indemnes de culture artistique […]. Nous y assistons à l’opération artistique toute pure, brute1, réinventée dans l’entier de toutes ses phases par son auteur, à partir seulement de ses propres impulsions. De l’art donc où se manifeste la seule fonction de l’invention, et non, celles, constantes dans l’art culturel, du caméléon et du singe2,3.

In English it reads:

We mean by that [Art Brut] works realized by people not affected by the artistic culture […]. With them, we can see the purest, rawest1 form of artistic creation, where all phases are reinvented from scratch by the author starting from him/her impulses. So this is a kind of art where only invention plays a role, and, differently from what usually happens in cultural art, there is no place for chameleons and monkeys2,3.

Pascal-Désir Maisonneuve -  L'éternelle infidèle

Pascal-Désir Maisonneuve
L’éternelle infidèle, entre 1927 et 1928
assemblage de coquillages divers
haut. : 42 cm
Photo : Claude Bornand.
Collection de l’Art Brut, Lausanne.

Some of the authors are then just talented people who, within an ordinary life, cultivated their passion for creating, but in fact most share the salient points of their biography: uneducated to art, born or grown up in straitened circumstances, after a period in a mental hospital they came to art as a mean to get in touch with the others, or just to express themselves. As one of them –  Vojislav Jakic – said about his works:

This is no drawing or painting: this is sedimentation of pain.

Vojislav Jakic - Les effrayants insectes cornus (1970)

Vojislav Jakic
Les effrayants inscectes cornus…, ca 1970
stylo à bille et crayon de couleur sur papier
141,5 x 101,5 cm
Photo : Henri Germond.
Collection de l’Art Brut, Lausanne.

Those similar personal backgrounds often imply some recurring features in their works: the obsession for filling the space – each empty room needs to be covered with details, that are everywhere and hence uninteresting or at least of different comprehension for the viewer. The canvas as a mean to explicitly express ideas with written words: many of them had physical or psychological inabilities to speak, hence they delegate their thoughts to the characters of their paintings or would even write around the pictures or in the empty room between objects. The repetition of the same subject, even within a single canvas: for instance, Madge Gill paints figures of the same woman, that constantly look at the viewer from slightly different poses, repeating her face multiple times over several slightly different canvas, often glued together in an hypnotic pastiche.

Madge Gill - untitled, undated

Madge Gill
sans titre (detail), s.d.
encre sur calicot
213 x 86,5 cm
Photo : Jean Genoud SA.
Collection de l’Art Brut, Lausanne.

Sylvain Fusco

Sylvain Fusco
Moire, 1938
pastel sur papier
62,5 x 47,5 cm
Photographe non identifié
Collection de l’Art Brut, Lausanne

Willem van Genk - Tube Station (1970)

Willem Van Genk
Tube Station, 1970
collage et peinture sur bois
75 x 124 cm
Photo : Claude Bornand
Collection de l’Art Brut, Lausanne

And originality is of course central, declined in many aspects: from the themes, to the choice of materials, with shells that become ears and lips and journal paper that is used to shape three-dimensional objects. To the canvas, often obtained by gluing more pieces together as the painting expands, as to form non-convex, strangely shaped pictures.

Charles Steffen is the star of the current exhibition. He did study art, but he had to stop after just one year because of psychiatric problems. After that, he spent 11 years in a mental hospital. He often paints images of nudes that are supposed to represent men and women, but actually look like wrinkled baby monsters of hybrid sex that lie somewhere between living beings and plants, and that look around with a grotesque gaze. Their details are carefully drawn as if Steffens was depicting something that was really appearing in front of him, and they are surrounded by inscriptions that explain their genesis and place them in the context of a fantastic world. I found the evolution of the sunflower especially imaginative (see below for the picture). It starts as a proto-human being with a single eye, and slowly, from top to bottom, it transforms itself. Its head becomes a flower, its hands twist into the stem, roots exit from its legs, and a sunflower is born.

Charles Steffen -  Development of the Sunflower Nude, from the One-Eyed Nude into a Sunflower (1994)

Charles Steffen
Development of the Sunflower Nude, from the One-Eyed Nude into a Sunflower, 1994
mine de plomb et crayon de couleur sur papier
90,9 x 122,5 cm
Photo : Atelier de numérisation – Ville de Lausanne
Collection de l’Art Brut, Lausanne

Charle-s Steffen - One of two Seated Nudes (1992)

Charles Steffen
One of two Seated Nudes, 1992
mine de plomb et crayon de couleur sur papier kraft
138 x 92 .6 cm
Photo : Atelier de numérisation – Ville de Lausanne
Collection de l’Art Brut, Lausanne

If you are looking for an aesthetic guiding thread through the exhibition, you will be disappointed. Most authors are represented just by a bunch of pieces (up to 5), and there is no link between one and another, or any of them and any artistic current, since none of those authors shared a past with mainstream art.

But some of them had in fact a future, influencing modern well-known artists (see eg here), as well as imposing their charm on popular culture (the Vivian Girls, named after some recurring characters in Henry Darger‘s work, is an indie American band, and the name of the English-German band Art Brut speaks by itself). For even though the images are often cryptic, the emotions behind them are clearly visible: the obsessions, the search for oneself, the fantastic worlds they created are not mediated by any artistic theory, hence they appear vividly to the eye of the spectator. This creates art that constantly swings between being disturbing, romantic, and grotesque, but is nevertheless direct and powerful.


1. I think the best English translation of brut is raw. A somewhat related, but more general concept, is that of Outsider art.

2. Jean Dubuffet, L’art brut préféré aux arts culturels, 1949.

3. I personally think that the idea that pure and innovative art only comes from people outside the artistic community is a cliche itself. But that’s another story.