# Francesco Tricomi on 'publish of perish'

Francesco Tricomi attended the 1958 International Congress of Mathematicians in Edinburgh, Scotland in August 1958. He addressed the Congress with a short address

*Quo vadimus?.*We give a version of this below.**Quo vadimus?**

Exactly thirty years ago Gino Loria made a communication with the same title as the present at the International Congress of Mathematicians in Bologna. As in the case of Loria, this title wants to have the meaning of a cry of alarm in the face of the enormous, uncontrolled development of today's mathematical publications.

Let us consider, as an example, the theory of differential equations, both ordinary and partial differential equations. I believe that, on average, about four hundred papers on this subject are now published annually. Who will ever actually read most of these works? Indeed, it can be considered that a not entirely superficial reading of a work of this kind requires, on average, about four hours. Linguistic difficulties aside, who is it that will be able to find six hours in their working day, just to keep up to date with the differential equation literature? The consequence is that, in most cases, one has to rely on reviews in Mathematical Reviews and similar publications, which are often, but not always, trustworthy!

I have the impression that we are facing a crisis in our system of diffusion of scientific truths, comparable to that which, in the mid-seventeenth century, gave rise to the first modern academies and the first scientific periodicals, for example the Philosophical Transactions of London and the Journal des Savants of Paris, both beginning in 1665. And in 1667 they also begin in Italy; the Acts of the Accademia del Cimento.

Before this epoch, the dissemination of scientific discoveries was mainly based on private correspondence between leading scientists and some of their friends. For example, in France, Father Mersenne (1588-1648), although a modest scientist himself, came to great fame and had an important part in the foundation (1635) of the Académie Française, mainly due to his correspondence with Galileo, Huygens, Fermat and other greats of his time. Subsequently, with the growth of scientific production, this system of the exchange of private letters proved to be insufficient and was replaced by communications through scientific periodicals and academic societies, a system that worked very well until a few decades ago, but has now entered into crisis.

The purpose of this communication is primarily to draw the attention of Congress to a problem which, in my opinion, cannot be further ignored, and not to indicate possible remedies. However, to avoid the accusation that it is too easy to diagnose a disease without worrying about it's possible treatment, I will conclude by mentioning some of my ideas on possible ways out of the indicated crisis.

One of these ideas is essentially an "experimental" observation: each of us has been able to experience what relief one gets when, dealing with a certain chapter of mathematics, one encounters a standard work, not too old-fashioned, of the genre, let's say, Watson's

*Bessel's Functions*or Szegö's

*Orthogonal Polynomials*. Why should such lucky cases be the exception and not the rule? Could it not be that some institution such as the International Mathematical Union would take care of the publication, at regular intervals, of such works in each of the main branches of modern mathematics?

Another important thing seems to me to be a correction in the scale of values in the appreciation of the so-called "research papers" in relation to the so-called "expository papers". Indeed, what is most needed today, alongside good treatises, is precisely these "expository papers" which, if done well by competent authors, are truly precious and save the reading of a number of special works. On the other hand, are all the "research works" really useful and interesting? And hasn't it happened that some of them have been published mainly for the author's career needs? The various "midwives" of scientific works reflect on this: members of academies, editorial boards of periodicals, etc. And let them think whether, even in mathematics, a little "birth control" is not a necessary enterprise!

In connection with the above, it is also necessary to correct the widespread opinion that every self-respecting mathematician should publish something, shall we say, annually. This is completely untrue, and is one of the main causes of the unfortunate but honestly indisputable fact that some part of today's mathematical production could be suppressed without any harm to science. Those who have nothing particularly important to let people know about, must be able to remain silent without fear of being belittled for it! In particular, it is not at all necessary for all participants in a congress to communicate with you. Or they can talk to you about "innocent" things, as I did this morning!

Last Updated January 2021