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Mathematics in the fifties was a marginal subject, like Latin. The profession of mathematician had not yet been recognized by the public, and it was not infrequent for a mathematics graduate student to be asked whether he was planning to become an actuary. The centers of mathematics were few and far between, and communication among them was infrequent. The only established departments were Princeton and Chicago. Harvard was a distant third, and Yale was in the process of overcoming its overdependence on the College. 8491 Rota.

Indeed, in this half-century we have gone at research with vim and vigor, and there have been spectacular successes. Within mathematics we have seen the classification of finite simple groups, the proof of (many cases of) the Shimura-Taniyama-Weil conjecture - and hence Fermat's last theorem, the solution of the Poincare' conjecture for four dimensions, substantial progress in pseudo-diffe- rential operators, with applications to the theory of partial differential equations and to index theory. But this specialization has its cost. As we mathematicians concentrated on our own discipline, connections with other fields diminished. Statistics separated from mathematics; in many universities, the two fields are now distinct departments. Computer science was largely shunned by mathematicians in the 1970s; it too developed outside of mathematics departments. Academic bean-counting often ensures that once disciplines are divided, walls go up. Why hire an applied mathematician if the physics or computer science departments can be convinced to do so instead? ... In splitting, we have lost a real resource for mathematics ... Without question, we cannot be good mathematicians without an appreciation and understanding of abstraction. But the inward focus that developed in university mathematics departments has not always served mathematics well, and a broadening of the definition of what constitutes mathematical research, and what a mathematician is, is in order. Susan Landau, in Notices AMS Nov. 1995

Il lavoro di un matematico muta nelle varie fasi della sua vita. Un matema- tico più anziano lavorerà su questioni più generali, mentre uno giovane sceglierà di lavorare su un singolo difficile problema. 5812 Rota, 156.

Una notevole caratteristica del talento matematico è l'abilità nel riconoscere analogie. Un'altra tra le più rare è il talento per la mate- matica applicata, il saper estrapolare dai dati sperimentali i due o tre parametri rilevanti e scartare quelli che non lo sono. 5812 Rota, 158.

From an article on the young PhD's difficulties in employment. There are general reasons, but some reasons come from a too traditional and narrow orientation of many mathematicians: "The research and development world seeks creative researchers and implementors with the flexibility to adapt techniques and ideas to new contexts. The sad irony is that sophisticated mathematical skills, but not traditional mathematicians, are often needed in precisely these disciplines. In both education and the industrial high-tech workplace, people not trained as mathematicians are doing mathematical work, often quite successfully. This phenomenon is the legacy of a long and profound failure of mathematicians to communi- cate with other groups."

Un buon insegnante non trasmette nozioni, bensì entusiasmo, apertura mentale e valori. Un buon insegnante deve essere capace di tirar fuori il meglio dai suoi studenti. Ciò che più serve ai giovani è l'incoraggiamento. 5812 Rota, 157.

In a world where hard decisions are being made, we are often the ones acted upon rather than the prime movers. Generally speaking, we are not organization people; instead, we are, by training, the misfits." Steven Krantz in Notices AMS, May 1996.

I also believe that changing fields of work during one's life is rejuvenating. If one stays too much with the same subfields or the same narrow class of problems a sort of self-poisoning prevents acquisition of new points of view and one may become stale. Unfortunately, this is not uncommon in mathematical creativity. 5653 Ulam, 290.

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Maria Teresa Borgato in Ferrara

Jeanine Daems in Leiden

Alessandra Fiocca in Ferrara

David Joyce in Worcester, MA

Karen Parshall in Charlottesville

Luigi Pepe in Ferrara