An example to young women (and men, too): the mathematician and professor Maria Gaetana Agnesi

Today I've met another mathematician! Or, to be precise, another person who, like me, declares having taken a degree in mathematics, "which means not to be a Real Mathematician". Including her, this week my personal version of the set "Wm*" of women mathematicians who declare themselves to be not Real Mathematicians has increased by two units.

But this time I'll not delve in the silly question "Why most women mathematicians I know are so proud to be not Real Mathematicians", whose answer would led us all towards a complex chain of the stereotype of Real Mathematician, the exclusionary and elitist spirit informing Real Mathematicians, and similar difficult topics way beyond my day share of the Quantum Neuron.

Rather, I'd like to tell of a hero of mathematics who, incidentally, was a woman (and who claimed herself not being a Real Mathematician, too, despite the mass of results she got during her life).

Her name was Maria Gaetana Agnesi, but her heighbours and acquaintances called her "la Signora", the Lady.

Born 1718, she was denied the opportunity to study in a regular university - women were not admitted on that era. But, given her evident brilliance (she was an enfant-prodige her father arranged things so way she was teached mathematics privately. This was possible, as their family was of ancient nobility and, well, quite rich.

The early 18th Century was a revolutionary age, respect to mathematics, and prof. Agnesi took part to it in full. The ideas of infinitesimal calculus, born in 17th century thanks to the pioneering works of Newton and Leibnitz, was literally flourishing. This was also the era of Euler and Lagrange, to mention two giants all math students still know very well to date.

Maria Gaetana Agnesi is remembered for the discovery of a now-almost-forgotten curve and other results which apparently do not rival her contemporaries' big theorem.

But where prof. Agnesi really excelled was in didactics. Her book, "Istituzioni analitiche ad uso della gioventù italiana" (originally conceived as a tool to teach advanced mathematics to her young brother) gained a widespread diffusion around the World, and was renowned as the main teaching reference in the Golden Age of infinitesimal calculus and analytic geometry. You may access a hardcopy of it through the Internet, just by googling a little bit.

If you take the little "disturb" to skim within of it, maybe you will initially feel not that surprised. All classical and then-less-classical results are described not so differently than in many other manuals which followed in later time, at least until the beginning of 20th century when formalization made big steps. In 1985, while studying at the University of Milan, I had my share of books written more or less the same style.

It took me days, and an intuition, to realize the sheer modernity of what I was distractly looking at. Sure it looked familiar: it was the first time infinitesimal calsulus was described this way!

You may get a feeling of how difficult it was to manipulate calculus and its symbols before prof. Agnesi by just having a quick look to Leibnitz and Newton works, and some their precursors: they look absolutely cryptic. Things today seemingly obvious to most high school students, like derivation chain rule, on these times were way off the grasp of most ordinary minds (the vast majority of then university professors included, I presume).

Then the "Istituzioni" came, and from a day to another calculus became "clear and understandable".

The impact of the book (actually two huge volumes) can not be overlooked. In some circles, "doing" or "discovering" (?) theorems is attached a higher prestige than explaining them in a clear way. But in the end it is the latter which paves the way to applications of mathematics.

Calculus, today, is the core language of physics (from classical mechanics to string theory), and is gaining acceptance in disciplines like biology and geology which formerly were considered observational, and are underwenting a quick "mathematization". But this fact, true today, was absolutely not obvious on beginning 18th century. The fact it became is largely due to prof. Agnesi and her pioneering work: without her help, our "ordinary" minds would have little hope to apply mathematics using the clumsy notation and hard concept of Newton and Leibnitz.

So in a sense, if I'm writing this note, and you can read it, one of the causes is prof. Maria Gaetana Agnesi work.

I mentioned prof. Agnesi did not really considered herself a Real Mathematician. Of course I never asked her :-) (although, under different circumstances, that might have been not that impossible: her "villa" is right on the top of Montevecchia hill, still inhabited by her family heirs: just fifteen drive from my home.) So "of course" mine is a little abuse. Sure, she was denied the possibility of a regular career as a mathematician, because she was a woman.

And, right the majority of women mathematicians in my circle of friends and acquaintances, she had many other deep interests. To mention one, she was one of the founders and former directors of Pio Albergo Trivulzio, a Milan institution still present, one of the first old and poor people's home in the World.

On her death in 1799 she had left many other traces in charity and institution building as a benefactress. Deeply religious, she spent the last part of the life in prayer, contemplation - and help.

My reason she's an example still today has not one facet only. Sure she was one of the major mathematicians in her times.

But also, she was the type of mathematician who defies the common stereotypes about mathematicians and the practice of doing mathematics: a complex personality, not confined to maths only, and not self-celebrating in math, as some Real Mathematicians seem to keenly do.

And, her massive impact, a giant's, did not occur where maximum prestige stood. She pursued science and maths because of a deep interest, a form of love, totally disjointed by the "professional" necessity of getting acknowledged and given a tenure which now plagues the pratice of science (the Damnation of Impact Factor!) A shining professor, she devoted to teaching (in very indirect way, by writing a seminal book) all her energies. This kind of devotion, motivated by intrinsic value, worth and beauty, resembles me very much of monsieur Fermat, or Charles Darwin.

This is precisely, in my modest view, the same kind of devotion so needed in today' specialized and parcelized science for some new real breakthrough to occur.