She told me that she was very sorry that the visit had taken the form of a thesis defence, and that she did not like to speak publicly of [mathematics], where for every one that was amused, twenty were bored to death. ...
Recounted about Maria Gatana Agnesi (1718 -1799), Italian mathematician and scholar who, along with contemporary Laura Bassi were the first women to be appointed chairs at a European university.

Nothing has afforded me so convincing a proof of the unity of the Deity as these purely mental conceptions of numerical and mathematical science which have been by slow degrees vouchsafed to man, and are still granted in these latter times by the Differential Calculus, now superseded by the Higher Algebra, all of which must have existed in that sublimely omniscient Mind from eternity.
Mary Fairfax Greig Somerville (1780-1872), Scottish mathematician.

The Analytical Engine weaves algebraic patterns, just as the Jacquard loom weaves flowers and leaves.
Augusta King, countess of Lovelace (1815-1852), scholar and mathematician, speaking enthusiastically of Charles Babbage's early computer for mathematics.

The meaning of these concepts I naturally could not yet grasp, but they acted on my imagination, instilling in me a reverence for mathematics as an exalted and mysterious science which opens up to its initiates a new world of wonders, inaccessible to ordinary mortals. (Recounting her childhood introduction to mathematics.)
Say what you know, do what you must, come what may. (Motto on her paper "On the Problem of the Rotation of a Solid Body about a Fixed Point.")
Sofia Vasilyevna Kovalevskaya, (1850-1891) Russian mathematician and first woman after Maria Agenesi and Laura Bassi to hold a chair at a European university.

It was clear to them [her students, mostly male] that I had much mathematics to give them and they forced it out of me.
Olga Taussky-Todd, (1906 -1995) Viennese mathematics professor and distinguished mathematician, speaking of her experience at California Institute of Technology.

When I had taken four of their six-credit graduate courses in mathematics and was beginning to think about a thesis, the word was conveyed to me - no official ever told me this but I learned - that the Columbia mathematics department was really not interested in having women candidates for Ph.D's. This was a very unpleasant shock. ...
Mina Rees, American mathematician (1902 - 1997), speaking of the difficulties women face in attempting a career in mathematics.

It is a pleasure for me to see with what diligence, skill and success you have worked and I wish you, in your further researches in this field as well, the finest results, which, with such depth and acuteness of mind on both your parts, you cannot fail to attain.
A colleague writing to English mathematician Grace Chisolm Young (1868-1944), coauthor with her husband William of numerous scholarly papers and books, commenting on their latest book "The Theory of Sets of Points."

I am very happy that you are getting on with the ideas. I feel partly as if I were teaching you and setting you problems which I could not quite do myself...
William Young, acknowledging Grace's equal contribution to their joint efforts.

I can personally testify to the importance of having role models and the companionship of other women colleagues. However, I think we need even more women mathematicians to prove good theorems and to contribute to the profession.
Sun Yung Alice Chang (1946) Professor of Mathematics, Berkley.

http://www-groups.dcs.st-and.ac.uk/history/Indexes/Women.html

The different branches of Arithmetic -- Ambition, Distraction, Uglification, and Derision.
Alice in Wonderland

"Can you do addition?" the White Queen asked. "What's one and one and one and one and one and one and one and one and one and one?" "I don't know," said Alice. "I lost count."
Alice Through the Looking Glass