Barriers to Female Achievement in the Field of Mathematics

What were the barriers to women's achievement in mathematics in the past? How did some women manage to overcome them? To what extent do these barriers still exist today?
Mathematical achievements throughout the ages have been well recognised and held in high esteem. However, the names of Ada Lovelace, Emmy Noether or Sonya Kovalevskaya are rarely highlighted and brought out for public attention, consideration, and admiration. These outstanding mathematicians seem to have been hidden from the public view and all for one simple fact - these talented mathematicians are all women.
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