As a "commonly educated" person, I can fire away a few of "famous artists" who are mentioned in the news, whose paintings are stolen, or sold at auctions for ridiculous prices: Monet, Manet, Van Gogh, Vermeer, Matiss, Da Vinci, Rembrandt, you know what I mean. However, I was recently surprised to realize that I don't know any famous women/female artists? OK, Frida Calo, but that's the XXth century. Even if you try to Google "famous artists" you get a long list of (mostly) men from different ages.
However, I remember that it was considered common for young women of higher class in all those centuries, when men were prevalent in the Painting industry, to study art in different forms, and to paint something as the pastime, instead of studying science, for example. So, the question is: why do we know so little of art done by those countless (maybe) unwilling female "art students"? Is it sold at auctions? Did someone throw it away deliberately, was it not worth to even keep in families? I would venture a guess that due to its age alone, any drawing made by an unknown female artist of 18th century, would fetch a hefty sum on an auction? Or is my logic inherently flawed somewhere?
The reasons for this are numerous and varied, and trying to cover all of history before 1900 will be challenging so I'm going to focus my answer on women and oil painting from around the 18th to 19th centuries. Answers focused on other periods and mediums may vary.
I think the main thing to keep in mind is there are a lot of famous works of art by women - it's just that presently those forms of art are perceived as less 'important' or 'artistic' than painting or oil sculpture. Women were significantly involved in textile arts like tapestry and embroidery, for example. At times, for example in 16th century England, those textiles were more highly valued than paintings, but attributing that work to an individual 'artist' was not seen as important. Often the forms of art women were involved in were collaborative, 'craft' forms that people did not think of in terms of the figure of the individual 'significant' artist. I'm someone who does work on uncovering this labour in the eigtheenth-century book trade - and increasingly it's evident that there are more and more domains in which worked creatively, they're just domains that have historically been called artisanal rather than artistic.
In the eighteenth and nineteenth centuries in Europe, the formalisation of art education through institutions like the Royal Academy privileged oil painting as the 'highest' form. At the same time, national museums were being established to preserve art. Those museums privileged what was valued at the time I.e. oil painting, sculpture and antiquities, and therefore the institutions created to train artists and preserve art excluded domains in which women were more likely to work. So women were excluded from art history by privileging male-dominated domains, but they were also excluded deliberately from these institutions. In France in the nineteenth century, for example, women could not go to art school at university level, could not go to art galleries unaccompanied, and faced strong cultural stigma against being an artist. The institutions of art that defined the canon have not been kind to women!
The next way women's work has been hidden and excluded has been through the very idea of 'the artist'. Many of the cultural assumptions about 'the artist' have been shaped by gendered beliefs. The lone, creative genius romanticised by art lovers from the late eighteenth century onwards is a cultural construction, and one that ignores the community of support an artists needs to work. William Blake, for example relied on help from his wife, Catherine Boucher, in his printing process. Art historians have done good work to better describe the exact processes Boucher worked on, but her name is largely unknown. Apart from directly working on art, most male artists relied upon their wives, partners, servants or 'muses' for their work. An artist can't paint if they're not kept warm, fed and well-supplied and many male artists relied on women to do this for them. The frame of 'the artist' as an individual genius takes the focus away from this wider community of work that brings a painting into existence, but feminist historians like myself argue that the people involved in those other tasks are just as important and interesting than the person who signs the painting. So, women's work has been largely unattributed by focusing on 'the artist' as a lone figure.
Finally, art historians have written women artists out of contemporary understanding by undervaluing their work historically and artistically. A good example of this would be Berthe Morisot. Morisot was a French woman whose paintings were deeply influential on Impressionists like Monet. At the time, Morisot's work was considered 'airy' and 'feminine' and her influence was downplayed by male critics. For much of the 19th and 20th centuries critics and historians saw Monet as the chief influence on Morisot, partly because they carried the sexist assumptions that a female artist could not birth an art movement, particularly one who was not as famous as Monet. However, since the 1980s, feminist art historians have attempted to recover the influence and significance of female artists like Morisot, although it takes time for academic work to be noticed by the public. Morisot is one example, but I think is a useful illustration of how art historians and critics have downplayed the significance of women.
There are more reasons than this, and you might do well to read one of the huge number of feminist histories of art that are available (I can give direct recommendations if asked!). In brief, women were excluded by the medium they worked in, the institutions that enabled artistic production, and the critics and historians who shaped the fame of artists.
You've gotten an answer that deals with one angle of your question, but it seems to me that half of what you're asking relates to something else - something I've written an answer about before, which I'll paste below:
In the eighteenth and nineteenth centuries, it was very important for young women of the middle and upper classes to be "accomplished", in the parlance of the day. Since you've read Pride and Prejudice, you probably remember this:
“It is amazing to me,” said Bingley, “how young ladies have patience to be so very accomplished as they all are.”
“All young ladies accomplished! My dear Charles, what do you mean?”
“Yes, all of them, I think. They all paint tables, cover screens, and net purses. I scarcely know any one who cannot do all this, and I am sure I never heard a young lady spoken of for the first time without being informed that she was very accomplished.”
“Your list of the common extent of accomplishments,” said Darcy, “has too much truth. The word is applied to many a woman who deserves it no otherwise than by netting a purse, or covering a screen. But I am very far from agreeing with you in your estimation of ladies in general. I cannot boast of knowing more than half a dozen, in the whole range of my acquaintance, that are really accomplished.”
“Nor I, I am sure,” said Miss Bingley.
“Then,” observed Elizabeth, “you must comprehend a great deal in your idea of an accomplished woman.”
“Yes, I do comprehend a great deal in it.”
“Oh! certainly,” cried his faithful assistant, “no one can be really esteemed accomplished who does not greatly surpass what is usually met with. A woman must have a thorough knowledge of music, singing, drawing, dancing, all the modern languages, to deserve the word; and besides all this, she must possess a certain something in her air and manner of walking, the tone of her voice, her address and expressions, or the word will be but half deserved.”
“All this she must possess,” added Darcy, “and to all this she must yet add something more substantial, in the improvement of her mind by extensive reading.”
“I am no longer surprised at your knowing only six accomplished women. I rather wonder now at your knowing any.”
"Accomplished" and "accomplishments" aren't just random word choices on Austen's part - they're what this society used to refer to women's non-essential, non-"work" skills. Being able to dust a room wasn't accomplishment and making jelly or preserves wasn't an accomplishment, because these were things that servants and housekeepers did, as well as women who couldn't afford servants, and in turn, servants, housekeepers, and women who couldn't afford them didn't have time to practice accomplishments. Miss Bingley's list of music (playing the piano or harp), singing, drawing (which was probably meant to encompass watercolor painting as well), dancing, and speaking/reading other modern languages (French, German, and/or Italian) states the typical list of necessary accomplishments for an upper-class woman, although it neglects embroidery. Women would learn these skills as children and teens, either at home or at a boarding school. If they learned at home, the skills would be taught to them by a governess, maybe with the help (if their parents could afford it, and/or very concerned with accomplishments) of an outside male teacher in music/dancing or art.
The concept was much critiqued at the time by activists for women's rights. Basically, young men of the same social status were educated to do white collar work, becoming a clerk, lawyer, doctor, etc., or to go on to university and then be landowners, while their sisters and future spouses learned these "ornamental" skills which could only be used as a source of income with a significant step down in social status and most likely material comfort. This definitely wasn't wrong. However, modern people taking this critique at face value has led to the general neglect and underestimation of the use value of accomplishments. They can also be seen as job skills in their own right, for the position of upper- or middle-class wife - skills that young women could work on to improve their chances on the marriage market. Far from being mindless and stultifying, these skills require a lot of practice to achieve mastery or even proficiency, and could be very useful for entertaining oneself and others, communicating, and adorning one's space.
ANYWAY. I'm getting around to your question now. The point of accomplishments was in the breadth, not the depth - the goal was to be proficient in several rather than a master of one specifically, which could imply some kind of vocational training, or the lack of enough money to pay for the proper instruction (given the class-based nature of the game). The actual paintings themselves, or the embroidered pictures or samplers, or the sung songs and played music, were also not the point. While a typical accomplished woman's family might value her paintings and visitors might comment favorably on them, she was not going to professionalize her talent unless she were in dire straits, so she would not become known as a painter and therefore future generations would have little reason to remember their names and pass them down along with the paintings, if they even did pass down the paintings at all, and so they didn't achieve any kind of fame and have not been written about. When these artworks still exist, they're generally in attics and local historical societies, and may be more known for being the product of a particular school than for their specific maker.