“I would be great,” wrote a 10-year-old Mary Putnam, circa 1852. “I would do deeds, so that after I had passed into that world, that region beyond the grave, I should be spoken of with affection.”

She would accomplish the first part — her greatness was undeniable. “The Cure for Women” is a valiant and timely effort to change the fact that 120 years after her death, few people speak of her at all.

Determined to train as a physician at the highest level, in 1868 Putnam — a daughter of the prominent New York publisher George Palmer Putnam — was the first woman to persuade the Sorbonne to admit her to its medical school. With one exam left to take as the Second Empire fell, she elected to stay in Paris through the siege. Back in America, she became a fiercely uncompromising professor of medicine and practitioner of women’s health care alongside her mentors Elizabeth and Emily Blackwell at their New York Infirmary and its affiliated Women’s Medical College.

Ignoring the general assumption that someone unwomanly enough to pursue a medical career couldn’t possibly attract a husband, Putnam married the pioneering pediatrician Abraham Jacobi, capturing his heart with her research in cardiology and ignoring the antisemitism that came with her choice.

In 1876, she was the first woman to win Harvard’s prestigious Boylston Medical Prize. The provocative essay topic — “Do women require mental and bodily rest during menstruation?” — was central to the larger women’s rights movement.

Womanhood itself was considered a kind of pathology; how could women claim equality if their own bodies betrayed them every month? Putnam Jacobi’s meticulously argued conclusion — that menstruation is an aspect of health, not illness — turned the prevailing wisdom upside down.

She did it with data, sending out questionnaires asking respondents about their periods. How long did they bleed and how much? Did it hurt? How far could they walk? How many hours did they spend at work? In school? She recorded volunteers’ heart rate, muscle strength, temperature.

Menstruation was no obstacle to achievement, Putnam Jacobi confirmed, nor did gynecological problems result from female ambition. Using the mind did not steal vital energy from the womb and the men who insisted on this zero-sum connection were, as she wrote with trademark tartness, reducing women “to the anatomical level of the crustacea.” (During this year of intense research, not incidentally, she gave birth to a healthy baby boy.)

In her own practice, she battled the misogyny of celebrity doctors like S. Weir Mitchell, a champion of the rest cure, who treated his affluent clientele of “neurasthenic” ladies with isolation, bed rest, massage, force-feeding, electric shocks and his own domineering charisma.

He sent them home with instructions to “live as domestic a life as possible” — exactly the kind of stifling existence that made his patients unwell in the first place. One of them, Charlotte Perkins Gilman, would write “The Yellow Wallpaper,” a horror story born of her own treatment that became a classic early-feminist text. In a satisfying turn, Gilman’s work inspired Putnam Jacobi to offer her medical services. Her prescription of study, drawing, writing and — delightfully — basketball restored her famous patient’s sense of agency.

Outside the consulting room, Putnam Jacobi worked to improve lives on a scale far beyond the individual, galvanizing a network of powerful friends into underwriting the admission of female students to medical schools and lending her strategic mind to the suffrage movement.

There was tragedy. Her beloved son died, aged 8, from diphtheria, while her husband, the pre-eminent expert on the disease, stood by, powerless to save him in an era before vaccines. Her final published paper, written in her early 60s, was titled “Description of the Early Symptoms of the Meningeal Tumor Compressing the Cerebellum, From Which the Author Died. Written by Herself.” It’s hard to imagine a more complete commitment to medicine.

Putnam Jacobi’s life story has everything: ambition, partnership, triumph and loss. What’s missing, to the chagrin of the biographer, is the kind of archival depth — journals, letters, diaries — that allows access to unfiltered emotion, and makes a subject’s passions and peculiarities jump off the page.

Lydia Reeder tells Putnam Jacobi’s story with uncritical enthusiasm and relies heavily on the work of previous scholars. She digresses at length into the lives of parallel figures, tangling her chronology, and she indulges in sentimental moments of seeming speculation. “Sometimes while they worked, their hands touched, causing Mary to feel electrified,” Reeder writes of Putnam Jacobi’s first love. Better to let her subject’s electrifying record speak for itself.

“The Cure for Women” reintroduces its subject as a hero for this moment. With relentless hard work, hard science and sharp analysis, Putnam Jacobi changed the ancient narrative that men had written for women. Writing a better narrative for women remains an urgent task.