1. Srinivasa Ramanujan

India's mathematician Srinivasa Ramanujan. Photo courtesy of CFAL India

Active in the early 20th century, Ramanujan made major contributions to mathematical analysis, number theory, infinite series and continued fractions that continue to influence mathematics and science more than a century after his death at age 32.

Born into a poor family in southern India in 1887, he largely taught himself mathematics using borrowed and outdated textbooks. His fascination with numbers was so intense that he neglected other subjects, causing him to lose scholarships and fail university exams despite his exceptional talent.

After an arranged marriage in 1909, Ramanujan was forced to work to support his family but continued pursuing mathematics, often carrying out calculations on stone slabs because he could not afford enough paper. His fortunes changed after he wrote to British mathematician Godfrey H. Hardy, who recognized his extraordinary ability and helped bring him to the University of Cambridge in the U.K.

Although he never received formal training in advanced mathematics, Ramanujan produced thousands of original results, many of them decades ahead of their time. His discoveries continue to influence modern mathematics and physics, including research into black holes and quantum theory.

India has observed National Mathematics Day every year since 2012 on Dec. 22, Ramanujan's birthday, to honor his contributions to the field.

2. Stefan Banach

Widely regarded as one of the most important mathematicians of the 20th century, Banach laid the foundations of modern functional analysis, a branch of mathematics that studies functions and their properties.

Born in Krakow, Poland, in 1892, Banach studied engineering rather than mathematics. Financial hardship and World War I interrupted his education, and much of his mathematical knowledge came through independent study.

His life changed after Polish mathematician Hugo Steinhaus overheard him discussing advanced mathematical concepts in a public park. Impressed by his talent, Steinhaus befriended the young Banach and later described him as his "greatest scientific discovery," as reported by The Independent.

Banach published influential research while working outside academia and eventually awarded a doctorate from the University of Lvov in 1922. He went on to establish the renowned Lwow School of Mathematics and founded the journal Studia Mathematica in 1929.

3. Oliver Heaviside

British mathematician Oliver Heaviside. Photo from X

Heaviside, an English self-taught mathematician and physicist, helped revolutionize electrical engineering despite leaving school at age 16. Born in London in 1850, Heaviside grew up in poverty and suffered partial deafness after contracting scarlet fever as a child. The condition made school difficult, and he received little formal education, according to U.K.-based higher education analyst Quacquarelli Symonds.

Determined to continue learning, he studied independently with support from his uncle, Sir Charles Wheatstone, a pioneer of telegraph technology. He later worked as a telegraph operator, where practical problems sparked his interest in applying mathematics to electrical systems.

Heaviside developed mathematical methods that simplified the analysis of electrical circuits and helped pave the way for modern telecommunications. He also predicted the existence of the ionosphere, the layer of Earth's atmosphere that reflects radio waves and enables long-distance radio communication.

4. Mary Everest Boole

Born in England in 1832, Boole was largely self-taught in mathematics after leaving formal schooling at age 11. At a time when women faced major barriers to higher education, she continued studying independently from textbooks and later received guidance from English mathematician George Boole, whose work laid the foundations for modern computing and who later became her husband.

Despite never earning a university degree in mathematics, Boole became a pioneering mathematics educator. While working at Queen's College London, she developed innovative ways of teaching mathematical concepts through play, experimentation and everyday objects rather than rote memorization.

She went on to publish influential works including "Philosophy and Fun of Algebra" and advocated hands-on learning long before it became widely accepted. Many of the teaching methods she promoted more than a century ago are still used in mathematics classrooms today, according to the U.K.'s Institute of Mathematics and its Applications.

Although often overshadowed by her husband's fame, Boole established her own legacy as a leading mathematics educator whose ideas helped transform how children learn mathematics.

5. Florence Nightingale

Florence Nightingale, a pioneering nurse and mathematician. Photo courtesy of the U.K.'s Science Museum

Nightingale is best known as the founder of modern nursing, but she was also a pioneering statistician whose work transformed public health.

Born in Florence, Italy, in 1820 to an English family, Nightingale did not study mathematics at university. Instead, she learned mathematics, languages and philosophy from her father and developed a strong interest in statistics from an early age.

During the Crimean War from 1853 to 1856, she systematically collected and analyzed data on disease, injuries and deaths among soldiers. Her findings revealed that poor sanitation, rather than battlefield wounds, was responsible for many fatalities.

According to the U.K.'s Science Museum, her statistical work helped drive major reforms in military and civilian healthcare. Nightingale was also among the first people to use circular diagrams to visualize data and is credited with developing the polar area diagram, also known as the "coxcomb chart." Her work helped popularize the use of statistical graphics, which became a common way of presenting complex information to people without mathematical training in the decades that followed.