Top 10 Women Mathematicians Who Changed the World of Mathematics (Remaining 5)

6. Shakuntala Devi — The Human Computer:

Shakuntala Devi was an extraordinary Indian mathematician who became globally famous as the "Human Computer" for her incredible mental calculation abilities. Born on November 4, 1929, in Bangalore, Karnataka. Shakuntala Devi came from a humble background. Her father, C.V. Sundararaja Rao, worked as a circus performer - a trapeze artist, lion tamer, tightrope walker, and magician. The discovery of her mathematical genius happened by pure chance when she was just three years old.

By age six, Shakuntala Devi was already performing at prestigious institutions like the University of Mysore, solving complex arithmetic problems without any formal education. She could handle numbers ranging from 13 to 200 digits, calculating square roots, cube roots, and performing multiplication and division with lightning speed.Despite her family's financial struggles, which prevented her from receiving formal schooling (she attended only three months of regular education), her natural mathematical abilities continued to flourish. At age 15, she moved to London with her father, marking the beginning of her international career.

World-Famous Achievements:

Shakuntala Devi's most celebrated accomplishments include several record-breaking calculations that astounded mathematicians and computer scientists worldwide:

• The Guinness World Record (1980): At Imperial College London, she multiplied two randomly selected 13-digit numbers (7,686,369,774,870 × 2,465,099,745,779) and provided the correct 26-digit answer (18,947,668,177,995,426,462,773,730) in just 28 seconds. This included the time it took her to speak the answer aloud.
• The 23rd Root Challenge (1977): At Southern Methodist University in Dallas, she calculated the 23rd root of a 201-digit number in 50 seconds, giving the answer as 546,372,891. A UNIVAC 1101 computer took 62 seconds to perform the same calculation.
• Lightning-Fast Calculations: She could instantly tell you what day of the week any date fell on, calculate cube roots of massive numbers in seconds, and solve complex mathematical problems faster than most people could write them down.

Beyond Numbers: Her Other Contributions

Shakuntala Devi was much more than just a calculator. She was a prolific author who wrote over 20 books covering various subjects:

Mathematics Books:

• "Figuring: The Joy of Numbers" - Her methods for mental calculations
• "Puzzles to Puzzle You" - Over 150 mathematical puzzles
• "More Puzzles to Puzzle You" - Over 300 brain teasers
• "In the Wonderland of Numbers"
• "The Book of Numbers"

Impact Today:

• Her mental-math techniques are integrated into modern math competitions and ed-tech apps teaching rapid calculation.
• Devi's advocacy for joyful, accessible mathematics supports initiatives to reduce math anxiety and promote numeracy in schools.

7.Emmy Noether (1882–1935):

Amalie Emmy Noether was born on March 23, 1882, in Erlangen, Germany, to mathematician Max Noether. Initially certified to teach French and English, she chose to study mathematics at the University of Erlangen-Nuremberg, earning her PhD in 1907 under Paul Gordan for a dissertation on algebraic invariants.

Despite her doctorate, women were barred from academic posts. From 1907 to 1914, Noether worked unpaid at Erlangen's Mathematical Institute. In 1915, David Hilbert and Felix Klein invited her to the University of Göttingen, then a global mathematics center. Although objections forced her to lecture under Hilbert's name until 1919, she secured habilitation that year, becoming Göttingen's first female Privatdozent.

Mathematical Work

1907–1919 (Invariants and Physics):

– Proved Noether's First and Second Theorems, establishing that every continuous symmetry of a physical system's action yields a conservation law (e.g., time invariance ⇒ energy conservation).

1920–1926 (Abstract Algebra – Ideals and Rings):

– Collaborated with Werner Schmeidler to define left/right ideals in rings.

– Published Idealtheorie in Ringbereichen (1921), proving the Lasker–Noether theorem and introducing the “ascending chain condition” concept; objects satisfying it are now called Noetherian.

1927–1935 (Noncommutative Algebras and Topology):

– Advanced the study of noncommutative algebras with Brauer and Hasse.

– Pioneered algebraic topology by suggesting homology groups as cycle-quotient groups, simplifying the Euler–Poincaré formula.

Impact Today

• Theoretical Physics: Noether's theorem remains indispensable in research on fundamental interactions, particle physics, and cosmology.
• Mathematics Education: University courses in rings and fields, algebraic topology, and invariant theory are structured around Noether's concepts, ensuring students learn "begriffliche Mathematik"—purely conceptual mathematics.
• Women in STEM: Recognized by Einstein as "the most significant creative mathematical genius" since women's higher education began, Noether's life inspires initiatives and fellowships (e.g., Noether Fellowships) supporting women mathematicians and scientists.

8. Maryam Mirzakhani (1977–2017)

Maryam Mirzakhani was born on May 12, 1977, in Tehran, Iran. From a young age, she excelled in mathematics, winning gold medals at the International Mathematical Olympiads in 1994 and 1995. She earned her B.Sc. in mathematics from Sharif University of Technology in 1999 and completed her Ph.D. at Harvard University in 2004 under Fields Medalist Curtis McMullen. 

Her doctoral thesis, Simple Geodesics on Hyperbolic Surfaces and Volume of the Moduli Space of Curves, solved longstanding problems in counting simple closed geodesics on hyperbolic surfaces and established volume formulas for moduli spaces.Maryam Mirzakhani's work on the geometry and dynamics of Riemann surfaces and their moduli spaces reshaped modern mathematics, earning her the Fields Medal in 2014 as the first woman and first Iranian recipient. Her insights continue to influence geometry, topology, and theoretical physics today.

Major Research Contributions

1. Counting Simple Closed Geodesics

Mirzakhani proved that "prime number theorem for geodesics" from exponential growth to precise polynomial asymptotics, unlocking the deep interplay between geometry and counting problems on surfaces.

2. Moduli Space Volume Formulas

By deriving a recursive volume formula for the moduli space of bounded Riemann surfaces, Mirzakhani linked geodesic counting to volume calculations in moduli space. Her work provided a new proof of the Witten–Kontsevich formula for intersection numbers on moduli space, bridging hyperbolic geometry, complex analysis, and algebraic geometry.

3. Teichmüller Dynamics and Earthquake Flow

She proved the long-standing conjecture that Thurston's earthquake flow on Teichmüller space is ergodic, showing that, over time, almost every trajectory equidistributes with respect to the natural measure. This result deepened understanding of the chaotic dynamics on moduli spaces and its connections to low-dimensional topology.

4. Rigidity of Complex Geodesics

In collaboration with Alex Eskin and Amir Mohammadi, Mirzakhani demonstrated that the closures of complex geodesics in moduli space are algebraic varieties rather than fractal sets. This "Magic Wand Theorem" revealed remarkable rigidity and regularity properties in a fundamentally inhomogeneous space, analogous to Ratner's theorems on homogeneous dynamics.

Impact Today

• Geometry & Topology: Mirzakhani's volume formulas and counting results underpin current research in low-dimensional topology, string theory, and quantum gravity, where moduli spaces play a critical role.
• Dynamical Systems: Her work on earthquake flow and rigidity informs studies of chaotic systems in mathematics and physics, influencing models in statistical mechanics and cosmology.
• Women in Mathematics: As the first woman Fields Medalist, she inspired global initiatives—such as the May12 Initiative, Maryam Mirzakhani New Frontiers Prize, and Maryam Mirzakhani Women in Mathematics Awards—promoting gender diversity in mathematical sciences.
• Educational Outreach: Her story and achievements feature prominently in university curricula, public lectures, and popular media, motivating young mathematicians to pursue research in geometry and dynamical systems.

9. Sophie Germain (1776–1831)

Born Marie-Sophie Germain on April 1, 1776, in Paris, she was the daughter of a prosperous silk merchant whose library fueled her self-education in mathematics. 

At a time when women were barred from École Polytechnique, she adopted the pseudonym "M. Le Blanc" to obtain lecture notes and corresponded with leading mathematicians, including Adrien-Marie Legendre and Carl Friedrich Gauss, who only discovered her identity in 1807.Sophie Germain's groundbreaking work on Fermat's Last Theorem and the mathematical theory of elasticity laid enduring foundations in number theory, cryptography, and engineering mechanics.

Number Theory Contributions

Sophie Germain Primes and Fermat's Last Theorem

• Germain tackled Fermat's Last Theorem by proving what is now known as Sophie Germain's Theorem: for an odd prime exponent p, if there exists an auxiliary prime q such that   and q does not divide any of the nonzero pth-power residues modulo q, then no nontrivial solution to to exists.
• She demonstrated this condition for all primes p<100 and showed that potential counterexamples must be exceptionally large, pioneering a "large-size" approach to Diophantine problems.
• Sophie Germain primes—primes p for which 2p+1 is also prime—bear her name, reflecting her study of primes critical to the auxiliary-prime strategy.

Elasticity Theory and Prize Recognition

• In 1809, the Paris Academy of Sciences offered a prize for a mathematical theory of vibrating elastic surfaces (Cladni plates). Germain submitted the only entry in 1809, 1813, and 1816, gradually refining her analysis despite initial critiques of rigor.
• Her third memoir won the Grand Prize in 1816 for deriving correct equations governing elastic vibrations on curved surfaces—foundational work for modern solid mechanics and structural engineering.

Impact Today

• Cryptography & Computing: Sophie Germain primes are vital in public-key cryptography (e.g., Diffie–Hellman key exchange), influencing secure digital communications.
• Engineering & Materials Science: Her elasticity equations underpin modern finite element analysis and the design of structures subject to dynamic loads (bridges, aircraft wings).
• Mathematics Education: Her story is taught as a paradigm of self-learning and resilience; Number
• theory courses highlight her theorem and primes in advanced modular arithmetic topics.

10.Katherine Johnson (1918–2020)

Creola Katherine Coleman was born on August 26, 1918, in White Sulfur Springs, West Virginia. A child prodigy, she completed high school at 14 and graduated summa cum laude with degrees in mathematics and French from West Virginia State College at 18. Despite segregation and gender bias, she became one of the first three African-American students admitted to West Virginia University's graduate program in mathematics.

She is doing mastery of orbital mechanics and her role in verifying critical spaceflight trajectories were essential to the success of America's crewed missions—from Alan Shepard's suborbital flight to Apollo's lunar landing. Her legacy endures in STEM diversity initiatives and computational research.

NACA/NASA Career Beginnings

In June 1953, Johnson joined the National Advisory Committee for Aeronautics (NACA) at Langley as a "human computer," calculating flight data in a segregated pool of female mathematicians. Her skill in analytical geometry earned her a transfer to the all-male Flight Research Division, where she attended engineering meetings—breaking gender and racial barriers.

Pivotal Spaceflight Contributions

• Freedom 7 Trajectory (1961): Johnson calculated the launch window and splashdown coordinates for Alan Shepard's suborbital flight, America's first human space mission.
• Friendship 7 Verification (1962): For John Glenn's orbital flight, she hand-computed Glenn's trajectory to confirm IBM computer results—Glenn insisted, "If she says they're good, then I'm ready to go".
• Apollo 11 and Apollo 13 Support: Johnson developed rendezvous and backup reentry procedures, enabling the first Moon landing and the safe return of Apollo 13's crew after an in-flight emergency.
• Space Shuttle and Earth Resources Satellite: In later decades, she contributed to trajectory analysis for the Shuttle program and the Landsat Earth-observation satellite.

Awards and Honors

• Presidential Medal of Freedom (2015): Awarded by President Barack Obama for her "refusal to be limited by society's expectations of her gender and race".
• Congressional Gold Medal (2019): Honored by the U.S. Congress for her pioneering space science contributions.
• NASA Facilities Named: The Katherine G. Johnson Computational Research Facility at Langley (2016) and the Katherine Johnson Independent Verification and Validation Facility in West Virginia (2019)

Impact Today

• Diversity: Johnson's achievements underpin diversity programs and scholarships encouraging underrepresented groups in science and engineering.
• Computational Research: The facility bearing her name advances cutting-edge computational methods, continuing her legacy in human-computer collaboration.
• Educational Inspiration: Her life is a staple in STEM curricula and outreach, demonstrating how rigorous mathematics and determination can propel humanity to the stars.
• Computational Research: The facility bearing her name advances cutting-edge computational methods, continuing her legacy in human-computer
• collaboration.Educational Inspiration: Her life is a staple in STEM curricula and outreach, demonstrating how rigorous mathematics and determination can propel humanity to the stars.

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