Chapter 1: The Foundation of Modern Mathematics

Mathematics is the cornerstone of contemporary society, built upon the remarkable contributions of countless exceptional individuals. These explorers, innovators, and problem solvers have expanded our understanding and reshaped our perception of the world.

Who stands as the most significant mathematician in history? How can one even determine that? Is it based on creative brilliance, prolific output, or the resolution of pivotal mathematical problems? This article presents a visualization of the greatest mathematicians, ranked according to their influence on mathematics today.

The primary sections include:

• An interactive data visualization.
• Insights into the top 10 ranked mathematicians.
• A categorized list of top mathematicians by discipline.
• An overview of the ranking methodology.

The Greatest Mathematicians: An Interactive Visualization

(Give it 10-20 seconds to load.)

You can click on a mathematician's image to reveal their name and additional details, or select a topic button to display the top-ranked mathematicians in that area.

Chapter 2: The Ten Most Influential Mathematicians

1. David Hilbert

While opinions may vary on his top ranking, Hilbert undeniably made significant contributions across various fields, including geometry, number theory, logic, and mathematical physics. His 1900 presentation of "Hilbert's problems" profoundly influenced subsequent mathematical research.

2. Albert Einstein

If you ask someone to name a mathematician, they’re likely to say Einstein, whose name is synonymous with genius. His groundbreaking work in 1905 with the Special Theory of Relativity, followed by the General Theory of Relativity a decade later, transformed our understanding of space and time.

3. Leonhard Euler

Euler is credited with establishing graph theory and topology, and his name appears throughout mathematical literature—Euler’s number, identity, and theorem are just a few examples. Gauss remarked that studying Euler’s work is unmatched in preparing one for various mathematical fields.

4. Carl Friedrich Gauss

From a young prodigy to the "prince of mathematicians," Gauss influenced nearly all branches of mathematics. His legacy is evident in terminology, including Gaussian distribution and Gaussian elimination.

5. Isaac Newton

Whether seen as a madman or a genius, Newton played a pivotal role in emerging from the Dark Ages. His laws of motion and the development of calculus are monumental achievements, alongside his famous rivalry with Leibniz.

6. Bernhard Riemann

This German mathematician introduced the Riemann integral, Riemannian manifolds, and the Riemann zeta function, with the Riemann hypothesis remaining one of the most famous unsolved problems today.

7. Euclid

Over 2,300 years ago, Euclid established the fundamentals of geometry and number theory, which continued to be foundational for millennia. His work, "Elements," still serves as the basis for high school geometry.

8. Henri Poincaré

Poincaré's diverse contributions to pure mathematics, physics, and engineering earned him a place among the greats of the late 19th century. The Poincaré conjecture's solution by Grigori Perelman was a landmark achievement in modern mathematics.

9. Aristotle

Primarily recognized for his philosophical contributions, Aristotle's inclusion on this list may surprise some. Nevertheless, he laid the groundwork for formal logic, which shaped Western education for generations.

10. Sophus Lie

Lie pioneered the theory of continuous symmetry, applying it to geometry and differential equations. His concepts, Lie groups and Lie algebras, continue to be significant in pure mathematics, physics, computer science, and statistics.

Chapter 3: Top Mathematicians by Discipline

• Algebra
  1. Sophus Lie
  2. John von Neumann
  3. David Hilbert
• Combinatorics
  1. Paul Erdős
  2. August Ferdinand Möbius
  3. Terence Tao
• Differential Equations
  1. Leonhard Euler
  2. Isaac Newton
  3. Sophus Lie
• Geometry
  1. Euclid
  2. Albert Einstein
  3. Carl Friedrich Gauss
• Graph Theory
  1. Paul Erdős
  2. Leonhard Euler
  3. László Lovász
• Group Theory
  1. Évariste Galois
  2. Sophus Lie
  3. Felix Klein
• Linear Algebra
  1. Alston Scott Householder
  2. Alexandre Théophile Vandermonde
  3. Hermann Grassmann
• Number Theory
  1. Carl Friedrich Gauss
  2. Leonhard Euler
  3. 7. 8. Hardy
• Probability
  1. Pierre Simon Laplace
  2. Andrey Kolmogorov
  3. Siméon Denis Poisson
• Set Theory
  1. Georg Cantor
  2. Ernst Zermelo
  3. Bertrand Russell
• Statistics
  1. Ronald Fisher
  2. Karl Pearson
  3. Albert Einstein
• Topology
  1. Henri Poincaré
  2. Bernhard Riemann
  3. David Hilbert

Chapter 4: Understanding the Ranking Methodology

In crafting this article and accompanying data visualization, I considered two potential data sources for ranking: mathematicians referenced on Wikipedia and those cited in papers on arxiv.org. Both sources are freely accessible and abundant in data, yet extracting meaningful rankings posed challenges.

Fortunately, I found that Academic Influence had developed a ranking system for scholars and institutions. Their machine learning model integrates data from Wikipedia, Wikidata, Crossref, and Semantic Scholar for ranking purposes. Although their model is not open source, they provide a concise overview on their website:

"In assessing influence by discipline for individuals, the InfluenceRanking engine avoids making influence a popularity contest. The focus is not on the sheer number of mentions but rather on the intersection of name and discipline mentions, awarding proximity of these mentions and tracking relevant hyperlinks and the digital space dedicated to them." — academicinfluence.com

This approach resembles Google's PageRank, where each site is assigned an authority score that informs the weighting of links and content.

Debate over the rankings is inevitable; every model has limitations, and objectivity regarding "influence" is complex. Throughout the visualization process, I encountered several rankings that appeared questionable, such as Einstein being listed as #3 in Statistics.

Feel free to share your thoughts—your feedback is welcome!