Number theory

110 cards. Each one is a 40-second story with a five-minute read behind it. Page 2 of 2.

61. Why mathematicians might jokingly label certain numbers as evil or problematicThis video explores the playful side of mathematics, where numbers are sometimes framed as problematic or evil. It highlights how even simple-sounding problems can lead to unexpec…
62. Why prime numbers never end: Euclid's elegant proof of mathematical infinityMathematician Eddie Woo explores the question of whether prime numbers eventually run out. By revisiting Euclid's classic proof, this video demonstrates how a simple, efficient lo…
63. Does adding every positive integer really result in a negative fraction?Mathematician Eddie Woo explores a famous and contentious calculation where summing all counting numbers appears to yield a specific, finite value. This video examines the logic b…
64. Why does this simple mathematical statement remain an unproven mystery for modern experts?This video examines a mathematical theorem that appears intuitively correct yet defies formal proof. It features insights from a wide range of mathematicians and researchers who e…
65. What is the oldest unsolved problem in mathematics that remains a mystery today?This video explores the history and enduring challenge of the oldest unsolved problem in mathematics. It features insights from experts like Professor Pace Nielsen, Dr. Asaf Karag…
66. How a modern mathematical discovery fundamentally changed our understanding of the constant pi.This video explores a significant mathematical breakthrough that reshaped the study of pi. Featuring insights from Rutgers University professor Alex Kontorovich, it examines the e…
67. Why does this simple arithmetic sequence baffle the world's greatest mathematicians?The Collatz conjecture, also known as the 3x+1 problem, is a deceptively simple mathematical sequence that remains unsolved. This video explores the mechanics of the problem and t…
68. What happens when you repeatedly square a number? The answer is surprisingly complex.This video explores the mathematical consequences of repeatedly squaring numbers. By examining the work of mathematicians like Neal Koblitz and Alex Kontorovich, it reveals the de…
69. Are alphamagic squares the most impressive mathematical grid ever discovered?Matt Parker explores the curious world of alphamagic squares, a mathematical curiosity where the letters of the numbers in a square form a new, equally valid magic square. This vi…
70. Can you divide a whole into thirds using only the process of halving?This video explores the mathematical concept of Thirdsday, a method for finding thirds by repeatedly applying halves. It highlights the work of Jim Propp and James Tanton, offerin…
71. Why solar eclipse cycles share a mathematical secret with the constant piMathematician Matt Parker explores the surprising connection between calculating pi and predicting solar eclipses. By using continued fractions, you can approximate both phenomena…
72. Can the tangent of an integer ever exceed the integer itself?Mathematician Matt Parker explores a specific class of integers where the tangent function produces a value larger than the input. This investigation highlights a curious property…
73. Can a matrix be a vampire? Exploring the mathematics of self-referential structures.This video investigates the concept of a vampire matrix, a mathematical curiosity involving matrices that relate to their own characteristic polynomials. It serves as an invitatio…
74. Can you discover your own mathematical triple for the famous ABC conjecture?Mathematician Matt Parker explores the ABC conjecture, a deep problem in number theory. This video guides you through the process of finding your own triples, offering a practical…
75. How abstract group theory unlocks fundamental secrets of number theoryUlrike Tillmann demonstrates how the principles of group theory can be applied to derive specific results in number theory. This lecture provides a foundational look at how these …
76. Oxford mathematicians explain their cutting-edge research in under two minutes each.This series features Oxford researchers distilling complex work into brief, accessible summaries. From quantum topology to social media contagion, these clips provide a window int…
77. Oxford mathematicians explain their latest research in under two minutes eachThis video series showcases Oxford researchers distilling complex work into brief, accessible summaries. It is a valuable look at how modern mathematical inquiry addresses practic…
78. Why a Fields Medal winner ignores warnings to pursue the world's hardest math problemsJames Maynard, a 2022 Fields Medal recipient, built his career by tackling notorious number theory problems that experts deemed unsolvable. Driven by an aesthetic obsession with p…
79. A 26-year-old mathematician has finally solved the long-standing Erdős Primitive Set ConjectureFor decades, the Erdős Primitive Set Conjecture remained an unsolved mystery in mathematics. Now, Oxford graduate student Jared Duker Lichtman has provided a proof. This video fea…
80. Why Dirichlet series are the fundamental building blocks of modern analytic number theoryThis lecture introduces arithmetic generating functions, specifically Dirichlet series, and their connection to the Riemann Zeta function. It provides a window into the advanced c…
81. How do mathematicians use analysis to uncover the secrets of prime numbers?Fields Medallist James Maynard introduces the core concepts of analytic number theory in this advanced Oxford lecture. By applying techniques from mathematical analysis to the stu…
82. How the Euclidean algorithm unlocks solutions to linear Diophantine equationsThis lecture from the Oxford Mathematics first-year undergraduate course explains how to solve linear Diophantine equations. By leveraging quotients derived from the Euclidean alg…
83. Why the number 16 is more than just a perfect squareExplore the unique properties of the number 16 and discover how a chance encounter at a specific table number sparked a larger mathematical journey for Matt Parker.
84. Why Endre Szemerédi was awarded the 2012 Abel Prize for his groundbreaking mathematics work.This video explores the prestigious Abel Prize, often considered the Nobel Prize of mathematics, and its 2012 recipient, Endre Szemerédi. It highlights the significant financial a…
85. Are there only three pairs of Brown Numbers in the entire infinite number line?Mathematicians have identified three specific pairs of numbers known as Brown Numbers, yet no one has proven that more do not exist. This video explores Brocard's Problem, a mathe…
86. Could you invent a new sequence of numbers and name it after yourself?Professor Copeland explores Keith numbers, also called repfigit numbers, which follow a repetitive Fibonacci-like pattern. Mike Keith explains how these sequences work and offers …
87. Why Graham's Number is far larger than you can possibly imagineThis video corrects a previous attempt to explain the true scale of Graham's Number. It serves as a standalone guide to understanding a figure so vast that it defies human intuiti…
88. Why Graham's Number is too vast for the human mind to comprehendMathematician Ron Graham attempts to explain the unfathomable scale of Graham's Number. This video explores the limits of mathematical notation and why even simple-looking express…
89. What are glitch primes and binary cyclops numbers in recreational mathematics?Mathematician Simon Pampena explores the curious properties of glitch primes and binary cyclops numbers. This video offers an accessible dive into these niche numerical concepts, …
90. Why is the number 33 such a persistent mystery for mathematicians?Mathematicians have long sought to express integers as the sum of three cubes. While many numbers have been solved, 33 remains the lowest integer that continues to defy a simple s…
91. Can a single sentence really solve a famous prime number puzzle?Matthias Kreck of the University of Bonn explores a classic prime number challenge originally proposed by Fermat. This video examines the history of the problem and the elegant, o…
92. Visualizing the Collatz Conjecture through a unique spectrum of mathematical colorAlex Bellos explores the Collatz Conjecture by mapping it into a colorful visual representation. This video highlights how abstract mathematical sequences can be transformed into …
93. Can you reach every number using only four fours and basic math?The Four 4s is a classic mathematical puzzle that challenges you to represent every integer using exactly four fours. This video explores the history of this famous problem and fe…
94. Discover the hidden mathematical patterns within the famous structure of Pascal's TriangleCasandra Monroe, a Princeton undergraduate, explores the intriguing properties of Pascal's Triangle. This video offers a concise look at the patterns embedded within this classic …
95. How a simple mathematical constant connects to the infinite sum of cubesTony Padilla, a physics educator at the University of Nottingham, explores the zeta function and the mysterious value known as Apéry's constant. This video breaks down the signifi…
96. Can you represent every natural number using only the digits one through nine?This video explores the mathematical challenge of representing natural numbers using the digits one through nine in increasing or decreasing order. It highlights the work of Inder…
97. Can we prove that there are infinitely many pairs of twin prime numbers?The Twin Prime Conjecture remains one of the most famous unsolved problems in mathematics. This video features Dr. James Maynard, a prominent mathematician who has contributed sig…
98. Is mathematics a process of discovery or a feat of human invention?This video explores the profound tension between mathematical discovery and invention. Through the lens of infinite sums, it examines how mathematicians navigate the boundary betw…
99. Why Does Squaring a Prime Number Always Yield a Specific Pattern?When you square any prime number, the resulting sequence of digits often reveals unexpected, beautiful patterns. This mathematical curiosity suggests a deeper, underlying structur…
100. The hidden patterns found within mathematical sequencesExplore the intricate beauty of mathematics through a visual journey into sequences. This video presents a collection of fascinating numerical patterns, demonstrating how complex …
101. Can a computer program resolve mathematics' most bitter dispute?In 2012, Shinichi Mochizuki claimed to have proven the ABC conjecture, but his 500-page proof sparked a decade of intense controversy. This video explores the mathematical impasse…
102. Can you find hidden images within the infinite digits of pi?Explore the fascinating intersection of mathematics and art. This video examines the concept of 'picture primes' and the creative methods used to uncover recognizable patterns and…
103. What is the hidden meaning behind this infinite string of digits?At first glance, this sequence of numbers appears entirely random. However, this video explores the mathematical identity hidden within the decimal expansion of a specific, signif…
104. Can we actually prove that one plus one equals two?Explore the fundamental origins of mathematics. This video traces the evolution of counting, the emergence of zero and negative numbers, and the complex distinctions between ratio…
105. Can the fundamental laws of arithmetic be generalized to more complex structures?This lecture from Dawid Kielak’s third-year course at Oxford explores the foundations of commutative algebra. It examines how the familiar process of breaking numbers and polynomi…
106. Why the number 210 holds a special place in number theoryExplore the mathematical significance of 210 and its unique connection to Goldbach's Conjecture. Professor Carl Pomerance of Dartmouth College explains why this specific integer i…
107. How a mathematician left a prime number gift for his collegeDiscover the construction of the Trinity Hall Prime. This video explores how Professor McKee engineered a specific prime number with a hidden pattern, using a clever method to ens…
108. Can a single number break the logic of Pythagorean triples?In this video, mathematician James Grime explores a fascinating proof involving Pythagorean triples. Discover how a specific numerical problem challenges our understanding of thes…
109. What happens to prime numbers when you redefine the rules of math?Explore the whimsical world of Lunar Arithmetic, also known as Dismal Arithmetic. This video examines how mathematical structures change when we intentionally bend the rules, inve…
110. Could a massive number break the Mertens Conjecture?Mathematics often relies on patterns that appear unbreakable, until they aren't. This video explores the Mertens Conjecture and the staggering scale of the numbers required to pot…

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