Mathematician Gerd Faltings Solves 60-Year-Old Mystery, Awarded 2026 Abel Prize

Gerd Faltings Wins 2026 Abel Prize

Gerd Faltings Wins 2026 Abel Prize

Peter Badge/Typos1

Gerd Faltings has been awarded the prestigious 2026 Abel Prize, often regarded as the “Nobel Prize of Mathematics,” in recognition of his revolutionary proof that reshaped mathematics in 1983. His seminal work laid the foundation for arithmetic geometry, a crucial domain in contemporary mathematics.

Faltings’ landmark achievement was his proof of the Mordell Conjecture, for which he was honored with the Fields Medal in 1986. This theorem, initially proposed by Louis Mordell in 1922, asserts that complex equations yield fewer solutions as their complexity increases.

Based at the Max Planck Institute for Mathematics in Germany, Faltings expressed his honor upon receiving the award, maintaining a modest view of his contributions. “Someone remarked that climbing Mount Everest was a challenge merely because the mountain exists,” Faltings stated. “While solving the Mordell Conjecture is a significant achievement, it doesn’t lead to cures for cancer or Alzheimer’s; it merely expands our understanding.”

The Mordell Conjecture pertains to Diophantine equations—an extensive category encompassing renowned equations like a² + b² = c², associated with the Pythagorean theorem, and aⁿ + bⁿ = cⁿ, pivotal to Fermat’s Last Theorem. The conjecture investigates which of these equations have infinitely many solutions and which possess only finite solutions.

Mordell suggested that by rewriting these equations as complex numbers, essentially two-dimensional numbers plotted on surfaces, the number of solutions is influenced by the number of “holes” in those surfaces. He postulated that surfaces with more holes than a donut could only possess a finite number of rational solutions but lacked proof for this hypothesis.

Faltings’ validation of Mordell’s intuition over six decades later astonished the mathematical community—not only for its findings but also for the innovative methods employed. His proofs harmonized concepts from distinct mathematical realms, including geometry and arithmetic. “It’s remarkably concise, almost miraculous,” states Akshay Venkatesh from the Institute for Advanced Study in Princeton. “Spanning just 18 pages, it intricately navigates various techniques and perspectives.”

Faltings attributes his success to his ability to embrace uncertainty and take bold risks based on unverified hunches. “Sometimes, you’re ahead of those who attempt to prove everything immediately, yet you may also err,” he observes.

“One remarkable aspect of his argument is its extensive coverage and coherence,” Venkatesh notes. “One wonders how he could trust the interconnection of these pieces before knowing how they would align.”

Many conjectures that Faltings resolved, along with the methodologies he pioneered, now underpin the most significant areas of mathematical research. For instance, p-adic Hodge theory explores the relationships between the geometry of shapes and their underlying structure while utilizing an entirely different number system. His work paved the way for Andrew Wiles’ proof of Fermat’s Last Theorem and mentored Shinichi Mochizuki, the prominent mathematician credited with resolving the ABC conjecture.

Faltings admits that his aim was never to tackle phenomena with such monumental implications. “My philosophy is that you shouldn’t pursue fame or wealth, but rather pursue what you love,” he concludes. “It’s far more enjoyable to work in a field that you are passionate about.”

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Source: www.newscientist.com

Why Jeff Goldblum Should Star in a Movie About This Legendary Mathematician

Paul Erdős and Jeff Goldblum resemblance

Striking Resemblance between Paul Erdős and Jeff Goldblum

Public domain; Matt Baron/BEI/Shutterstock

In my latest mathematics column, I present an exciting idea: Hollywood should create a comedic biopic about Paul Erdős, one of history’s greatest mathematicians.

Why does Erdős, pronounced “air-dish,” deserve such recognition? With approximately 1,500 published papers, he is arguably the most prolific mathematician of all time. Known for his innovative collaborations, Erdős made significant contributions to various mathematical fields, including probability, number theory, and graph theory.

Born in Hungary in 1913, Erdős had a nomadic lifestyle, often traveling without a permanent residence. Following the rise of Nazism in Europe, he relocated to the United States in 1938. However, due to his connections to communist sympathizers, he faced entry issues in the 1950s and 1960s. He famously carried a suitcase of his belongings and visited fellow mathematicians, offering to collaborate with the phrase “My brain is open.” His unique approach allowed him to work on groundbreaking mathematics.

Many fascinating stories about Erdős are chronicled in A Man Who Loved Only Numbers, a biography by Paul Hoffman. I first encountered this book as a teenager and believe its potential to captivate a broader audience is unfortunately overlooked. Therefore, I’m launching a campaign to cast Jeff Goldblum in the lead role.

Why Goldblum? Both he and Erdős have striking similarities, and Goldblum has successfully portrayed mathematician Ian Malcolm in the Jurassic Park franchise. More than that, Goldblum’s quirky eccentricity aligns perfectly with Erdős’ unique lifestyle.

Erdős had unconventional views on religion; he described himself as an atheist yet often spoke about God, referring to Him as “the best fascist” or “science fiction.” He sought to uncover the evidence of a magical book that he believed contained proofs for every mathematical theorem.

His linguistic quirks were equally captivating. He called children “Epsilon,” a nod to the Greek letter representing small quantities in mathematics. Friends who left mathematics were, in his eyes, “dead,” while those who actually passed away were simply “gone.” He humorously remarked, “A mathematician is a device that turns coffee into theorems,” a quote borrowed from colleague Alfred Rényi. I can easily envision Goldblum delivering those lines.

An intriguing aspect of Erdős’ legacy is the concept of the “Erdős number.” This measure indicates the collaborative distance between mathematicians, where those who co-authored with him have an Erdős number of 1, and others have higher numbers based on collaboration distance. My Erdős number is 3, having quoted Terrence Tao from UCLA in my writing.

This concept mirrors the “Six Degrees of Kevin Bacon” game. Goldblum also holds a Bacon number of 1 because they both appeared in the mockumentary Tour de Pharmacy. I only discovered this connection while advocating for my biopic project.

Some individuals hold both Erdős and Bacon numbers, bridging the worlds of mathematics and film. The minimum recorded Erdős-Bacon number is 3, held since 1997 by mathematician Daniel Kreitman, who appeared in Good Will Hunting.

While Erdős’ eccentricities paint a charming picture, it’s important to acknowledge his flaws. A Man Who Loved Only Numbers touches upon his problematic attitudes towards gender, as he often referred to women and men in derogatory ways. However, he was more than willing to collaborate with female mathematicians.

While dreaming of an Erdős biopic raises the concern of reinforcing the “absent-minded professor” stereotype, I argue that current mathematical biopics, like A Beautiful Mind, are serious dramas. A comedic portrayal has yet to be attempted.

Moreover, Erdős left behind numerous open mathematical problems, many offering monetary rewards for solutions. A film could inspire a new generation of puzzle enthusiasts and spark interest in mathematics—an endeavor Erdős would surely endorse. Jeff, if you (or your agent!) are reading this, let’s connect. I’m ready to collaborate on this exciting project!

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Source: www.newscientist.com

Renowned Mathematician Masaki Kashiwara Awarded the 2025 Abel Prize for Breakthrough Equation-solving Tool

Kashiwara’s work is very abstract, but is seen as important

Peter Bagde / Typos1 / The Abel Prize

Red-tailed For his research on algebraic analysis, he received the 2025 Abel Prize, known as the Nobel Prize in Mathematics.

Professor of Kashiwara Kyoto UniversityJapan received the award “for his fundamental contributions to algebraic analysis and representational theory, particularly for the development of the theory of D-modules and the discovery of crystal bases.”

His work involves the use of algebra, focusing on investigating geometry and symmetry, and using those ideas to find solutions to differential equations that include the relationship between mathematical functions and their rate of change. Finding solutions to such equations can be particularly difficult, especially for functions with several variables, and therefore with several rates of change. These are known as partial differential equations (PDEs).

Kashiwara’s important work on the D-module, a highly specific area of ​​algebraic analysis, including Linear PDE, was conducted surprisingly early in his career during his doctoral dissertation. He has worked with over 70 collaborators. Kashiwara said New Scientist He was pleased to win the Abel Prize, but he is still active and would like to make further contributions.

“I’m currently working on representative theory of quantum affine algebra and its related topics,” he says. “There’s a great guess: [the] “Affine epicenter speculation,” but I still don’t know how to solve it. ”

David Craven At the University of Birmingham, UK, Kashiwara’s work is very abstract and far from a direct real-world application, and even basic summary says that a minimum of a doctorate in mathematics is required. “That’s the level of these things being difficult,” he says. “It’s incredibly esoteric.”

However, Craven says that Kashiwara had a major impact on his field. “What he did is permeate theories of expression. If you want to do geometrical expression theory, you can’t escape from Kashiwara.

Gwyn Bellamy “All the big results on the field are [algebraic analysis] It was more or less due to him, and Kashiwara’s Abel Prize victory has been a long time.

Named after Norwegian mathematician Neils Henrik Abel, the Abel Prize is awarded annually by the King of Norway. Last year, Michelle Taragland won for his work in extreme studies of probability theory and randomness.

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Source: www.newscientist.com

Japanese mathematician Kashiwara Kuniyama awarded the Abel Prize in 2025.

Kashiwara Kuniki, a Japanese mathematician, has been awarded the Abel Prize, considered the equivalent of the Nobel Prize in mathematics. Dr. Kashiwara’s work combines algebra, geometry, and differential equations in a unique and abstract manner.

The Norwegian Academy of Sciences and Letters, responsible for the Abel Prize, announced the honor on Wednesday morning.

“He resolved difficult open speculations and connected previously unknown areas, surprising mathematicians,” said Helge Holden, chairman of the awards committee.

Mathematicians can use connections between different mathematical domains to address complex problems and gain a deeper understanding.

Kawakaze, 78, from Kyoto University, is considered “very important in many different fields of mathematics,” stated Holden.

Dr. Kashiwara, when asked if his work solved real-world problems, responded with a negative. The honor comes with approximately $700,000 in prize money.

Unlike Nobel Prize winners, Dr. Kashiwara was informed of his accolade a week prior to the public announcement.

The Norwegian Academy surprises Abel Prize winners with notifications similar to surprise birthday parties.

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Marit Westerguard, executive director of the Norwegian Academy, personally informed Dr. Kashiwara of his selection as Abel of the year.

Dr. Kashiwara, initially confused due to internet issues, was eventually able to grasp the news conveyed to him in Japanese.

Having been attracted to mathematics from a young age, Dr. Kashiwara’s work reflects his passion for algebraic analysis.

Real-world phenomena are explained using real and imaginary numbers, showcasing the interconnection between mathematics and the physical world.

Dr. Kashiwara’s impactful work in mathematics links abstract ideas to insightful combinations for mathematicians across various disciplines.

His innovative approaches, such as the Crystal Base, have opened new avenues of research in the field.

Source: www.nytimes.com