"Notes in Modern Analysis" is a new 2026 collection of lecture notes from Columbia University that provides a rigorous introduction to real analysis.
The notes cover the foundations of mathematical reasoning, including logic, sets, functions, and proof techniques, before moving through real numbers and completeness, countability, metric spaces, open and closed sets, compactness, sequences and convergence, limits and continuity, derivatives, Taylor’s theorem, analyticity, Riemann integration, and the Fundamental Theorem of Calculus.
This collection is a great resource if you want to study real analysis from the foundations with a rigorous and modern approach.
https://t.co/0twEWCXvPh
"The Great Story of Numbers" is a new, free book that provides a comprehensive introduction to elementary number theory.
The book starts from the nature of numbers and mathematical induction, then develops counting, integers, number representations, divisibility, linear Diophantine equations, congruences and modular arithmetic, the Chinese Remainder Theorem, rational numbers and continued fractions, Pythagorean triples, and infinite descent.
It then moves into prime numbers and the Fundamental Theorem of Arithmetic, multiplicative functions, Fermat's Little Theorem, Euler's and Wilson's theorems, Fermat's Two-Squares Theorem, Gaussian integers, polynomials, primitive roots, discrete logarithms, polynomial congruences, cyclotomic polynomials, quadratic residues, Legendre symbols, quadratic reciprocity, and much more.
It's a useful resource if you want to study number theory from its foundations and gradually move toward more advanced topics. The current edition is almost 500 pages long.
https://t.co/obTB2jmrh2
The news today of progress on resolving the Navier–Stokes problem, one of mathematics’ great longstanding challenges concerning the equations that govern the flow of fluids, represents a milestone advance in human knowledge. This story began with Navier, Stokes, Leray, and Ladyzhenskaya and has culminated in the recent breakthroughs of Córdoba and Martínez-Zoroa, then — assisted by new technologies — Alpöge and Buckmaster, with the final steps taken by OpenAI mathematicians. The purpose of mathematics is human understanding, and this achievement, and the process that led to it, will bear fruit for a long time to come.
Ravi Vakil, President of the AMS, and John Meier, CEO of the AMS
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She treats mathematical objects like people - and that’s how she rewrote a 150-year-old theory.
Hannah Larson grew up in Eugene, Oregon, chasing theorems after watching her older brother Eric fall in love with math. By 18 she was the first woman to win the Davidson Fellowship in mathematics.
Today the UC Berkeley professor and Clay Fellow has extended Brill-Noether theory, giving us new ways to understand the wild special curves that old theorems couldn’t tame.
Her work on intersection theory and moduli spaces earned the 2024 Maryam Mirzakhani New Frontiers Prize. When she’s not mapping abstract geometries, she plays cello and piano. A quiet force writing the next chapter of algebraic geometry.
Math & Mystery.
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Credit: https://t.co/u9bReLRu6t. I didn’t upload this video to 𝕏. I’m pointing to a video within the 𝕏 stream of “Interesting Universe”, 𝕏 ID “InterestingUni” (Mar 19, 2026).
Get ready for the 2027 Joint Mathematics Meetings next January. View the program on the web—explore special sessions, workshops, panels, and invited addresses.
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To celebrate Joint Statistical Meetings 2026, we have created a new article collection featuring content from Forum of Mathematics, Pi, Forum of Mathematics, Sigma and many more. Where not already #OpenAccess, articles are free to read until 31st August. https://t.co/3QxdhlQdc4
With an abundance of exercises, examples and illustrations, J.J.P. Veerman’s “Numbers from all Angles”, covers a full year’s course for advanced undergraduates. Check it out! https://t.co/Cf6CHtP4ZX
📍Happening today at #JSM2026! Stop by Cambridge University Press Booth #506 at 4PM to meet Richard J. Samworth, chat about Modern Statistical Methods and Theory, and ask your questions. See you there! https://t.co/Ee1WThBCJJ
Four AMS research fellowships are now open—apply by Sept. 30 (U.S.-based mathematicians). Opportunities are for research support to advance mathematical research and broaden participation. Applicants are encouraged to apply for all fellowship opportunities for which they are eligible.
Interested? Know someone who is? Please share!
Learn more & apply: https://t.co/7uYO7DeIke
Join the American Mathematical Society at ICM on Saturday, July 25 for an evening of conversation and community. Explore AMS membership, programs, publications, and resources that support mathematicians at every stage of their careers. Enjoy light refreshments as you build new connections and celebrate the global mathematical community. Open to all ICM attendees!
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🎉We're delighted to announce the publication of the ICM 2026 Special Issue of The Mathematical Intelligencer!
View the full TOC: https://t.co/inP68gn0PH
Editors-in-Chief: Karen Parshall @UVA, Sergei Tabachnikov @PSUScience#TheMathematicalIntelligencer#ICM2026#HistoryOfICM
We see the fundamental theorem of arithmetic and the sieve of Eratosthenes in the decomposition into weight × level + jump of natural numbers. Applied to prime numbers this decomposition leads to a new classification of primes.
#decompwlj#math#sieve#sequence#numbers#graph
"Squaring the circle" was proven impossible in 1882.
In 1913, Ramanujan published a 1-page construction that does it anyway - off by one inch for a circle roughly the size of Japan.
We annotated it here: https://t.co/tPDmlEyBp7