Robert Jaffe is a prominent physicist known for his work in theoretical physics, particularly in areas related to particle physics and cosmology. He is a professor and has been associated with institutions such as the Massachusetts Institute of Technology (MIT). Jaffe has contributed to research on topics such as the strong force, confinement in quantum chromodynamics (QCD), and the properties of hadrons.

A set of axioms is consistent if they don't lead to any contradictions.

When a set of axioms is not consistent, false can be proven, and then everything is true, making the set of axioms useless.

This section groups conjectures that are famous, solved or unsolved.

They are usually conjectures that have a strong intuitive reasoning, but took a very long time to prove, despite great efforts.

The list: en.wikipedia.org/wiki/List_of_unsolved_problems_in_mathematics

Jacob Palis is a Brazilian mathematician known for his significant contributions to dynamical systems and differential equations. Born on August 13, 1931, in Rio de Janeiro, he has made substantial advancements in the field, particularly in the study of chaos and stability in dynamical systems. Palis has been involved in various mathematical initiatives and has served in prominent academic positions. He has also been recognized with several awards for his work in mathematics.

Jean-François Quint is a French filmmaker and artist known for his work in various media, including film, video, and multimedia installations. He often explores themes of identity, memory, and the human experience in his art. Though not overly mainstream, his work is recognized within art circles and festivals.

Given stuff like arxiv.org/pdf/2107.12475.pdf on Erdős' conjecture on powers of 2, it feels like this one will be somewhere close to computer science/Halting problem issues than number theory. Who knows. This is suggested e.g. at The Busy Beaver Competition: a historical survey by Pascal Michel.

Jean Écalle is a French mathematician known for his work in the fields of algebra and mathematics education. He is particularly noted for developing the theory of "analytic prolongation" and for his contributions to the field of "resurgence," which involves the study of asymptotic expansions and their analytic properties. Écalle's work has influenced various areas within mathematics, including differential equations and complex analysis.

An easy to prove theorem that follows from a harder to prove theorem.

A theorem that is not very important on its own, often an intermediate step to proving something that the author feels deserves the name "theorem".

Proof of Work (PoW) is a consensus mechanism used in blockchain networks to secure transactions and create new blocks in the blockchain. Its primary purpose is to prevent double spending and to ensure that network participants (nodes) agree on the correct version of the blockchain. Here are the key features of Proof of Work: 1. **Computational Effort**: In PoW, participants (miners) must solve complex mathematical problems that require significant computational power and energy.

John H. Hubbard is a notable mathematician, particularly recognized for his contributions to the fields of mathematical analysis and differential equations. He has also co-authored several influential textbooks, most notably in the areas of calculus and advanced mathematics. Alongside his academic work, he has been involved in mathematical education and has contributed to the development of teaching materials for students. If you are referring to a different John H. Hubbard or seeking information in a different context (e.g.

The size of a set.

For finite sizes, the definition is simple, and the intuitive name "size" matches well.

But for infinity, things are messier, e.g. the size of the real numbers is strictly larger than the size of the integers as shown by Cantor's diagonal argument, which is kind of what justifies a fancier word "cardinality" to distinguish it from the more normal word "size".

The key idea is to compare set sizes with bijections.

John Milnor is a prominent American mathematician known for his work in differential topology, differential geometry, and algebraic topology. Born on February 20, 1931, he has made significant contributions to various areas of mathematics, including the study of manifolds, Morse theory, and the topology of high-dimensional spaces. Milnor is particularly famous for his discovery of exotic spheres—manifolds that are homeomorphic but not diffeomorphic to the standard sphere.

It is so mind blowing that people believed in this theory. How can you think that, when you turn on a lamp and then you see? Obviously, the lamp must be emitting something!!!

Then comes along this epic 2002 paper: pubmed.ncbi.nlm.nih.gov/12094435/ "Fundamentally misunderstanding visual perception. Adults' belief in visual emissions". TODO review methods...

Mnemonic: sur means over. So we are going over the codomain, and covering it entirely.