"Notably, we demonstrated through AlphaGeometry a neuro-symbolic approach for theorem proving by means of large-scale exploration from scratch, sidestepping the need for human-annotated proof examples and human-curated problem statements."

"This paper discusses the archive and library of the Royal Dutch Mathematical Society, as a starting point for research into the history of Dutch mathematics."

Wigner's claim is a clear-cut case of survivor bias:
Of all the possible mathematical claims a vanishingly small number can be adapted to physics (in itself unsurprising, considering that's what we have developed it for).

His claim is popular because a large number of people want the world to be orderly, despite evidence to the contrary, not because it is in any way correct.

For it to be "unreasonable" one would expect physicists to be able to forego empiricism, and just roll out physics from mathematical first principles.

THAT would be "unreasonable effectiveness".

But of the severally several infinities of possible math statements, a non-contiguous spattering of statements find some use in physics - to describe patterns that are found empirically.

The Best of All Possible Worlds: Mathematics and Destiny

Optimists believe this is the best of all possible worlds. And pessimists fear that might really be the case. But what is the best of all possible worlds? How do we define it? Is it the world that operates the most efficiently? Or the one in which most people are comfortable and content?

"In his Remarks on the Foundations of Mathematics, Wittgenstein claims, puzzlingly, that ‘the proof creates a new concept’ (RFM III-41). This paper aims to contribute to clarifying this idea, and to showing how it marks a major break with the traditional conception of proof."

Russian mathematician and geometer Nikolai Lobachevsky was born #OTD in 1792.

He is known primarily for his work on hyperbolic geometry, otherwise known as Lobachevskian geometry, and also for his fundamental study on Dirichlet integrals, known as the Lobachevsky integral formula.

Another of his achievements was developing a method for the approximation of the roots of algebraic equations (Lobachevsky method). via @wikipedia

"Abraham de Moivre (born May 26, 1667, Vitry, Fr.—died Nov. 27, 1754, London) French mathematician who was a pioneer in the development of analytic trigonometry and in the theory of probability"

Prime Numbers: The Most Mysterious Figures in Math

A fascinating journey into the mind-bending world of prime numbers.

Mathematicians have been asking questions about prime numbers for more than twenty-five centuries, and every answer seems to generate a new rash of questions.

"After introducing plural logic and its main applications, the book provides a systematic analysis of the relation between this logic and other theoretical frameworks such as set theory, mereology, higher-order logic, and modal logic."