Publications

Here are the latest versions of our papers.

• Algorithm-assisted discovery of an intrinsic order among mathematical constants
  Elimelech R., David O., De la Cruz Mengual C., Kalisch R., Berndt W., Shalyt M., Silberstein M., Hadad Y., & Kaminer I.
  Proceedings of the National Academy of Sciences (PNAS) 121, e2321440121 (2024) (previous version on arXiv)
  A massively parallel computer algorithm has discovered an unprecedented number of continued fraction formulas for fundamental mathematical constants. These formulas unveil a novel mathematical structure that we refer to as the conservative matrix field. This field not only unifies thousands of existing formulas but also generates an infinite array of new formulas. Most importantly, it reveals unexpected relationships among various mathematical constants.
  
• The conservative matrix field
  David O.
  arXiv 2303.09318 (2023)
  A mathematical structure used to study mathematical constants by combining polynomial continued fractions in an interesting way. In particular it is used to reprove and motivate Apery’s original proof of the irrationality of \(\zeta(3)\).
  (see also here for some details and examples).
  
• On Euler polynomial continued fraction
  David O.
  arXiv 2308.02567v2 (2023)
  Euler polynomial continued fraction, are those that in a sense come from “simple” infinite sums via Euler conversion. We describe a method to find if a given polynomial continued fraction is of this form and how to convert it back to infinite sums.
  (see also here for some details and examples).

• Automated Search for Conjectures on Mathematical Constants using Analysis of Integer Sequences
  Razon O., Harris Y., Gottlieb S., Carmon D., David O., & Kaminer I.
  International Conference on Machine Learning, PMLR, 28809-28842 (2023)
  This algorithm is a different approach for finding conjectures on mathematical constants. Instead of searching for continued fractions, we search for patterns in integer sequences.
  The implementation of this algorithm can be found here.

• On the Connection Between Irrationality Measures and Polynomial Continued Fractions
  Ben David N., Nimri G., Mendlovic U., Manor Y., De la Cruz Mengual C., Kaminer I.
  Arnold Mathematical Journal (2024) (previous version on arXiv)
  The mathematical phenomenon found in this work is to date the basis of the algorithm used in our BOINC project. It is currently the most successful algorithm found in the Ramanujan Machine project.

• Generating conjectures on fundamental constants with the Ramanujan Machine
  Raayoni G., Gottlieb S., Manor Y. et al.  
  Nature 590, 67–73 (2021) (previous version on arXiv)
  Presenting the first algorithm for generating conjectures on fundamental constants: the meet-in-the-middle and the gradient-descent algorithm.