A user claims to have discovered two new proofs of the Pythagorean theorem, one of which is particularly simple and another for the special case of 45-degree angles. They express a desire to publish these findings in a scientific journal but are uncertain about the process. Other participants suggest various publication avenues, including educational journals and platforms like arXiv, while noting that new proofs of an ancient theorem may not attract significant interest from professional mathematicians. The discussion touches on the nature of mathematical proofs, emphasizing that while the Pythagorean theorem itself is not new, novel proofs can still be valuable for educational purposes. Participants encourage the user to share their work for the joy of mathematics, highlighting the importance of engaging with new ideas, even if they are not groundbreaking. The conversation also briefly diverges into discussions about Galois theory and the significance of different mathematical proofs.