[CALL] Ignite the Future: Help Us Find the Next Generation of Wolfram Innovators

[lyman (Lyman Hurd)]

I would like to nominate Aaditya Bilakanti whom it was my pleasure to mentor in WSRP 2025 for his project On functional trees which was based (as are many projects) on a note in New Kind of Science. The basic idea is relat9ively simple, to see how many different numbers can be obtained by fixing a function of two integer variables, f, and constructing arbitrary binary trees and giving the value 1 to each leaf node and assigning to each interior node, the value of applying f to the value of its children. I suggested generalizations such as measuring the growth rate of the number of solutions as a function of the number of leaves in a tree. In the end, he produced many interesting theor3etical results and even gave a proof of a conjecture in the original note. We came close but did not quite complete a proof that the question as to whether a particular value can occur is most likely undecidable. Other interesting results included producing a function f such that every different binary tree led to a different answer and with further refinement showing a function where every binary tree produced a different answer and which took as values all possible positive integers (thus achieving the theoretical upper bound on the number of results for a given number of leaves).