Update August 11, 2018: in the summer of 2018, I wrote down a list of theorems. Here is the top ten list:
The document (PDF) Here on Arxiv for a time stamp on July 23, 2018 is likely to be extended a bit more in the future as time permits.

What are the best ideas/theorems/formulas in mathematics? Any list is a matter of taste and personal preferences. Due to the vastness of mathematics, it is quite challenging to build a list, because one tends to focus on things which one uses most. Here is a first shot written in 31. December 2007:

Formulas

Theorems

Algorithms

Concepts


Oliver Knill, Department of Mathematics, Harvard University, One Oxford Street, Cambridge, MA 02138, USA. SciCenter 432 Tel: (617) 495 5549, Email: knill@math.harvard.edu Quantum calculus blog, Twitter, Youtube, Vimeo, Linkedin, Scholar Harvard, Academia, Google plus, Google Scholar, ResearchGate, Slashdot, Ello, Webcam, Fall 2018 office hours: TBA Mon-Fri 11:30-12:30 AM and by appointment.