The reader is introduced to higher mathematics in an experimental way. He works with numerous interactive Java- simulations treating mathematical topics from number theory to infinitesimal calculus and partial differential equations. On the way he playfully learns the EJS simulation technique. Beyond the mathematics simulations the data pool contains a structured collection of over 2,000 physics simulations. The unique, extensive and well documented data pool can be operated comfortably online or with files stored at the hard disk. (For download of the digital package or questions concerning the online operation contact service@degruyter.com.) This is an ideal, modern approach to visualize mathematics and physics and to teach and learn their basic concepts by doing.