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The old system existed long before NetIDs, and there are many people who are still using their pre-NetID accounts for regular work. Also, there are many rules and constraints to connecting math department machines to the central Cornell system.
The biggest one is performance. Some parts of the system need to make many calls across the network for some operations, and it would be much slower. Also, the central system can be changed without notice, or may go down for maintenance. So we've had better speed and reliability with our separate system.
The next reason is security. The Math account is controlled by the NetID, such as for password reset, but there is nothing in a person's NetID account that is accessible from their Math account. So, math researchers can do what they want, and this separation keeps the Cornell system safe.
In the future, it may be desirable to set up access to the system that uses NetIDs as the primary username. This is possible if it's found to be necessary.
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