There are several online forums and study groups available for Mathematics optional aspirants to connect, discuss, and collaborate with fellow UPSC aspirants. These platforms provide a conducive environment for sharing knowledge, clarifying doubts, and gaining insights into various topics related to the Mathematics optional subject. Here are some popular online forums and study groups for Mathematics optional aspirants:

1. EduRev's UPSC Mathematics Optional Community:
- EduRev, a trusted online learning platform, offers a dedicated community for UPSC Mathematics optional aspirants.
- This community allows aspirants to connect with like-minded individuals, share study materials, ask questions, and participate in discussions.
- EduRev's community is designed to provide a supportive and interactive learning experience for Mathematics optional aspirants.

2. ClearIAS Forum:
- ClearIAS is a popular online platform that provides guidance and resources for UPSC preparation.
- They have a dedicated forum where aspirants can discuss Mathematics optional topics, share strategies, and seek guidance from experts.
- The ClearIAS forum is user-friendly and encourages active participation from aspirants.

3. Quora:
- Quora is a well-known question and answer platform that covers a wide range of topics, including UPSC preparation.
- Mathematics optional aspirants can find numerous discussions and threads related to their subject on Quora.
- By following relevant topics, participating in discussions, and asking questions, aspirants can engage with a larger community of UPSC aspirants and experts.

4. Telegram Groups:
- Telegram, a popular instant messaging app, hosts several study groups and channels specifically focused on UPSC preparation.
- Mathematics optional aspirants can join these groups to connect with peers, share study resources, and discuss important topics.
- Some popular Telegram groups for UPSC Mathematics optional include "Mathematics Optional for UPSC" and "UPSC Mathematics Optional Discussion Group."

It is important to note that while these online forums and study groups can provide valuable support and resources, it is equally important to verify the accuracy and reliability of the information shared. Aspirants should use these platforms as a supplement to their regular study routine and consult standard textbooks and guidance from experienced faculty members.