The work Va'yomer Meir addresses the situation of a Jew who was involved in a court case, and the courthouse officials forbade him from wearing a Kippa. The question arose as to whether this man was permitted to review Torah topics in his mind during his time in the courthouse, despite being bareheaded.

This issue hinges on the question of "Hirhur Ke'dibbur" – whether or not we consider thinking akin to speaking. The Rambam maintains that silent thoughts are indeed halachically equivalent to spoken words, in which case one may not think Torah thoughts while not wearing a Kippa. However, Hacham Ovadia Yosef writes that Halacha does not follow this ruling of the Rambam, and even if one is entirely unclothed, he is allowed to think about Torah matters as long as he does not verbally express these thoughts. Certainly, then, it is entirely permissible to think Torah matters when one is fully clothed but not wearing a Kippa.

Summary: Although one may not speak any words of Torah while not wearing a Kippa, it is permissible to silently think about Torah matters without a Kippa.

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