教授ともあろう人がそんな基本的な定理を間違えるとは。
- For a professor of all people to make such a basic mistake in a theorem!

教授ともあろう人がそんな基本的な定理を間違えるとは。 meaning: For a person who is supposed to be a professor, to make a mistake on such a basic theorem!

This is a fixed expression indicating "someone of the status/position of...". ⚫︎ It is formed by combining the particle と, the particle も, and the verb ある（to be/exist）in its potential form あろう. ⚫︎ This expression implies that the person mentioned is expected to possess certain abilities, knowledge, or behavior befitting their position. ⚫︎ The implication is often surprise or disbelief that someone of that position would act in the way described. ⚫︎ Example: 社長ともあろう人が、そんな小さなことで怒るなんて信じられない。 (For a person who is supposed to be a president, I can't believe he'd get angry over such a trivial matter.)

This is a demonstrative adjective. ⚫︎ そんな (such; that kind of) is used to refer to something that is related to the listener or the context. ⚫︎ It modifies the noun that follows it, in this case, 基本的な定理 (basic theorem). ⚫︎ It implies that the basic theorem mentioned is known to the speaker and perhaps also the listener. ⚫︎ Other demonstrative adjectives include: この (this), その (that), and あんな (that kind of - over there). ⚫︎ The meaning can vary based on the context, but in this case, it indicates surprise at the mistake being made on a theorem considered well-known.

This is an adjectival noun (な-adjective). ⚫︎ 基本的な (basic; fundamental) modifies the noun 定理 (theorem). ⚫︎ Adjectival nouns describe nouns with characteristics or qualities. They conjugate differently than い-adjectives. ⚫︎ They end in な before the noun they modify. ⚫︎ The base form is 基本 (basic). ⚫︎ Other examples include: 静かな (quiet), 有名な (famous), and 特別な (special).

This is a sentence-ending particle with a nuance of surprise or exclamation. ⚫︎ It is a combination of the topic marking particle は and the quoting particle と. ⚫︎ It's used to express a strong feeling, like surprise, shock, or disbelief. ⚫︎ In this sentence, it emphasizes the speaker's astonishment at the professor making a mistake on a basic theorem. ⚫︎ Similar sentence-ending particles that convey similar meanings are ものだ and ものがある.