Hi, I wrote to chatgpt to make a summary, because it would take a lot of pages to write everthing down.

Hi everyone, I’d really appreciate some perspective from people with more experience in mathematics teaching or research.

I’m a math student, and my friends and I are trying to understand a very unusual situation involving one of our colleagues (let’s call him “M”) and a teaching assistant (let’s call her “D”). We’re not trying to judge — we’re genuinely confused and curious whether this is a known pattern in mathematics education or something more unusual.

Background and timeline

At the beginning of our studies, we had an “elementary mathematics” type course (basically high school review), where D was the teaching assistant.

From the very first sessions:

• M stood out immediately as extremely fast and active
• He would solve problems mentally, often skipping steps
• He was by far the most active student

At one point, D approached him after class (he initially thought he was being accused of making noise), but she actually told him he had been very active.

After that:

• In courses where D was involved (as assistant), M was consistently one of the best students — often the best
• In courses where she was not involved (linear algebra, analysis early on, analytic geometry), M struggled significantly — sometimes being among the weakest students

Later:

• When D returned in other courses (number theory, linear algebra 2, analysis again), M again became one of the strongest students
• In one case, his improvement was described by an assistant as “unreal”

His abilities

M has some very strong and unusual abilities:

1. Extreme speed on certain problems

In some exams (especially when aligned with D’s style):

• He solves computational or conceptual problems almost instantly (seconds)
• He reads a problem and immediately writes the final solution
• For example, limits, series, or standard constructions — he often finishes in under a minute

2. Proof recognition

Even more unusual:

• When he sees a proof-based problem that resembles something D once showed, he can reproduce the proof almost immediately
• He sometimes recalls very specific past exercises (even exact session and problem numbers), and the structure matches exactly

3. Pattern-based thinking

He doesn’t rely on many separate techniques.

Instead:

• He reduces topics to a few core strategies
• Builds “algorithms” like:
  • “for functional series: do these 3–4 steps”
  • “for limits: reduce to known exponential/polynomial forms”

These strategies:

• work extremely well on real exams
• often match exam problems very closely

He even created written notes and YouTube-style explanations so others can use them.

Teaching ability

• He explains concepts extremely clearly
• Many students rely on him more than on assistants
• He can simplify complex topics into a few key ideas that actually work

Weaknesses and inconsistencies

• He often skips formal steps in proofs
• Relies heavily on intuition
• Performance varies a lot depending on the instructor
• Sometimes fails or struggles badly in courses not aligned with his style
• Occasionally leaves parts of exams blank

The most unusual part: his relationship to D’s teaching

M strongly attributes everything to D.

He often says things like:

• “I’m just following D”
• “This is how D would do it”

More strikingly:

• While solving problems, he says he can visualize D standing in front of a board explaining the solution
• He describes it almost like replaying a lecture in his mind
• He claims that when he reads a problem, the solution “appears” as something D has already shown

Example:

• He reads a problem → instantly says the result
• When asked why → he says “D did this exact type before”
• Sometimes we later verify, and he is correct

Behavior on exams

• When solving tasks aligned with D’s teaching, he is extremely fast and accurate
• He sometimes finishes problems in seconds that take others 20–30 minutes
• He focuses only on a few key methods and ignores others

However:

• He admits he sometimes skips logical steps
• Says he is “willing to risk it” if he thinks the grader is not strict
• Believes some professors “just want students to pass”

Specific example of speed and method

For example, given something like:

• limits involving (x^n) → he immediately converts to exponential form
• functional series → immediately applies asymptotic/logarithmic reasoning + supremum + standard tests
• proofs → recalls structure from earlier exposure and reproduces it

All of this happens extremely fast, often with no visible “thinking time”.

Additional detail

• He has created full “exam systems” (step-by-step strategies) that allow other students to pass efficiently
• These systems actually work — students improve significantly using them
• Assistants are aware and sometimes joke about him being “clever” or “knowing the system”

Our confusion

We don’t understand:

• how someone can be this fast and precise in some contexts, but struggle heavily in others
• how much of this is true understanding vs pattern recall
• whether the “visualization of D” is just internalized learning or something unusual

Questions

1. Is this kind of extreme pattern compression and exam optimization something you’ve seen before?
2. How common is it for a student to be extremely fast and accurate on familiar structures, but weak elsewhere?
3. Is “mentally replaying an instructor” a known learning phenomenon?
4. Would you interpret this as high potential but lack of rigor/discipline?
5. Does this kind of student usually improve into a strong mathematician, or plateau?

We are genuinely curious and a bit confused. Any insights from professors, TAs, or experienced students would mean a lot.

Thanks in advance.