This is the first part of post series that serve as a concise guide to harnessing the possibilities of the Wolfram plugin for mathematics, physics and Wolfram Language coding, with a special focus on effective problem-solving prompting techniques, exemplified with 100+ plugin-using ChatGPT chat sessions.
Check out other parts of this guide here:
Guide 1: https://community.wolfram.com/groups/-/m/t/3070428​
Guide 3: https://community.wolfram.com/groups/-/m/t/3077476​
Guide 4: https://community.wolfram.com/groups/-/m/t/3077667​
Guide 5: https://community.wolfram.com/groups/-/m/t/3078038

Contents

The Importance of Prompt Engineering​ Some Recently Discussed Prompt Techniques (All from the Literature) Prompt Examples (All from the Literature)

Cell coloring conventions


The Importance of Prompt Engineering

Some Recently Discussed Prompt Techniques (All from the Literature)

Inferential exclusion prompting (IEP)

Eliminating Reasoning via Inferring with Planning: A New Framework to Guide LLMs’ Non-linear Thinking (https://arxiv.org/abs/2310.12342)

Least-to-Most prompting

Least-to-Most Prompting Enables Complex Reasoning in Large Language Models (https://arxiv.org/abs/2205.10625)

Step-back prompting 

Tell the LLM to literally ‘step’ back and reflect/remember how the concrete problem could be embedded in a larger class of problems.
Encourage the LLM to put the problem in a larger context and remember related problems.
Take a Step Back: Evoking Reasoning via Abstraction in Large Language Models (https://arxiv.org/abs/2310.06117)

Review-Rephrase-Resolve
(
3
R
)


Tell the LLM to review a problem and rephrase it before solving.
3
R
Prompting: Review, Rephrase and Resolve for Chain-of-Thought Reasoning in Large Language Models under Noisy Context (https://arxiv.org/abs/2310.16535)

Progressive hints

Progressive-Hint Prompting Improves Reasoning in Large Language Models (https://arxiv.org/abs/2304.09797)

Self-ask

ThoughtSource: A central hub for large language model reasoning data (https://arxiv.org/abs/2301.11596)
Measuring and Narrowing the Compositionality Gap in Language Models (https://arxiv.org/abs/2210.03350)
Tell the LLM to generate follow-up questions and then answer them.

Self-asking and self-understanding

Metacognitive Prompting Improves Understanding in Large Language Models (https://arxiv.org/abs/2308.05342)

Self-consistency 

Tell the LLM to do multiple CoT and check consistency.
Self-consistency Improves Chain of Thought Reasoning in Language Models (https://arxiv.org/abs/2203.11171)

Self-check

SelfCheckGPT: Zero-Resource Black-Box Hallucination Detection for Generative Large Language Models (https://arxiv.org/abs/2303.08896)
Enhancing Large Language Models in Coding Through Multi-Perspective Self-Consistency (https://arxiv.org/abs/2309.17272)
PS: The Wolfram plugin is perfect and powerful for a LLM to get external feedback.
Pure self-correction is quite limited:
​Large Language Models Cannot Self-Correct Reasoning Yet (https://arxiv.org/abs/2310.01798)

Self-refinement and self-critiquing

It is an ongoing discussion whether this is a valuable approach.
Self-Refine: Iterative Refinement with Self-Feedback (https://arxiv.org/abs/2303.17651)
Can Large Language Models Really Improve by Self-critiquing Their Own Plans? (https://arxiv.org/abs/2310.08118)

Foresee and Reflect (FaR)

How FaR Are Large Language Models From Agents with Theory-of-Mind? (https://arxiv.org/abs/2310.03051)

Monte Carlo tree search

Monte Carlo Thought Search: Large Language Model Querying for Complex Scientific Reasoning in Catalyst Design (https://arxiv.org/abs/2310.14420)

EmotionPrompt 

Tell the LLM why you want the LLM to solve this problem.
Large Language Models Understand and Can Be Enhanced by Emotional Stimuli (https://arxiv.org/abs/2307.11760)

Branch-Solve-Merge (BSM)

Branch-Solve-Merge Improves Large Language Model Evaluation and Generation (https://arxiv.org/abs/2310.15123)

Multi-agent

Towards CausalGPT: A Multi-Agent Approach for Faithful Knowledge Reasoning via Promoting Causal Consistency in LLMs (https://arxiv.org/abs/2308.11914)
Exploring the Intersection of Large Language Models and Agent-Based Modeling via Prompt Engineering (https://arxiv.org/abs/2308.07411)
AgentBench: Evaluating LLMs as Agents (https://arxiv.org/abs/2308.03688)
Language Agent Tree Search Unifies Reasoning Acting and Planning in Language Models (https://arxiv.org/abs/2310.04406)

Prompt Examples (All from the Literature)

None of the prompt examples from this section are especially important. The goal of the prompt collection of this subsection is to give a good impression of the breadth and variety of instructions and details that one could (and often should) put in a prompt, as well as to demonstrate the variety of tasks that can be accomplished with the above-discussed prompting techniques.

High-school physics competitions

Innovative approaches to high school physics competitions: Harnessing the power of AI and open science (https://arxiv.org/abs/2309.02986)

Problem solving

Large Language Models as Optimizers (https://arxiv.org/abs/2309.03409)

Math teacher

“A Tale of Two Prompts”: Investigating the Impact of Guidance and Interaction Strategies for LLM Use on Learner Performance and Perception (https://arxiv.org/abs/2310.13712)

Vehicle accident analysis

Large Language Models in Analyzing Crash Narratives—A Comparative Study of ChatGPT, BARD and GPT-4 (https://arxiv.org/abs/2308.13563)

Special relativity consistency

Assessing GPT-4’s role as a co-collaborator in scientific research: a case study analyzing Einstein’s special theory of relativity (DOI:10.1007/s44163-023-00075-3)

Multi-choice questions

Large Language Models Are Not Robust Multiple Choice Selectors (https://arxiv.org/abs/2309.03882)

Summarization

Prevalence and prevention of large language model use in crowd work (https://arxiv.org/abs/2310.15683)

Summarization II

From Sparse to Dense: GPT-4 Summarization with Chain of Density Prompting (https://arxiv.org/abs/2309.04269)

Summarization III

Less is More for Long Document Summary Evaluation by LLMs (https://arxiv.org/abs/2309.07382)

Summarization VI

Can GPT models Follow Human Summarization Guidelines? Evaluating ChatGPT and GPT-4 for Dialogue Summarization (https://arxiv.org/abs/2310.16810)

Translation

Beyond Static Datasets: A Deep Interaction Approach to LLM Evaluation (https://arxiv.org/abs/2309.04369)

Gender reversal

Will the Prince Get True Love’s Kiss? On the Model Sensitivity to Gender Perturbation over Fairytale Texts (https://arxiv.org/abs/2310.10865)

Communication games

Exploring Large Language Models for Communication Games: An Empirical Study on Werewolf (https://arxiv.org/abs/2309.04658)

Geometric transformations

Hypothesis Search: Inductive Reasoning with Language Models (https://arxiv.org/abs/2309.05660)

Long-form answers

Strategic Behavior of Large Language Models: Game Structure vs. Contextual Framing (https://arxiv.org/abs/2309.05898)

Evaluator

Investigating Answerability of LLMs for Long-Form Question Answering (https://arxiv.org/abs/2309.08210)

“The Importance of Prompt Engineering” section continues in the following post.

CITE THIS NOTEBOOK

Guide 2: The Wolfram Plugin for ChatGPT​
by Michael Trott​
Wolfram Community, STAFF PICKS, December 1, 2023
​https://community.wolfram.com/groups/-/m/t/3075538