Construct and verify mathematical proofs using LaTeX typesetting and computational verification via jupyter_execute. Use when the user asks to prove a theorem, verify a mathematical argument, construct a formal proof, or check proof correctness computationally.
Assist with constructing, verifying, and typesetting mathematical proofs. Combines rigorous logical reasoning with computational verification.
latex_compile - Typeset proofs and mathematical documents (auto-switches to LaTeX editor)update_latex - Write LaTeX content to the editor for review before compilingjupyter_execute - Verify results computationally (sympy, numpy)update_notes - Write proof outlines and scratch work to Notes editorWhen user says: "Prove that [statement]"
When user says: "Is it true that [conjecture]?"
update_latex content="\\documentclass{article}\n\\usepackage{amsthm,amsmath}\n\\newtheorem{theorem}{Theorem}\n\\begin{document}\n\\begin{theorem}\nFor all $n \\geq 1$, $\\sum_{k=1}^{n} k = \\frac{n(n+1)}{2}$.\n\\end{theorem}\n\\begin{proof}\nBy induction on $n$. Base case $n=1$: $1 = \\frac{1 \\cdot 2}{2}$. Inductive step: assume true for $n$, then $\\sum_{k=1}^{n+1} k = \\frac{n(n+1)}{2} + (n+1) = \\frac{(n+1)(n+2)}{2}$.\n\\end{proof}\n\\end{document}"
jupyter_execute code="from sympy import symbols, summation, simplify\nk, n = symbols('k n', positive=True, integer=True)\nresult = simplify(summation(k, (k, 1, n)) - n*(n+1)/2)\nprint(f'Difference: {result}') # Should be 0"