-
synthetic data.
AlphaProof is an AI model,
which couples a pre-trained
language model with the
AlphaZero
reinforcement learning algorithm.
AlphaZero has previously...
- by
generating and
checking Lean code. In 2024,
Google DeepMind created AlphaProof which proves mathematical statements in Lean at the
level of a silver...
- {\displaystyle p_{i}\leq {\frac {\
alpha }{m}}} ,
thereby controlling the FWER at ≤ α {\displaystyle \leq \
alpha } .
Proof of this
control follows from Boole's...
-
language theory and
proof theory, the Curry–Howard
correspondence is the
direct relationship between computer programs and
mathematical proofs. It is also known...
-
precision for the
outcome including proof of
theorems have been
developed such as
AlphaTensor,
AlphaGeometry and
AlphaProof all from
Google DeepMind, Llemma...
- human-coded
rules to
generate rigorous proofs,
which makes them lack
flexibility in
unusual situations.
AlphaGeometry
combines such a
symbolic engine...
- are
several equivalent ways for
defining trigonometric functions, and the
proofs of the
trigonometric identities between them
depend on the
chosen definition...
- {Abs}}]&(1)\\3:&id:\
alpha \rightarrow \
alpha \vdash _{D}id:\
alpha \rightarrow \
alpha &[{\mathtt {Var}}]&(id:\
alpha \rightarrow \
alpha \in \left\{id:\
alpha \rightarrow...
-
cannot exist. A few w****s later,
Felix Hausdorff found a
mistake in the
proof. It
turned out, though, that in first-order
logic the well-ordering theorem...
- for all t ∈ [ t 0 − α , t 0 + α ] {\displaystyle t\in [t_{0}-\
alpha ,t_{0}+\
alpha ]}
Proof.
Induction on m. For the base of the
induction (m = 1) we have...
