diff --git a/RELEASE-NOTES.txt b/RELEASE-NOTES.txt
index 6bf8651365e..9f04f448f04 100644
--- a/RELEASE-NOTES.txt
+++ b/RELEASE-NOTES.txt
@@ -5,6 +5,19 @@ Note: these are the release notes for the stan-dev/stan repository.
 Further changes may arise at the interface level (stan-dev/{rstan,
 pystan, cmdstan}) and math library level (stan-dev/math).
 
+v2.40.0 (16 September 2026)
+======================================================================
+
+ - Fixed standalone generated quantities not respecting the chain ID for rng seeding. (#3402)
+ - Added `max_tries` as an argument to `stan::services::util::initialize`. (#3395)
+ - Fixed the output format of standalone generated quantities differing between the single- and multi-chain overloads. (#3404)
+ - Switched to using explicitly sized integer types in the structured_writer interface. (#3406)
+ - Fixed several edge case issues in the summary and analysis functions. (#3423)
+ - Reduce dependencies on the Boost library headers. (#3409, #3410, #3411, #3415, #3419)
+ - JSON writers are now flushed whenever the json object is finished, rather than at the end of the program. (#3418)
+ - Fixed some edge cases in JSON file writing. (#3427)
+ - Fixed an infinite loop when reading certain invalid CSV files. (#3428)
+
 v2.39.0 (19 May 2026)
 ======================================================================
 
@@ -28,7 +41,7 @@ v2.37.0 (2 September 2025)
 
  - Fixed a memory leak in `laplace_sample`. (#3324)
  - Dramatically reduce the memory footprint of Pathfinder when PSIS resampling is disabled. Note that this change involves changes to thread scheduling that may result in the same seed returning draws in a different order when multiple threads are used, but the unordered set of draws should be unchanged. (#3325)
- - Fixed a missing size check by directing all std::vector assigns through size-aware version. (#3352) 
+ - Fixed a missing size check by directing all std::vector assigns through size-aware version. (#3352)
  - Implemented serialization and deserializtion for `sum_to_zero` matrix. (#3342)
  - Fixed stepsize adaption being completely reset when passing `0` for the size of `term_buffer`. (#3346)
 
@@ -280,11 +293,11 @@ v.2.19.0 (20 March 2019)
 ======================================================================
 Stan now comes with GPU support for certain functions; see the Math library
 release notes for more details: https://github.com/stan-dev/math/releases/tag/v2.19.0
-The manual is now online in HTML format! 
+The manual is now online in HTML format!
 
 New Features
 --------------------------------------------------
-* #2618 - Add a new Variational Inference diagnostic 
+* #2618 - Add a new Variational Inference diagnostic
 * #2627 - 1d integrator
 * #2725 - standalone generated quantities
 * #2717, #2669 - offset/multiplier transformations for easier non-centering, etc
diff --git a/lib/stan_math b/lib/stan_math
index 655a8b27ce2..5252d51d47c 160000
--- a/lib/stan_math
+++ b/lib/stan_math
@@ -1 +1 @@
-Subproject commit 655a8b27ce233fa300d5def946bd14d2b3654864
+Subproject commit 5252d51d47c1d5e78005fc043ad996fad6dd8da8