diff --git a/math/flint/Makefile b/math/flint/Makefile
index f0e149abf009..652cd8119eca 100644
--- a/math/flint/Makefile
+++ b/math/flint/Makefile
@@ -1,6 +1,5 @@
 PORTNAME=	flint
-DISTVERSION=	3.1.2
-PORTREVISION=	1
+DISTVERSION=	3.2.0
 CATEGORIES=	math
 MASTER_SITES=	http://www.flintlib.org/download/
 
@@ -16,20 +15,38 @@ LIB_DEPENDS=	libgmp.so:math/gmp \
 		libmpfr.so:math/mpfr \
 		libopenblas.so:math/openblas
 
-USES=		cmake compiler:c++11-lang pkgconfig python:build
+USES=		compiler:c++11-lang gmake localbase pkgconfig python:build # cmake is only intended for Widows, see https://github.com/flintlib/flint/issues/2251#issuecomment-2720292171
 USE_LDCONFIG=	yes
 
-OPTIONS_DEFINE=		NTL
-OPTIONS_DEFAULT=	NTL
+GNU_CONFIGURE=	yes
 
-NTL_DESC=		Victor Shoup's Number Theory Library
-NTL_CMAKE_BOOL=		WITH_NTL
-NTL_LIB_DEPENDS=	libntl.so:math/ntl
+.if !defined(WITH_DEBUG)
+CONFIGURE_ARGS=	--disable-debug
+.endif
 
-do-test:
-	@cd ${BUILD_WRKSRC} && \
-		${SETENV} ${CONFIGURE_ENV} ${CMAKE_BIN} ${CMAKE_ARGS} -DBUILD_TESTING:BOOL=ON ${CMAKE_SOURCE_PATH} && \
-		${SETENV} ${MAKE_ENV} ${MAKE_CMD} ${MAKE_ARGS} ${ALL_TARGET} && \
-		${SETENV} ${MAKE_ENV} ${MAKE_CMD} ${MAKE_ARGS} test
+TEST_TARGET=	check
+
+OPTIONS_DEFINE=			NTL
+OPTIONS_GROUP=			OPTIMIZATIONS
+OPTIONS_GROUP_OPTIMIZATIONS=	AVX2 AVX512
+OPTIONS_DEFAULT=		NTL
+
+AVX2_DESC=			Enable AVX2 instructions
+AVX2_CONFIGURE_ENABLE=		avx2
+
+AVX512_DESC=			Enable AVX512 instructions
+AVX512_CONFIGURE_ENABLE=	avx512
+
+NTL_DESC=			Victor Shoup's Number Theory Library
+NTL_CONFIGURE_WITH=		ntl
+NTL_LIB_DEPENDS=		libntl.so:math/ntl
+
+MAKE_ENV+=	VERBOSE=1
+MAKE_ARGS+=	VERBOSE=1
+
+post-install:
+	@${STRIP_CMD} ${STAGEDIR}${PREFIX}/lib/libflint.so.20.0.0
+
+# tests as of 3.2.0: All tests passed.
 
 .include <bsd.port.mk>
diff --git a/math/flint/distinfo b/math/flint/distinfo
index 55f2c2cc8341..91a90dc16a1a 100644
--- a/math/flint/distinfo
+++ b/math/flint/distinfo
@@ -1,3 +1,3 @@
-TIMESTAMP = 1728287409
-SHA256 (flint-3.1.2.tar.gz) = fdb3a431a37464834acff3bdc145f4fe8d0f951dd5327c4c6f93f4cbac5c2700
-SIZE (flint-3.1.2.tar.gz) = 8098136
+TIMESTAMP = 1741882945
+SHA256 (flint-3.2.0.tar.gz) = 6d182c4a05d3d6bfc611565d6331d02f94066a3be32df36ed880264afa9c30f4
+SIZE (flint-3.2.0.tar.gz) = 8384561
diff --git a/math/flint/pkg-plist b/math/flint/pkg-plist
index 930173daa916..b293f9f6d6b5 100644
--- a/math/flint/pkg-plist
+++ b/math/flint/pkg-plist
@@ -31,8 +31,10 @@ include/flint/ca_ext.h
 include/flint/ca_field.h
 include/flint/ca_mat.h
 include/flint/ca_poly.h
+include/flint/ca_types.h
 include/flint/ca_vec.h
 include/flint/calcium.h
+include/flint/config.h
 include/flint/crt_helpers.h
 include/flint/d_mat.h
 include/flint/d_vec.h
@@ -44,8 +46,8 @@ include/flint/fexpr.h
 include/flint/fexpr_builtin.h
 include/flint/fft.h
 include/flint/fft_small.h
-include/flint/fft_tuning.h
 include/flint/flint-config.h
+include/flint/flint-mparam.h
 include/flint/flint.h
 include/flint/fmpq.h
 include/flint/fmpq_mat.h
@@ -120,6 +122,7 @@ include/flint/gr_mat.h
 include/flint/gr_mpoly.h
 include/flint/gr_poly.h
 include/flint/gr_special.h
+include/flint/gr_types.h
 include/flint/gr_vec.h
 include/flint/hypgeom.h
 include/flint/limb_types.h
@@ -127,6 +130,7 @@ include/flint/long_extras.h
 include/flint/longlong.h
 include/flint/longlong_asm_clang.h
 include/flint/longlong_asm_gcc.h
+include/flint/longlong_asm_gnu.h
 include/flint/longlong_div_gnu.h
 include/flint/longlong_msc_arm64.h
 include/flint/longlong_msc_x86.h
@@ -136,12 +140,14 @@ include/flint/mpf-impl.h
 include/flint/mpfr_mat.h
 include/flint/mpfr_vec.h
 include/flint/mpn_extras.h
+include/flint/mpn_mod.h
 include/flint/mpoly.h
 include/flint/mpoly_types.h
 include/flint/n_poly.h
 include/flint/n_poly_types.h
 include/flint/nf.h
 include/flint/nf_elem.h
+include/flint/nfloat.h
 include/flint/nmod.h
 include/flint/nmod_mat.h
 include/flint/nmod_mpoly.h
@@ -168,6 +174,6 @@ include/flint/thread_pool.h
 include/flint/thread_support.h
 include/flint/ulong_extras.h
 lib/libflint.so
-lib/libflint.so.19
-lib/libflint.so.19.0.0
+lib/libflint.so.20
+lib/libflint.so.20.0.0
 libdata/pkgconfig/flint.pc