diff --git a/commons-math-legacy/src/main/java/org/apache/commons/math4/legacy/analysis/differentiation/DerivativeStructure.java b/commons-math-legacy/src/main/java/org/apache/commons/math4/legacy/analysis/differentiation/DerivativeStructure.java
index 66c52b7..1b7c069 100644
--- a/commons-math-legacy/src/main/java/org/apache/commons/math4/legacy/analysis/differentiation/DerivativeStructure.java
+++ b/commons-math-legacy/src/main/java/org/apache/commons/math4/legacy/analysis/differentiation/DerivativeStructure.java
@@ -17,7 +17,6 @@
 package org.apache.commons.math4.legacy.analysis.differentiation;
 
 import java.util.Arrays;
-import java.io.Serializable;
 
 import org.apache.commons.numbers.core.Sum;
 import org.apache.commons.math4.legacy.core.Field;
@@ -59,11 +58,7 @@
  * @see DSCompiler
  * @since 3.1
  */
-public class DerivativeStructure implements RealFieldElement<DerivativeStructure>, Serializable {
-
-    /** Serializable UID. */
-    private static final long serialVersionUID = 20120730L;
-
+public class DerivativeStructure implements RealFieldElement<DerivativeStructure> {
     /** Compiler for the current dimensions. */
     private transient DSCompiler compiler;
 
@@ -1205,54 +1200,4 @@
     public int hashCode() {
         return 227 + 229 * getFreeParameters() + 233 * getOrder() + 239 * Arrays.hashCode(data);
     }
-
-    /**
-     * Replace the instance with a data transfer object for serialization.
-     * @return data transfer object that will be serialized
-     */
-    private Object writeReplace() {
-        return new DataTransferObject(compiler.getFreeParameters(), compiler.getOrder(), data);
-    }
-
-    /** Internal class used only for serialization. */
-    private static class DataTransferObject implements Serializable {
-
-        /** Serializable UID. */
-        private static final long serialVersionUID = 20120730L;
-
-        /** Number of variables.
-         * @serial
-         */
-        private final int variables;
-
-        /** Derivation order.
-         * @serial
-         */
-        private final int order;
-
-        /** Partial derivatives.
-         * @serial
-         */
-        private final double[] data;
-
-        /** Simple constructor.
-         * @param variables number of variables
-         * @param order derivation order
-         * @param data partial derivatives
-         */
-        DataTransferObject(final int variables, final int order, final double[] data) {
-            this.variables = variables;
-            this.order     = order;
-            this.data      = data;
-        }
-
-        /** Replace the deserialized data transfer object with a {@link DerivativeStructure}.
-         * @return replacement {@link DerivativeStructure}
-         */
-        private Object readResolve() {
-            return new DerivativeStructure(variables, order, data);
-        }
-
-    }
-
 }
diff --git a/commons-math-legacy/src/main/java/org/apache/commons/math4/legacy/analysis/differentiation/FiniteDifferencesDifferentiator.java b/commons-math-legacy/src/main/java/org/apache/commons/math4/legacy/analysis/differentiation/FiniteDifferencesDifferentiator.java
index 6aa3924..0c422a7 100644
--- a/commons-math-legacy/src/main/java/org/apache/commons/math4/legacy/analysis/differentiation/FiniteDifferencesDifferentiator.java
+++ b/commons-math-legacy/src/main/java/org/apache/commons/math4/legacy/analysis/differentiation/FiniteDifferencesDifferentiator.java
@@ -16,8 +16,6 @@
  */
 package org.apache.commons.math4.legacy.analysis.differentiation;
 
-import java.io.Serializable;
-
 import org.apache.commons.math4.legacy.analysis.UnivariateFunction;
 import org.apache.commons.math4.legacy.analysis.UnivariateMatrixFunction;
 import org.apache.commons.math4.legacy.analysis.UnivariateVectorFunction;
@@ -69,12 +67,9 @@
  * @since 3.1
  */
 public class FiniteDifferencesDifferentiator
-    implements UnivariateFunctionDifferentiator, UnivariateVectorFunctionDifferentiator,
-               UnivariateMatrixFunctionDifferentiator, Serializable {
-
-    /** Serializable UID. */
-    private static final long serialVersionUID = 20120917L;
-
+    implements UnivariateFunctionDifferentiator,
+               UnivariateVectorFunctionDifferentiator,
+               UnivariateMatrixFunctionDifferentiator {
     /** Number of points to use. */
     private final int nbPoints;
 
diff --git a/commons-math-legacy/src/main/java/org/apache/commons/math4/legacy/analysis/differentiation/SparseGradient.java b/commons-math-legacy/src/main/java/org/apache/commons/math4/legacy/analysis/differentiation/SparseGradient.java
index 7f7714a..579eeb6 100644
--- a/commons-math-legacy/src/main/java/org/apache/commons/math4/legacy/analysis/differentiation/SparseGradient.java
+++ b/commons-math-legacy/src/main/java/org/apache/commons/math4/legacy/analysis/differentiation/SparseGradient.java
@@ -16,7 +16,6 @@
  */
 package org.apache.commons.math4.legacy.analysis.differentiation;
 
-import java.io.Serializable;
 import java.util.Collections;
 import java.util.HashMap;
 import java.util.Map;
@@ -40,11 +39,7 @@
  *
  * @since 3.3
  */
-public final class SparseGradient implements RealFieldElement<SparseGradient>, Serializable {
-
-    /** Serializable UID. */
-    private static final long serialVersionUID = 20131025L;
-
+public final class SparseGradient implements RealFieldElement<SparseGradient> {
     /** Value of the calculation. */
     private double value;
 
diff --git a/commons-math-legacy/src/main/java/org/apache/commons/math4/legacy/analysis/interpolation/DividedDifferenceInterpolator.java b/commons-math-legacy/src/main/java/org/apache/commons/math4/legacy/analysis/interpolation/DividedDifferenceInterpolator.java
index 9a7e474..135cd1a 100644
--- a/commons-math-legacy/src/main/java/org/apache/commons/math4/legacy/analysis/interpolation/DividedDifferenceInterpolator.java
+++ b/commons-math-legacy/src/main/java/org/apache/commons/math4/legacy/analysis/interpolation/DividedDifferenceInterpolator.java
@@ -16,8 +16,6 @@
  */
 package org.apache.commons.math4.legacy.analysis.interpolation;
 
-import java.io.Serializable;
-
 import org.apache.commons.math4.legacy.analysis.polynomials.PolynomialFunctionLagrangeForm;
 import org.apache.commons.math4.legacy.analysis.polynomials.PolynomialFunctionNewtonForm;
 import org.apache.commons.math4.legacy.exception.DimensionMismatchException;
@@ -37,10 +35,7 @@
  * @since 1.2
  */
 public class DividedDifferenceInterpolator
-    implements UnivariateInterpolator, Serializable {
-    /** serializable version identifier. */
-    private static final long serialVersionUID = 107049519551235069L;
-
+    implements UnivariateInterpolator {
     /**
      * Compute an interpolating function for the dataset.
      *
diff --git a/commons-math-legacy/src/main/java/org/apache/commons/math4/legacy/analysis/interpolation/LoessInterpolator.java b/commons-math-legacy/src/main/java/org/apache/commons/math4/legacy/analysis/interpolation/LoessInterpolator.java
index 933f5b2..b533665 100644
--- a/commons-math-legacy/src/main/java/org/apache/commons/math4/legacy/analysis/interpolation/LoessInterpolator.java
+++ b/commons-math-legacy/src/main/java/org/apache/commons/math4/legacy/analysis/interpolation/LoessInterpolator.java
@@ -16,7 +16,6 @@
  */
 package org.apache.commons.math4.legacy.analysis.interpolation;
 
-import java.io.Serializable;
 import java.util.Arrays;
 
 import org.apache.commons.math4.legacy.analysis.polynomials.PolynomialSplineFunction;
@@ -47,7 +46,7 @@
  * @since 2.0
  */
 public class LoessInterpolator
-    implements UnivariateInterpolator, Serializable {
+    implements UnivariateInterpolator {
     /** Default value of the bandwidth parameter. */
     public static final double DEFAULT_BANDWIDTH = 0.3;
     /** Default value of the number of robustness iterations. */
@@ -57,8 +56,6 @@
      * @since 2.1
      */
     public static final double DEFAULT_ACCURACY = 1e-12;
-    /** serializable version identifier. */
-    private static final long serialVersionUID = 5204927143605193821L;
     /**
      * The bandwidth parameter: when computing the loess fit at
      * a particular point, this fraction of source points closest
diff --git a/commons-math-legacy/src/main/java/org/apache/commons/math4/legacy/analysis/interpolation/NevilleInterpolator.java b/commons-math-legacy/src/main/java/org/apache/commons/math4/legacy/analysis/interpolation/NevilleInterpolator.java
index dadde89..c6b50b7 100644
--- a/commons-math-legacy/src/main/java/org/apache/commons/math4/legacy/analysis/interpolation/NevilleInterpolator.java
+++ b/commons-math-legacy/src/main/java/org/apache/commons/math4/legacy/analysis/interpolation/NevilleInterpolator.java
@@ -16,8 +16,6 @@
  */
 package org.apache.commons.math4.legacy.analysis.interpolation;
 
-import java.io.Serializable;
-
 import org.apache.commons.math4.legacy.analysis.polynomials.PolynomialFunctionLagrangeForm;
 import org.apache.commons.math4.legacy.exception.DimensionMismatchException;
 import org.apache.commons.math4.legacy.exception.NonMonotonicSequenceException;
@@ -34,12 +32,7 @@
  *
  * @since 1.2
  */
-public class NevilleInterpolator implements UnivariateInterpolator,
-    Serializable {
-
-    /** serializable version identifier. */
-    static final long serialVersionUID = 3003707660147873733L;
-
+public class NevilleInterpolator implements UnivariateInterpolator {
     /**
      * Computes an interpolating function for the data set.
      *
diff --git a/commons-math-legacy/src/main/java/org/apache/commons/math4/legacy/analysis/polynomials/PolynomialFunction.java b/commons-math-legacy/src/main/java/org/apache/commons/math4/legacy/analysis/polynomials/PolynomialFunction.java
index b85cffc..b1d0254 100644
--- a/commons-math-legacy/src/main/java/org/apache/commons/math4/legacy/analysis/polynomials/PolynomialFunction.java
+++ b/commons-math-legacy/src/main/java/org/apache/commons/math4/legacy/analysis/polynomials/PolynomialFunction.java
@@ -16,7 +16,6 @@
  */
 package org.apache.commons.math4.legacy.analysis.polynomials;
 
-import java.io.Serializable;
 import java.util.Arrays;
 
 import org.apache.commons.math4.legacy.analysis.ParametricUnivariateFunction;
@@ -34,11 +33,7 @@
  * is used to evaluate the function.</p>
  *
  */
-public class PolynomialFunction implements UnivariateDifferentiableFunction, Serializable {
-    /**
-     * Serialization identifier.
-     */
-    private static final long serialVersionUID = -7726511984200295583L;
+public class PolynomialFunction implements UnivariateDifferentiableFunction {
     /**
      * The coefficients of the polynomial, ordered by degree -- i.e.,
      * coefficients[0] is the constant term and coefficients[n] is the
diff --git a/commons-math-legacy/src/main/java/org/apache/commons/math4/legacy/stat/descriptive/rank/PSquarePercentile.java b/commons-math-legacy/src/main/java/org/apache/commons/math4/legacy/stat/descriptive/rank/PSquarePercentile.java
index ed064a9..6b8a276 100644
--- a/commons-math-legacy/src/main/java/org/apache/commons/math4/legacy/stat/descriptive/rank/PSquarePercentile.java
+++ b/commons-math-legacy/src/main/java/org/apache/commons/math4/legacy/stat/descriptive/rank/PSquarePercentile.java
@@ -16,9 +16,6 @@
  */
 package org.apache.commons.math4.legacy.stat.descriptive.rank;
 
-import java.io.IOException;
-import java.io.ObjectInputStream;
-import java.io.Serializable;
 import java.text.DecimalFormat;
 import java.util.ArrayList;
 import java.util.Arrays;
@@ -53,7 +50,7 @@
  * {@link Percentile} should be used.</p>
  */
 public class PSquarePercentile extends AbstractStorelessUnivariateStatistic
-        implements StorelessUnivariateStatistic, Serializable {
+    implements StorelessUnivariateStatistic {
 
     /**
      * The maximum array size used for psquare algorithm.
@@ -67,11 +64,6 @@
     private static final double DEFAULT_QUANTILE_DESIRED = 50d;
 
     /**
-     * Serial ID.
-     */
-    private static final long serialVersionUID = 20150412L;
-
-    /**
      * A decimal formatter for print convenience.
      */
     private static final DecimalFormat DECIMAL_FORMAT = new DecimalFormat("00.00");
@@ -311,12 +303,7 @@
      * Markers is an encapsulation of the five markers/buckets as indicated in
      * the original works.
      */
-    private static final class Markers implements PSquareMarkers, Serializable {
-        /**
-         * Serial version id.
-         */
-        private static final long serialVersionUID = 1L;
-
+    private static final class Markers implements PSquareMarkers {
         /** Low marker index. */
         private static final int LOW = 2;
 
@@ -525,25 +512,6 @@
         }
 
         /**
-         * Sets previous and next markers after default read is done.
-         *
-         * @param anInputStream the input stream to be deserialized
-         * @throws ClassNotFoundException thrown when a desired class not found
-         * @throws IOException thrown due to any io errors
-         */
-        private void readObject(ObjectInputStream anInputStream)
-                throws ClassNotFoundException, IOException {
-            // always perform the default de-serialization first
-            anInputStream.defaultReadObject();
-            // Build links
-            for (int i = 1; i < PSQUARE_CONSTANT; i++) {
-                markerArray[i].previous(markerArray[i - 1]).next(markerArray[i + 1]).index(i);
-            }
-            markerArray[0].previous(markerArray[0]).next(markerArray[1]).index(0);
-            markerArray[5].previous(markerArray[4]).next(markerArray[5]).index(5);
-        }
-
-        /**
          * Return marker height given index.
          *
          * @param markerIndex index of marker within (1,6)
@@ -591,13 +559,7 @@
     /**
      * The class modeling the attributes of the marker of the P-square algorithm.
      */
-    private static final class Marker implements Serializable {
-
-        /**
-         * Serial Version ID.
-         */
-        private static final long serialVersionUID = -3575879478288538431L;
-
+    private static final class Marker {
         /**
          * The marker index which is just a serial number for the marker in the
          * marker array of 5+1.
@@ -833,20 +795,6 @@
         }
 
         /**
-         * Read Object to deserialize.
-         *
-         * @param anInstream Stream Object data
-         * @throws IOException thrown for IO Errors
-         * @throws ClassNotFoundException thrown for class not being found
-         */
-        private void readObject(ObjectInputStream anInstream)
-                throws ClassNotFoundException, IOException {
-            anInstream.defaultReadObject();
-            previous=next=this;
-            linear = new LinearInterpolator();
-        }
-
-        /**
          * Copy this instance.
          *
          * @return a new instance.
@@ -877,12 +825,7 @@
      *
      * @param <E> type for fixed capacity list
      */
-    private static class FixedCapacityList<E> extends ArrayList<E> implements Serializable {
-
-        /**
-         * Serialization Version Id.
-         */
-        private static final long serialVersionUID = 2283952083075725479L;
+    private static class FixedCapacityList<E> extends ArrayList<E> {
         /**
          * Capacity of the list.
          */
diff --git a/commons-math-legacy/src/test/java/org/apache/commons/math4/legacy/analysis/differentiation/DerivativeStructureTest.java b/commons-math-legacy/src/test/java/org/apache/commons/math4/legacy/analysis/differentiation/DerivativeStructureTest.java
index 941dd66..b32b020 100644
--- a/commons-math-legacy/src/test/java/org/apache/commons/math4/legacy/analysis/differentiation/DerivativeStructureTest.java
+++ b/commons-math-legacy/src/test/java/org/apache/commons/math4/legacy/analysis/differentiation/DerivativeStructureTest.java
@@ -1565,15 +1565,6 @@
         }
     }
 
-    @Test
-    public void testSerialization() {
-        DerivativeStructure a = new DerivativeStructure(3, 2, 0, 1.3);
-        DerivativeStructure b = (DerivativeStructure) TestUtils.serializeAndRecover(a);
-        Assert.assertEquals(a.getFreeParameters(), b.getFreeParameters());
-        Assert.assertEquals(a.getOrder(), b.getOrder());
-        checkEquals(a, b, 1.0e-15);
-    }
-
     private void checkF0F1(DerivativeStructure ds, double value, double...derivatives) {
 
         // check dimension
diff --git a/commons-math-legacy/src/test/java/org/apache/commons/math4/legacy/analysis/differentiation/FiniteDifferencesDifferentiatorTest.java b/commons-math-legacy/src/test/java/org/apache/commons/math4/legacy/analysis/differentiation/FiniteDifferencesDifferentiatorTest.java
index 8e42d4c..a49611a 100644
--- a/commons-math-legacy/src/test/java/org/apache/commons/math4/legacy/analysis/differentiation/FiniteDifferencesDifferentiatorTest.java
+++ b/commons-math-legacy/src/test/java/org/apache/commons/math4/legacy/analysis/differentiation/FiniteDifferencesDifferentiatorTest.java
@@ -48,16 +48,6 @@
     }
 
     @Test
-    public void testSerialization() {
-        FiniteDifferencesDifferentiator differentiator =
-                new FiniteDifferencesDifferentiator(3, 1.0e-3);
-        FiniteDifferencesDifferentiator recovered =
-                (FiniteDifferencesDifferentiator) TestUtils.serializeAndRecover(differentiator);
-        Assert.assertEquals(differentiator.getNbPoints(), recovered.getNbPoints());
-        Assert.assertEquals(differentiator.getStepSize(), recovered.getStepSize(), 1.0e-15);
-    }
-
-    @Test
     public void testConstant() {
         FiniteDifferencesDifferentiator differentiator =
                 new FiniteDifferencesDifferentiator(5, 0.01);
diff --git a/commons-math-legacy/src/test/java/org/apache/commons/math4/legacy/analysis/differentiation/SparseGradientTest.java b/commons-math-legacy/src/test/java/org/apache/commons/math4/legacy/analysis/differentiation/SparseGradientTest.java
index ada18e5..72e22ee 100644
--- a/commons-math-legacy/src/test/java/org/apache/commons/math4/legacy/analysis/differentiation/SparseGradientTest.java
+++ b/commons-math-legacy/src/test/java/org/apache/commons/math4/legacy/analysis/differentiation/SparseGradientTest.java
@@ -1107,13 +1107,6 @@
         }
     }
 
-    @Test
-    public void testSerialization() {
-        SparseGradient a = SparseGradient.createVariable(0, 1.3);
-        SparseGradient b = (SparseGradient) TestUtils.serializeAndRecover(a);
-        Assert.assertEquals(a, b);
-    }
-
     private void checkF0F1(SparseGradient sg, double value, double...derivatives) {
 
         // check value
diff --git a/commons-math-legacy/src/test/java/org/apache/commons/math4/legacy/analysis/polynomials/PolynomialFunctionTest.java b/commons-math-legacy/src/test/java/org/apache/commons/math4/legacy/analysis/polynomials/PolynomialFunctionTest.java
index 4a7d3f1..7bab530 100644
--- a/commons-math-legacy/src/test/java/org/apache/commons/math4/legacy/analysis/polynomials/PolynomialFunctionTest.java
+++ b/commons-math-legacy/src/test/java/org/apache/commons/math4/legacy/analysis/polynomials/PolynomialFunctionTest.java
@@ -216,12 +216,6 @@
         }
     }
 
-    @Test
-    public void testSerial() {
-        PolynomialFunction p2 = new PolynomialFunction(new double[] { 3, 2, 1 });
-        Assert.assertEquals(p2, TestUtils.serializeAndRecover(p2));
-    }
-
     /**
      * tests the firstDerivative function by comparison
      *
diff --git a/commons-math-legacy/src/test/java/org/apache/commons/math4/legacy/stat/descriptive/StorelessUnivariateStatisticAbstractTest.java b/commons-math-legacy/src/test/java/org/apache/commons/math4/legacy/stat/descriptive/StorelessUnivariateStatisticAbstractTest.java
index 4c87cbe..86db911 100644
--- a/commons-math-legacy/src/test/java/org/apache/commons/math4/legacy/stat/descriptive/StorelessUnivariateStatisticAbstractTest.java
+++ b/commons-math-legacy/src/test/java/org/apache/commons/math4/legacy/stat/descriptive/StorelessUnivariateStatisticAbstractTest.java
@@ -76,33 +76,6 @@
     }
 
     @Test
-    public void testSerialization() {
-
-        StorelessUnivariateStatistic statistic =
-            (StorelessUnivariateStatistic) getUnivariateStatistic();
-
-        TestUtils.checkSerializedEquality(statistic);
-
-        statistic.clear();
-
-        for (int i = 0; i < testArray.length; i++) {
-            statistic.increment(testArray[i]);
-            if(i % 5 == 0) {
-                statistic = (StorelessUnivariateStatistic)TestUtils.serializeAndRecover(statistic);
-            }
-        }
-
-        TestUtils.checkSerializedEquality(statistic);
-
-        Assert.assertEquals(expectedValue(), statistic.getResult(), getTolerance());
-
-        statistic.clear();
-
-        checkClearValue(statistic);
-
-    }
-
-    @Test
     public void testEqualsAndHashCode() {
         StorelessUnivariateStatistic statistic =
             (StorelessUnivariateStatistic) getUnivariateStatistic();
@@ -210,13 +183,6 @@
         Assert.assertEquals(master, replica);
     }
 
-    @Test
-    public void testSerial() {
-        StorelessUnivariateStatistic s =
-            (StorelessUnivariateStatistic) getUnivariateStatistic();
-        Assert.assertEquals(s, TestUtils.serializeAndRecover(s));
-    }
-
     /**
      * Make sure that evaluate(double[]) does not alter the internal state.
      */