PRICING SUPPLEMENT NO. 32                                       Rule 424(b)(3)
DATED: March 29, 2001                                       File No. 333-52902
(To Prospectus dated January 11, 2001,
and Prospectus Supplement dated January 11, 2001)

                                 $9,015,893,162
                         THE BEAR STEARNS COMPANIES INC.
                           MEDIUM-TERM NOTES, SERIES B

Principal Amount: $10,000,000    Floating Rate Notes [x]  Book Entry Notes [x]

Original Issue Date: 03/30/2001  Fixed Rate Notes [  ]    Certificated Notes [ ]

Maturity Date: 3/28/2002         CUSIP#: 073928TP8

Option to Extend Maturity:    No    [x]
                              Yes   [ ]  Final Maturity Date:


                                              Optional            Optional
                         Redemption           Repayment           Repayment
   Redeemable On          Price(s)             Date(s)            Price(s)
   -------------       --------------       -------------        -----------

        N/A                  N/A                 N/A                 N/A

Applicable Only to Fixed Rate Notes:
-----------------------------------

Interest Rate:

Interest Payment Dates:

Applicable Only to Floating Rate Notes:
--------------------------------------

Interest Rate Basis:                    Maximum Interest Rate:  N/A

[ ]  Commercial Paper Rate              Minimum Interest Rate:  N/A

[x] Federal Funds Rate                  Interest Reset Date(s):  Daily

[ ]  Treasury Rate                      Interest Reset Period:  Daily

[ ]  LIBOR Reuters                      Interest Payment Date(s):  *

[ ]  LIBOR Telerate

[ ]  Prime Rate

[ ]  CMT Rate

Initial Interest Rate:  5.555%          Interest Payment Period: Quarterly

Index Maturity:  N/A

Spread (plus or minus):  + 0.18%

* On the 28th of June, September, December and at Maturity.

The distribution of Notes will conform to the requirements set forth in Rule
2720 of the NASD Conduct Rules.