Do you have any preference as to the size of the screen?
With the criterions that you've placed forth, you have a LOT of choices.
Here are some that I would consider if I were in your place.
But before I tell you, here's a little disclaimer: I dont know which proc is best for number crunching(P4,AMD, Turion, P-M).
*Having said that, with 1500 you could pick up a nice Dell 600m with a pentium-m 1.6, 1gb ram, 40-80gb hd, and whatever basic IGP solution they provide. i believe the 600m have a 14 in lcd which isn't too shabby and they are pretty lightweight. around 5-6 lbs if im not mistaken.
*Another one that I would reccomend is Averatec's 3350. I have the same one, it cost me 999. It has a p-m 1.6 w/ 2mb cache, 512mb, 80gb hd, dual layer/dual format dvd burner, wireless g, 12in lcd, full 4 hr batt life and weighs about 4.5lbs w/ batt. Without reabtes and such it goes for about 1300 so with tax say about 1400-1500.
*If you really dont mind the weight then maybe you could opt for an emachines which has an athlon 64 proc and radeon 9600 vid card and a dvd burner. it weighs about 7-8lbs and costs about 1000-1200...probably even less now. I doubt the batt life is all that high.
*I use to work at the tech support for my univ and one of the techs used a mac to do all of her programming. She said it worked very well for what she wanted to do so thats another route you might be able to take...but I dont know much about macs so I will leave the mac suggestions and advice to a mac expert.
*I am an averatec fanboy as I have many many averatecs in my house so I reccomend you go check out their website. They have a wide selection of laptops.
*HP and Compaq are pretty good too though I can't say much about those.
*If possible, you should try and hop on the 400-500 dollar laptop deal(i have seen one particular acer model go on sale a few times for that price). They have a sempron 2800-3000 proc w/ 256mb which can be upped to 512 w/out costing a lot.
Again...I dont know exactly how MUCH programming and number crunching you will be doing on your computer so I cant say for sure if the sempron will suffice or if you need a P4 Extreme Edition or an Athlon FX. So having said all that, I hope some of these suggestions point you in the right direction. I'm sure others will give you plenty of suggestions as well that will help you out. But if you really want more advice more specifically tailored to your needs then provide more information on what you will be doing with this laptop. hope this helps! good luck in finding a nice laptop for yourself. i dont know how often i check this forum, so if you want any additional help from me feel free to PM me, though I'm sure you'll get plenty of help in this forum, people tend to be pretty nice around here.